,transcriber's ,note ,this book uses a number of astronomical symbols1 including signs of the ,zodiac 71 1 1 1 1 1 1 1 1 1 1 71 symbols for planets 71 1 1 1 1 7 and for the sun and moon 71 74 ,if these characters do not display correctly1 you may have to use an alternative font1 such as ,arial ,unicode ,,ms or ,deja,vu4 ,when italics were used in the original book1 the corresponding text has been surrounded by underscores4 ,mixed fractions have been displayed with a hyphen between whole number and fraction for clarity4 ,superscripted characters are preceded by and when more than one character is superscripted1 they are surrounded by 4 ,some corrections have been made to the printed text4 ,these are listed in a second transcriber's note at the end of the text4 ,illustration3 ,the ,,orrery1 made by ,,james ,,ferguson4 ,n4 #a4 ,the ,sun1 #b4 ,mercury1 #c4 ,venus1 #d4 ,the ,earth1 #e4 ,the ,moon1 #f4 ,the ,sydereal ,dial plate1 #g4 ,the ,hour ,circle1 #h4 ye ,circle for ye4 ,moon's ,age1 #i4 ,the ,moon's ,orbit1 #aj4 ye ,pointer1 ,shewing the ,sun's ,place ,day of the ,month1 #aa4 ,the ,ecliptic1 #ab4 ,the ,handle for turning ye whole machine ,j4 ,ferguson inv4 et delin4 ,g4 ,child4 ,sculp4 ,,astronomy ,,explained ,,upon ,sir ,,isaac ,,newton's ,,principles1 ,,and ,,made ,,easy ,,to ,,those ,,who ,,have ,,not ,,studied ,,mathematics4 ,by ,,james ,,ferguson4 ,,heb4 ,,xi4 #c4 ,the ,worlds were framed by the ,word of ,,god4 ,,job ,,xxvi4 #ac4 ,by his ,spirit he hath garnished the ,heavens4 ,,the ,,second ,,edition4 ,illustration3 decoration ,,london3 ,printed for1 and sold by the ,,author1 at the ,,globe1 opposite ,cecil-,street in the ,strand4 ,,mdcclvii4 ,,to ,,the ,,right ,,honourable ,,george ,,earl of ,,macclesfield1 ,,viscount ,,parker of ,,ewelme in ,,oxfordshire1 ,,and ,,baron of ,,macclesfield in ,,cheshire2 ,,president of the ,,royal ,,society of ,,london1 ,,member of the ,,royal ,,academy ,,of ,,sciences at ,,paris1 ,,of ,,the ,,imperial ,,academy ,,of ,,sciences at ,petersburg1 ,,and ,,one ,,of ,,the ,,trustees of the ,,british ,,museum2 ,,distinguished ,by his ,,generous ,,zeal for promoting every ,,branch of ,,useful ,,knowledge2 ,,this ,,treatise of ,,astronomy ,,is ,,inscribed1 ,with the ,,most ,,profound ,,respect1 ,by ,,his ,,lordship's ,,most ,,obliged1 ,and ,,most ,,humble ,,servant1 ,,james ,,ferguson4 ,,the ,,contents4 ,,chap4 ,i4 ,of ,astronomy in general ,page #a ,,chap4 ,,ii4 ,a brief ,description of the ,,solar ,,system #e ,,chap4 ,,iii4 ,the ,,copernican or ,,solar ,,system demonstrated to be #ca true ,,chap4 ,,iv4 ,the ,phenomena of the ,heavens as seen from different #ci parts of the ,earth ,,chap4 ,v4 ,the ,phenomena of the ,heavens as seen from different #de parts of the ,solar ,system ,,chap4 ,,vi4 ,the ,ptolemean ,system refuted4 ,the ,motions and ,phases #ej of ,mercury and ,venus explained ,,chap4 ,,vii4 ,the physical ,causes of the ,motions of the ,planets4 ,the #ed ,excentricities of their ,orbits4 ,the times in which the ,action of ,gravity would bring them to the ,sun4 ,,archimedes',s ideal ,problem for moving the ,earth4 ,the world not eternal ,,chap4 ,,viii4 ,of ,light4 ,it's proportional quantities on the #fb different ,planets4 ,it's ,refractions in ,water and ,air4 ,the ,atmosphere1 it's ,weight and ,properties4 ,the ,horizontal ,moon ,,chap4 ,,ix4 ,the ,method of finding the ,distances of the ,sun1 ,moon #gc and ,planets ,,chap4 ,x4 ,the ,circles of the ,globe described4 ,the different #gh lengths of days and nights1 and the vicissitude of ,seasons1 explained4 ,the explanation of the ,phenomena of ,saturn's ,ring concluded ,,chap4 ,,xi4 ,the ,method of finding the ,longitude by the ,eclipses of #hg ,jupiter's ,satellites3 ,the amazing velocity of ,light demonstrated by these ,eclipses ,,chap4 ,,xii4 ,of ,solar and ,sidereal ,time #ic ,,chap4 ,,xiii4 ,of the ,equation of ,time #ig ,,chap4 ,,xiv4 ,of the ,precession of the ,equinoxes #ajh ,,chap4 ,,xv4 ,the ,moon's ,surface mountainous3 ,her ,phases described3 #abd ,her ,path1 and the ,paths of ,jupiter's ,moons delineated3 ,the proportions of the ,diameters of their ,orbits1 and those of ,saturn's ,moons to each other2 and to the ,diameter of the ,sun ,,chap4 ,,xvi4 ,the ,phenomena of the ,harvest-,moon explained by a #acf common ,globe3 ,the ,years in which the ,harvest-,moons are least and most beneficial1 from #agea to #ahfa4 ,the long duration of ,moon-light at the ,poles in ,winter ,page ,,chap4 ,,xvii4 ,of the ebbing and flowing of the ,sea #adg ,,chap4 ,,xviii4 ,of ,eclipses3 ,their ,number and ,period4 ,a large #aef ,catalogue of ,ancient and ,modern ,eclipses ,,chap4 ,,xix4 ,the ,calculation of ,new and ,full ,moons and ,eclipses4 #ahi ,the geometrical ,construction of ,solar and ,lunar ,eclipses4 ,the examination of ancient ,eclipses ,,chap4 ,,xx4 ,of the fixed ,stars #bcj ,,chap4 ,,xxi4 ,of the ,division of ,time4 ,a perpetual ,table of ,new #bdh ,moons4 ,the ,times of the ,birth and ,death of ,,christ4 ,a ,table of remarkable ras or ,events ,,chap4 ,,xxii4 ,a ,description of the ,astronomical ,machinery serving to #bfj explain and illustrate the foregoing part of this ,treatise ,,errata4 ,in the ,table facing ,page #ca1 the ,sun's quantity of matter should be #bbgejj4 ,page #dj1 l4 last1 for infinite read indefinite4 ,page #ig1 l4 #bj1 for this read the next4 ,page #afd1 l4 #b from the bottom1 for without any acceleration read as above1 without any acceleration4 ,page #aii1 l4 #af for ,,xiv read ,,xv4 ,page #bch1 l4 #af1 for #dj read #djf4 ,page #bdj1 l4 #ae from the bottom1 for ,tifri read ,tisri1 ,page #bdi l4 #ac2 from the bottom for ,,xvii read ,v4 ,,astronomy ,,explained ,,upon ,sir ,,isaac ,,newton's ,,principles4 ,,chap4 ,i4 ,of ,astronomy in general4 ,sidenote3 ,the general use of ,astronomy4 #a4 ,of all the sciences cultivated by mankind1 ,astronomy is acknowledged to be1 and undoubtedly is1 the most sublime1 the most interesting1 and the most useful4 ,for1 by knowledge derived from this science1 not only the bulk of the ,earth is discovered1 the situation and extent of the countries and kingdoms upon it ascertained1 trade and commerce carried on to the remotest parts of the world1 and the various products of several countries distributed for the health1 comfort1 and conveniency of its inhabitants2 but our very faculties are enlarged with the grandeur of the ideas it conveys1 our minds exalted above the low contracted prejudices of the vulgar1 and our understandings clearly convinced1 and affected with the conviction1 of the existence1 wisdom1 power1 goodness1 and superintendency of the ,,supreme ,,being6 ,so that without an hyperbole1 8,an undevout ,astronomer is mad#a40 #b4 ,from this branch of knowledge we also learn by what means or laws the ,almighty carries on1 and continues the admirable harmony1 order1 and connexion observable throughout the planetary system2 and are led by very powerful arguments to form the pleasing deduction1 that minds capable of such deep researches not only derive their origin from that adorable ,being1 but are also incited to aspire after a more perfect knowledge of his nature1 and a stricter conformity to his will4 ,sidenote3 ,the ,earth but a point as seen from the ,sun4 #c4 ,by ,astronomy we discover that the ,earth is at so great a distance from the ,sun1 that if seen from thence it would appear no bigger than a point2 although it's circumference is known to be #be1jbj miles4 ,yet that distance is so small1 compared with the distance of the ,fixed ,stars1 that if the ,orbit in which the ,earth moves round the ,sun were solid1 and seen from the nearest ,star1 it would likewise appear no bigger than a point1 although it is at least #afb millions of miles in diameter4 ,for the ,earth in going round the ,sun is #afb millions of miles nearer to some of the ,stars at one time of the year than at another2 and yet their apparent magnitudes1 situations1 and distances from one another still remain the same2 and a telescope which magnifies above #bjj times does not sensibly magnify them3 which proves them to be at least #djj thousand times farther from us than we are from the ,sun4 ,sidenote3 ,the ,stars are ,suns4 #d4 ,it is not to be imagined that all the ,stars are placed in one concave surface1 so as to be equally distant from us2 but that they are scattered at immense distances from one another through unlimited space4 ,so that there may be as great a distance between any two neighbouring ,stars1 as between our ,sun and those which are nearest to him4 ,therefore an ,observer1 who is nearest any fixed ,star1 will look upon it alone as a real ,sun2 and consider the rest as so many shining points1 placed at equal distances from him in the ,firmament4 ,sidenote3 ,and innumerable4 #e4 ,by the help of telescopes we discover thousands of ,stars which are invisible to the naked eye2 and the better our glasses are1 still the more become visible3 so that we can set no limits either to their number or their distances4 ,the celebrated ,,huygens carries his thoughts so far1 as to believe it not impossible that there may be ,stars at such inconceivable distances1 that their light has not yet reached the ,earth since it's creation2 although the velocity of light be a million of times greater than the velocity of a cannon bullet1 as shall be demonstrated afterwards #aig1 #baf3 and1 as ,mr4 ,,addison very justly observes1 this thought is far from being extravagant1 when we consider that the ,universe is the work of infinite power1 prompted by infinite goodness2 having an infinite space to exert itself in2 so that our imaginations can set no bounds to it4 ,sidenote3 ,why the ,sun appears bigger than the ,stars4 #f4 ,the ,sun appears very bright and large in comparison of the ,fixed ,stars1 because we keep constantly near the ,sun1 in comparison of our immense distance from the ,stars4 ,for1 a spectator1 placed as near to any ,star as we are to the ,sun1 would see that ,star a body as large and bright as the ,sun appears to us3 and a spectator1 as far distant from the ,sun as we are from the ,stars1 would see the ,sun as small as we see a ,star1 divested of all its circumvolving ,planets2 and would reckon it one of the ,stars in numbering them4 ,sidenote3 ,the ,stars are not enlightened by the ,sun4 #g4 ,the ,stars1 being at such immense distances from the ,sun1 cannot possibly receive from him so strong a light as they seem to have2 nor any brightness sufficient to make them visible to us4 ,for the ,sun's rays must be so scattered and dissipated before they reach such remote objects1 that they can never be transmitted back to our eyes1 so as to render these objects visible by reflection4 ,the ,stars therefore shine with their own native and unborrowed lustre1 as the ,sun does2 and since each particular ,star1 as well as the ,sun1 is confined to a particular portion of space1 'tis plain that the ,stars are of the same nature with the ,sun4 ,sidenote3 ,they are probably surrounded by ,planets4 #h4 ,it is no ways probable that the ,almighty1 who always acts with infinite wisdom and does nothing in vain1 should create so many glorious ,suns1 fit for so many important purposes1 and place them at such distances from one another1 without proper objects near enough to be benefited by their influences4 ,whoever imagines they were created only to give a faint glimmering light to the inhabitants of this ,globe1 must have a very superficial knowledge of ,astronomy1 and a mean opinion of the ,divine ,wisdom3 since1 by an infinitely less exertion of creating power1 the ,deity could have given our ,earth much more light by one single additional ,moon4 #i4 ,instead then of one ,sun and one ,world only in the ,universe1 as the unskilful in ,astronomy imagine1 that ,science discovers to us such an inconceivable number of ,suns1 ,systems1 and ,worlds1 dispersed through boundless ,space1 that if our ,sun1 with all the ,planets1 ,moons1 and ,comets belonging to it were annihilated1 they would be no more missed out of the ,creation than a grain of sand from the sea-shore4 ,the space they possess being comparatively so small1 that it would scarce be a sensible blank in the ,universe2 although ,saturn1 the outermost of our planets1 revolves about the ,sun in an ,orbit of #dhhd millions of miles in circumference1 and some of our ,comets make excursions upwards of ten thousand millions of miles beyond ,saturn's ,orbit2 and yet1 at that amazing distance1 they are incomparably nearer to the ,sun than to any of the ,stars2 as is evident from their keeping clear of the attractive ,power of all the ,stars1 and returning periodically by virtue of the ,sun's attraction4 ,sidenote3 ,the stellar ,planets may be habitable4 #aj4 ,from what we know of our own ,system it may be reasonably concluded that all the rest are with equal wisdom contrived1 situated1 and provided with accommodations for rational inhabitants4 ,let us therefore take a survey of the ,system to which we belong2 the only one accessible to us2 and from thence we shall be the better enabled to judge of the nature and end of the other ,systems of the ,universe4 ,for although there is almost an infinite variety in all the parts of the ,creation which we have opportunities of examining2 yet there is a general analogy running through and connecting all the parts into one scheme1 one design1 one whole6 ,sidenote3 ,as our ,solar ,planets are4 #aa4 ,and then1 to an attentive considerer1 it will appear highly probable1 that the ,planets of our ,system1 together with their attendants called ,satellites or ,moons1 are much of the same nature with our ,earth1 and destined for the like purposes4 ,for1 they are solid opaque ,globes1 capable of supporting animals and vegetables4 ,some of them are bigger1 some less1 and some much about the size of our ,earth4 ,they all circulate round the ,sun1 as the ,earth does1 in a shorter or longer time according to their respective distances from him3 and have1 where it would not be inconvenient1 regular returns of summer and winter1 spring and autumn4 ,they have warmer and colder climates1 as the various productions of our ,earth require3 and1 in such as afford a possibility of discovering it1 we observe a regular motion round their ,axes like that of our ,earth1 causing an alternate return of day and night2 which is necessary for labour1 rest1 and vegetation1 and that all parts of their surfaces may be exposed to the rays of the ,sun4 ,sidenote3 ,the farthest from the ,sun have most ,moons to enlighten their nights4 #ab4 ,such of the ,planets as are farthest from the ,sun1 and therefore enjoy least of his light1 have that deficiency made up by several ,moons1 which constantly accompany1 and revolve about them1 as our ,moon revolves about the ,earth4 ,the remotest ,planet has1 over and above1 a broad ,ring encompassing it2 which like a lucid ,zone in the ,heavens reflects the ,sun's light very copiously on that ,planet3 so that if the remoter ,planets have the ,sun's light fainter by day than we1 they have an addition made to it morning and evening by one or more of their ,moons1 and a greater quantity of light in the night-time4 ,sidenote3 ,our ,moon mountainous like the ,earth4 #ac4 ,on the surface of the ,moon1 because it is nearer us than any other of the celestial ,bodies are1 we discover a nearer resemblance of our ,earth4 ,for1 by the assistance of telescopes we observe the ,moon to be full of high mountains1 large valleys1 and deep cavities4 ,these similarities leave us no room to doubt but that all the ,planets and ,moons in the ,system are designed as commodious habitations for creatures endowed with capacities of knowing and adoring their beneficent ,creator4 ,illustration3 ,plate ,i4 ,,the ,,solar ,,system ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 #ad4 ,since the ,fixed ,stars are prodigious spheres of fire1 like our ,sun1 and at inconceivable distances from one another1 as well as from us1 it is reasonable to conclude they are made for the same purposes that the ,sun is2 each to bestow light1 heat1 and vegetation on a certain number of inhabited ,planets1 kept by gravitation within the sphere of it's activity4 ,sidenote3 ,numberless ,suns and ,worlds4 #ae4 ,what an august6 what an amazing conception1 if human imagination can conceive it1 does this give of the works of the ,creator6 ,thousands of thousands of ,suns1 multiplied without end1 and ranged all around us1 at immense distances from each other1 attended by ten thousand times ten thousand ,worlds1 all in rapid motion1 yet calm1 regular1 and harmonious1 invariably keeping the paths prescribed them2 and these ,worlds peopled with myriads of intelligent beings1 formed for endless progression in perfection and felicity4 #af4 ,if so much power1 wisdom1 goodness1 and magnificence is displayed in the material ,creation1 which is the least considerable part of the ,universe1 how great1 how wise1 how good must ,,he be1 who made and governs the ,whole6 ,,chap4 ,,ii4 ,a brief ,description of the ,,solar ,,system4 ,sidenote3 ,,plate ,i4 ,fig4 #a4 ,the ,solar ,system4 #ag4 ,the ,planets and ,comets which move round the ,sun as their center1 constitute the ,solar ,system4 ,those ,planets which are nearer the ,sun not only finish their circuits sooner1 but likewise move faster in their respective ,orbits than those which are more remote from him4 ,their motions are all performed from west to east1 in ,orbits nearly circular4 ,their names1 distances1 bulks1 and periodical revolutions1 are as follows4 ,sidenote3 ,the ,sun4 #ah4 ,the ,,sun 1 an immense globe of fire1 is placed near the common center1 or rather in the lower#b focus1 of the ,orbits of all the ,planets and ,comets#c2 and turns round his axis in #be days #f hours1 as is evident by the motion of spots seen on his surface4 ,his diameter is computed to be #gfc1jjj miles2 and1 by the various attractions of the circumvolving ,planets1 he is agitated by a small motion round the center of gravity of the ,system4 ,all the ,planets1 as seen from him1 move the same way1 and according to the order of ,signs in the graduated ,circle c4 which represents the great ,ecliptic in the ,heavens3 but1 as seen from any one ,planet1 the rest appear sometimes to go backward1 sometimes forward1 and sometimes to stand still2 not in circles nor ellipses1 but in#d looped curves which never return into themselves4 ,the ,comets come from all parts of the ,heavens1 and move in all sorts of directions4 ,sidenote3 ,,plate ,i4 ,fig4 ,i4 ,the ,sun4 ,the ,axes of the ,planets1 what4 #ai4 ,having mentioned the ,sun's turning round his axis1 and as there will be frequent occasion to speak of the like motion of the ,earth and other ,planets1 it is proper here to inform the young ,tyro in ,astronomy1 that neither the ,sun nor ,planets have material axes to turn upon1 and support them1 as in the little imperfect ,machines contrived to represent them4 ,for the axis of a ,planet is a line conceived to be drawn through it's center1 about which it revolves as on a real axis4 ,the extremities of this line1 terminating in opposite points of the ,planet's surface1 are called its ,poles4 ,that which points towards the northern part of the ,heavens is called the ,north ,pole2 and the other1 pointing towards the southern part1 is called the ,south ,pole4 ,a bowl whirled from one's hand into the open air turns round such a line within itself1 whilst it moves forward2 and such are the lines we mean1 when we speak of the ,axes of the ,heavenly bodies4 ,sidenote3 ,their ,orbits are not in the same plane with the ,ecliptic4 ,,plate ,i4 ,their ,nodes4 ,where situated4 #bj4 ,let us suppose the ,earth's ,orbit to be a thin1 even1 solid plane2 cutting the ,sun through the center1 and extended out as far as the ,starry ,heavens1 where it will mark the great ,circle called the ,ecliptic4 ,this ,circle we suppose to be divided into #ab equal parts1 called ,signs2 each ,sign into #cj equal parts1 called ,degrees2 each ,degree into #fj equal parts1 called ,minutes2 and every ,minute into #fj equal parts1 called ,seconds3 so that a ,second is the #fjth part of a ,minute2 a ,minute the #fjth part of a ,degree2 and a ,degree the #cfjth part of a ,circle1 or #cjth part of a ,sign4 ,the ,planes of the ,orbits of all the other ,planets likewise cut the ,sun in halves2 but extended to the ,heavens1 form ,circles different from one another1 and from the ,ecliptic2 one half of each being on the north side1 and the other on the south side of it4 ,consequently the ,orbit of each ,planet crosses the ,ecliptic in two opposite points1 which are called the ,planet's ,nodes4 ,these ,nodes are all in different parts of the ,ecliptic2 and therefore1 if the planetary ,tracks remained visible in the ,heavens1 they would in some measure resemble the different rutts of waggon-wheels crossing one another in different parts1 but never going far asunder4 ,that ,node1 or ,intersection of the ,orbit of any ,planet with the ,earth's ,orbit1 from which the ,planet ascends northward above the ,ecliptic1 is called the ,ascending ,node of the ,planet2 and the other1 which is directly opposite thereto1 is called it's ,descending ,node4 ,saturn's ,ascending ,node is in #ba deg4 #ac min4 of ,cancer 1 ,jupiter's in #g deg4 #bi min4 of the same ,sign1 ,mars's in #ag deg4 #ag min4 of ,taurus 1 ,venus's in #ac deg4 #ei min4 of ,gemini 1 and ,mercury's in #ad deg4 #dc min4 of ,taurus4 ,here we consider the ,earth's ,orbit as the standard1 and the ,orbits of all the other ,planets as oblique to it4 ,sidenote3 ,the ,planets ,orbits1 what4 #ba4 ,when we speak of the ,planets ,orbits1 all that is meant is their ,paths through the open and unresisting ,space in which they move2 and are kept in1 by the attractive power of the ,sun1 and the projectile force impressed upon them at first3 between which power and force there is so exact an adjustment1 that without any solid ,orbits to confine the ,planets1 they keep their courses1 and at the end of every revolution find the points from whence they first set out1 much more truly than can be imitated in the best machines made by human art4 ,sidenote3 ,mercury4 ,fig4 ,i4 ,may be inhabited4 ,,plate ,i4 #bb4 ,,mercury1 the nearest ,planet to the ,sun1 goes round him 7as in the circle marked 7 in #hg days #bc hours of our time nearly2 which is the length of his year4 ,but1 being seldom seen1 and no spots appearing on his surface or disc1 the time of his rotation on his axis1 or the length of his days and nights1 is as yet unknown4 ,his distance from the ,sun is computed to be #cb millions of miles1 and his diameter #bfjj4 ,in his course1 round the ,sun1 he moves at the rate of #ie thousand miles every hour4 ,his light and heat from the ,sun are almost seven times as great as ours2 and the ,sun appears to him almost seven times as large as to us4 ,the great heat on this ,planet is no argument against it's being inhabited2 since the ,almighty could as easily suit the bodies and constitutions of it's inhabitants to the heat of their dwelling1 as he has done ours to the temperature of our ,earth4 ,and it is very probable that the people there have such an opinion of us1 as we have of the inhabitants of ,jupiter and ,saturn2 namely1 that we must be intolerably cold1 and have very little light at so great a distance from the ,sun4 ,sidenote3 ,has like phases with the ,moon4 #bc4 ,this ,planet appears to us with all the various phases of the ,moon1 when viewed at different times by a good telescope2 save only that he never appears quite ,full1 because his enlightened side is never turned directly towards us but when he is so near the ,sun as to be lost to our sight in it's beams4 ,and1 as his enlightened side is always toward the ,sun1 it is plain that he shines not by any light of his own2 for if he did1 he would constantly appear round4 ,that he moves about the ,sun in an ,orbit within the ,earth's ,orbit is also plain 7as will be more largely shewn by and by1 #ada1 seq47 because he is never seen opposite to the ,sun1 nor above #ef times the ,sun's breadth from his center4 ,sidenote3 ,his ,orbit and ,nodes4 #bd4 ,his ,orbit is inclined seven degrees to the ,ecliptic2 and that ,node #bj1 from which he ascends northward above the ,ecliptic is in the #adth degree of ,taurus2 the opposite1 in the #adth degree of ,scorpio4 ,the ,earth is in these points on the #eth of ,november and #dth of ,may1 new style2 and when ,mercury comes to either of his ,nodes at his#e inferior ,conjunction about these times1 he will appear to pass over the disc or face of the ,sun1 like a dark round spot4 ,but in all other parts of his ,orbit his ,conjunctions are invisible1 because he either goes above or below the ,sun4 ,sidenote3 ,when he will be seen as if upon the ,sun4 #be4 ,mr4 ,,whiston has given us an account of several periods at which ,mercury may be seen on the ,sun's disc1 viz4 ,in the year #aghb1 ,nov4 #abth1 at #c h4 #dd m4 in the afternoon3 #aghf1 ,may #dth1 at #f h4 #eg m4 in the forenoon3 #aghi1 ,dec4 #fth1 at #c h4 #ee m4 in the afternoon2 and #agii1 ,may #gth1 at #b h4 #cd m4 in the afternoon4 ,there will be several intermediate ,transits1 but none of them visible at ,london4 ,sidenote3 ,fig4 ,i4 ,venus4 #bf4 ,,venus1 the next ,planet in order1 is computed to be #ei millions of miles from the ,sun2 and by moving at the rate of #fi thousand miles every hour in her ,orbit 7as in the circle marked 71 she goes round the ,sun in #bbd days #ag hours of our time nearly2 in which1 though it be the full length of her year1 she has only #i-a_/d days1 according to ,,bianchini's observations2 so that in her1 every day and night together is as long as #bd-a_/c days and nights with us4 ,this odd quarter of a day in every year makes every fourth year a leap-year to ,venus2 as the like does to our ,earth4 ,her diameter is #gijf miles2 and by her diurnal motion the inhabitants about her ,equator are carried #dc miles every hour3 besides the #fi1jjj above-mentioned4 ,sidenote3 ,her ,orbit lies between the ,earth and ,mercury4 #bg4 ,her ,orbit includes that of ,mercury within it2 for at her greatest ,elongation1 or apparent distance from the ,sun1 she is #if times his breadth from his centre2 which is almost double of ,mercury's4 ,her ,orbit is included by the ,earth's2 for if it were not1 she might be seen as often in ,opposition to the ,sun as in ,conjunction with him2 but she was never seen #ij degrees1 or a fourth part of a ,circle1 from the ,sun4 ,sidenote3 ,she is our morning and evening ,star by turns4 #bh4 ,when ,venus appears west of the ,sun she rises before him in the morning1 and is called the ,morning ,star3 when she appears east of the ,sun she shines in the evening after he sets1 and is then called the ,evening ,star3 being each in it's turn for #bij days4 ,it may perhaps be surprising at first1 that ,venus should keep longer on the east or west of the ,sun than the whole time of her ,period round him4 ,but the difficulty vanishes when we consider that the ,earth is all the while going round the ,sun the same way1 though not so quick as ,venus3 and therefore her relative motion to the ,earth must in every ,period be as much slower than her absolute motion in her ,orbit1 as the ,earth during that time advances forward in the ,ecliptic2 which is #bbj degrees4 ,to us she appears through a telescope in all the various shapes of the ,moon4 #bi4 ,the ,axis of ,venus is inclined #ge degrees to the ,axis of her ,orbit2 which is #ea-a_/b degrees more than our ,earth's ,axis is inclined to the ,axis of the ,ecliptic3 and therefore the variation of her seasons is much greater than of ours4 ,the ,north ,pole of her ,axis inclines toward the #bjth degree of ,aquarius1 our ,earth's to the beginning of ,cancer2 and therefore the northern parts of ,venus have summer in the ,signs where those of our ,earth have winter1 and vice vers4 ,sidenote3 ,remarkable appearances4 #cj4 ,the #f;artificial day at each ,pole of ,venus is as long as #aab-a_/b #gnatural days on our ,earth4 ,sidenote3 ,her ,tropics and polar ,circles1 how situated4 #ca4 ,the ,sun's greatest ,declination on each side of her ,equator amounts to #ge degrees2 therefore her#h ,tropics are only #ae degrees from her ,poles2 and her #i,polar ,circles as far from her ,equator4 ,consequently1 the ,tropics of ,venus are between her ,polar ,circles and her ,poles2 contrary to what those of our ,earth are4 ,sidenote3 ,the ,sun's daily ,course4 #cb4 ,as her annual ,revolution contains only #i-a_/d of her days1 the ,sun will always appear to go through a ,sign1 or twelfth ,part of her ,orbit1 in little more that three quarters of her natural day1 or nearly in #ah-c_/d of our days and nights4 ,sidenote3 ,and great declination4 #cc4 ,because her day is so great a part of her year1 the ,sun changes his ,declination in one day so much1 that if he passes vertically1 or directly over head of any given place on the ,tropic1 the next day he will be #bf degrees from it3 and whatever place he passes vertically over when in the ,equator1 one day's revolution will remove him #cf-a_/d degrees from it4 ,so that the ,sun changes his ,declination every day in ,venus about #ad degrees more at a mean rate1 than he does in a quarter of a year on our ,earth4 ,this appears to be providentially ordered1 for preventing the too great effects of the ,sun's heat 7which is twice as great on ,venus as on the ,earth7 so that he cannot shine perpendicularly on the same places for two days together2 and by that means1 the heated places have time to cool4 ,sidenote3 ,to determine the points of the ,compass at her ,poles4 #cd4 ,if the inhabitants about the ,north ,pole of ,venus fix their ,south1 or ,meridian ,line1 through that part of the ,heavens where the ,sun comes to his greatest ,height1 or ,north ,declination1 and call those the ,east and ,west points of their ,horizon1 which are #ij degrees on each side from that point where the ,horizon is cut by the ,meridian ,line1 these inhabitants will have the following remarkables4 ,sidenote3 ,surprising appearances at her ,poles2 ,the ,sun will rise #bb-a_/b degrees#aj north of the ,east1 and going on #aab-a_/b degrees1 as measured on the plane of the #aa;,horizon1 he will cross the ,meridian at an altitude of #ab-a_/b degrees2 then making an entire revolution without setting1 he will cross it again at an altitude of #dh-a_/b degrees2 at the next revolution he will cross the ,meridian as he comes to his greatest height and declination1 at the altitude of #ge degrees2 being then only #ae degrees from the ,zenith1 or that point of the ,heavens which is directly over head3 and thence he will descend in the like spiral manner2 crossing the ,meridian first at the altitude of #dh-a_/b degrees2 next at the altitude of #ab-a_/b degrees2 and going on thence #aab-a_/b degrees1 he will set #bb-a_/b degrees north of the ,west2 so that1 after having been #d-e_/h revolutions above the ,horizon1 he descends below it to exhibit the like appearances at the ,south ,pole4 #ce4 ,at each ,pole1 the ,sun continues half a year without setting in summer1 and as long without rising in winter2 consequently the polar inhabitants of ,venus have only one day and one night in the year2 as it is at the ,poles of our ,earth4 ,but the difference between the heat of summer and cold of winter1 or of mid-day and mid-night1 on ,venus1 is much greater than on the ,earth3 because in ,venus1 as the ,sun is for half a year together above the ,horizon of each ,pole in it's turn1 so he is for a considerable part of that time near the ,zenith2 and during the other half of the year1 always below the ,horizon1 and for a great part of that time at least #gj degrees from it4 ,whereas1 at the ,poles of our ,earth1 although the ,sun is for half a year together above the ,horizon1 yet he never ascends above1 nor descends below it1 more than #bc-a_/b degrees4 ,when the ,sun is in the ,equinoctial1 or in that ,circle which divides the northern half of the ,heavens from the southern1 he is seen with one half of his ,disc above the ,horizon of the ,north ,pole1 and the other half above the ,horizon of the ,south ,pole2 so that his center is in the ,horizon of both ,poles3 and then descending below the ,horizon of one1 he ascends gradually above that of the other4 ,hence1 in a year1 each ,pole has one spring1 one harvest1 a summer as long as them both1 and a winter equal in length to the other three seasons4 ,sidenote3 ,at her polar ,circles2 #cf4 ,at the ,polar ,circles of ,venus1 the seasons are much the same as at the ,equator1 because there are only #ae degrees betwixt them1 #ca2 only the winters are not quite so long1 nor the summers so short3 but the four seasons come twice round every year4 ,sidenote3 ,at her ,tropics2 #cg4 ,at ,venus's ,tropics1 the ,sun continues for about fifteen of our weeks together without setting in summer2 and as long without rising in winter4 ,whilst he is more than #ae degrees from the ,equator1 he neither rises to the inhabitants of the one ,tropic1 nor sets to those of the other3 whereas1 at our terrestrial ,tropics he rises and sets every day of the year4 #ch4 ,at ,venus's ,tropics1 the ,seasons are much the same as at her ,poles2 only the summers are a little longer1 and the winters a little shorter4 ,sidenote3 ,at her ,equator4 #ci4 ,at her ,equator1 the days and nights are always of the same length2 and yet the diurnal and nocturnal ,arches are very different1 especially when the ,sun's declination is about the greatest3 for then1 his meridian altitude may sometimes be twice as great as his midnight depression1 and at other times the reverse4 ,when the ,sun is at his greatest ,declination1 either ,north or ,south1 his rays are as oblique at ,venus's ,equator1 as they are at ,london on the shortest day of winter4 ,therefore1 at her ,equator there are two winters1 two summers1 two springs1 and two autumns every year4 ,but because the ,sun stays for some time near the ,tropics1 and passes so quickly over the ,equator1 every winter there will be almost twice as long as summer3 the four seasons returning twice in that time1 which consists only of #i-a_/d days4 #dj4 ,those parts of ,venus which lie between the ,poles and ,tropics1 and between the ,tropics and ,polar ,circles1 and also between the ,polar ,circles and ,equator1 partake more or less of the ,phenomena of these ,circles1 as they are more or less distant from them4 ,sidenote3 ,great difference of the ,sun's amplitude at rising and setting4 #da4 ,from the quick change of the ,sun's declination it happens1 that when he rises due east on any day1 he will not set due west on that day1 as with us2 for if the place where he rises due east be on the ,equator1 he will set on that day almost west-north-west2 or about #ah-a_/b degrees north of the west4 ,but if the place be in #de degrees north latitude1 then on the day that the ,sun rises due east he will set north-west by west1 or #cc degrees north of the west4 ,and in #fb degrees north latitude when he rises in the east1 he sets not in that revolution1 but just touches the ,horizon #aj degrees to the west of the north point2 and ascends again1 continuing for #c-a_/d revolutions above the ,horizon without setting4 ,therefore1 no place has the forenoon and afternoon of the same day equally long1 unless it be on the ,equator or at the ,poles4 ,sidenote3 ,the longitude of places easily found in ,venus4 #db4 ,the ,sun's altitude at noon1 or any other time of the day1 and his amplitude at rising and setting1 being so different at places on the same parallels of latitude1 according to the different longitudes of those places1 the longitude will be almost as easily found on ,venus as the latitude is found on the ,earth3 which is an advantage we can never enjoy1 because the daily change of the ,sun's declination is by much too small for that purpose4 ,sidenote3 ,her ,equinoxes shift a quarter of a day forward every year4 #dc4 ,on this ,planet1 wherever the ,sun crosses the ,equator in any year1 he will have #i degrees of declination from that place on the same day and hour next year2 and will cross the ,equator #ij degrees farther to the west2 which makes the time of the ,equinox a quarter of a day 7almost equal to six of our days7 later every year4 ,hence1 although the spiral in which the ,sun's motion is performed1 be of the same sort every year1 yet it will not be the very same1 because the ,sun will not pass vertically over the same places till four annual revolutions are finished4 ,sidenote3 ,every fourth year a leap-year to ,venus4 ,,plate ,i4 #dd4 ,we may suppose that the inhabitants of ,venus will be careful to add a day to some particular part of every fourth year2 which will keep the same seasons to the same days4 ,for1 as the great annual change of the ,equinoxes and ,solstices shifts the seasons a quarter of a day every year1 they would be shifted through all the days of the year in #cf years4 ,but by means of this intercalary day1 every fourth year will be a leap-year2 which will bring her time to an even reckoning1 and keep her ,calendar always right4 ,sidenote3 ,when she will appear on the ,sun4 #de4 ,venus's ,orbit is inclined #c-a_/b degrees to the ,earth's2 and crosses it in the #adth degree of ,gemini and of ,sagittarius2 and therefore1 when the ,earth is about these points of the ,ecliptic at the time that ,venus is in her inferiour conjunction1 she will appear like a spot on the ,sun1 and afford a more certain method of finding the distances of all the ,planets from the ,sun than any other yet known4 ,but these appearances happen very seldom2 and will only be thrice visible at ,london for three hundred years to come4 ,the first time will be in the year #agfa1 ,june the #fth1 at #e hours #ee minutes in the morning4 ,the second #aiif1 ,june the #ith1 at #b hours #ac minutes in the afternoon4 ,and the third in the year #bjjd1 ,june the #fth1 at #g hours #ah minutes in the forenoon4 ,excepting such ,transits as these1 she shews the same appearances to us regularly every eight years2 her ,conjunctions1 ,elongations1 and ,times of rising and setting being very nearly the same1 on the same days1 as before4 ,sidenote3 ,she may have a ,moon although we cannot see it4 #df4 ,venus may have a ,satellite or ,moon1 although it be undiscovered by us3 which will not appear very surprising1 if we consider how inconveniently we are placed for seeing it4 ,for it's enlightened side can never be fully turned towards us but when ,venus is beyond the ,sun2 and then1 as ,venus appears little bigger than an ordinary ,star1 her ,moon may be too small to be perceptible at such a distance4 ,when she is between us and the ,sun1 her full ,moon has it's dark side towards us2 and then1 we cannot see it any more than we can our own ,moon at the time of ,change4 ,when ,venus is at her greatest ,elongation1 we have but one half of the enlightened side of her ,full ,moon towards us2 and even then it may be too far distant to be seen by us4 ,but if she has a ,moon1 it may certainly be seen with her upon the ,sun1 in the year #agfa1 unless it's ,orbit be considerably inclined to the ,ecliptic3 for if it should be in conjunction or opposition at that time1 we can hardly imagine that it moves so slow as to be hid by ,venus all the six hours that she will appear on the ,sun's ,disc4 ,sidenote3 ,the ,earth4 ,fig4 ,i4 ,it's diurnal and annual motion4 #dg4 ,the ,,earth is the next ,planet above ,venus in the ,system4 ,it is #ha millions of miles from the ,sun1 and goes round him 7as in the circle 7 in #cfe days #e hours #di minutes1 from any ,equinox or ,solstice to the same again3 but from any fixed ,star to the same again1 as seen from the ,sun1 in #cfe days #f hours and #i minutes2 the former being the length of the ,tropical year1 and the latter the length of the ,sidereal4 ,it travels at the rate of #eh thousand miles every hour1 which motion1 though #abj times swifter than that of a cannon ball1 is little more than half as swift as ,mercury's motion in his ,orbit4 ,the ,earth's diameter is #gigj miles2 and by turning round it's ,axis every #bd hours from ,west to ,east1 it causes an apparent diurnal motion of all the heavenly ,bodies from ,east to ,west4 ,by this rapid motion of the ,earth on it's ,axis1 the inhabitants about the ,equator are carried #ajdb miles every hour1 whilst those on the parallel of ,london are carried only about #ehj1 besides the #eh thousand miles by the annual motion above-mentioned1 which is common to all places whatever4 ,sidenote3 ,inclination of it's ,axis4 #dh4 ,the ,earth's ,axis makes an angle of #bc-a_/b degrees with the ,axis of it's ,orbit2 and keeps always the same oblique direction2 inclining towards the same fixed ,stars#ab throughout it's annual course2 which causes the returns of spring1 summer1 autumn1 and winter2 as will be explained at large in the tenth ,chapter4 ,sidenote3 ,a proof of it's being round4 #di4 ,the ,earth is round like a globe2 as appears1 #a4 from it's shadow in ,eclipses of the ,moon2 which shadow is always bounded by a circular line #cad4 #b4 ,from our seeing the masts of a ship whilst the hull is hid by the convexity of the water4 #c4 ,from it's having been sailed round by many navigators4 ,the hills take off no more from the roundness of the ,earth in comparison1 than grains of dust do from the roundness of a common ,globe4 ,sidenote3 ,it's number of square miles4 #ej4 ,the seas and unknown parts of the ,earth 7by a measurement of the best ,maps7 contain #afj million #ebb thousand and #bf square miles2 the inhabited parts #ch million #iij thousand #efi3 ,europe #d million #def thousand and #fe2 ,asia #aj million #gfh thousand #hbc2 ,africa #i million #fed thousand #hjg2 ,america #ad million #aaj thousand #hgd4 ,in all1 #aii million #eab thousand #eie2 which is the number of square miles on the whole surface of our ,globe4 ,sidenote3 ,the proportion of land and sea4 ,,plate ,i4 #ea4 ,dr4 ,,long1 in the first volume of his ,astronomy1 pag4 #afh1 mentions an ingenious and easy method of finding nearly what proportion the land bears to the sea2 which is1 to take the papers of a large terrestrial globe1 and after separating the land from the sea with a pair of scissars1 to weigh them carefully in scales4 ,this supposes the globe to be exactly delineated1 and the papers all of equal thickness4 ,the ,doctor made the experiment on the papers of ,mr4 ,,senex's seventeen inch globe2 and found that the sea papers weighed #cdi grains1 and the land only #abd3 by which it appears that almost three fourth parts of the surface of our ,earth between the ,polar ,circles are covered with water1 and that little more than one fourth is dry land4 ,the ,doctor omitted weighing all within the ,polar ,circles2 because there is no certain measurement of the land there1 so as to know what proportion it bears to the sea4 ,sidenote3 ,the ,moon4 #eb4 ,the ,,moon is not a ,planet1 but only a ,satellite or ,attendant of the ,earth1 moving round the ,earth from ,change to ,change in #bi days #ab hours and #dd minutes2 and going round the ,sun with it every year4 ,the ,moon's diameter is #bahj miles2 and her distance from the ,earth #bdj thousand4 ,she goes round her ,orbit in #bg days #g hours #dc minutes1 moving about #bbij miles every hour2 and turns round her ,axis exactly in the time that she goes round the ,earth1 which is the reason of her keeping always the same side towards us1 and that her day and night taken together is as long as our lunar month4 ,sidenote3 ,her ,phases4 #ec4 ,the ,moon is an opaque ,globe like the ,earth1 and shines only by reflecting the light of the ,sun3 therefore whilst that half of her which is toward the ,sun is enlightened1 the other half must be dark and invisible4 ,hence1 she disappears when she comes between us and the ,sun2 because her dark side is then toward us4 ,when she is gone a little way forward1 we see a little of her enlightened side2 which still increases to our view1 as she advances forward1 until she comes to be opposite to the ,sun2 and then her whole enlightened side is towards the ,earth1 and she appears with a round1 illumined ,orb2 which we call the ,full ,moon3 her dark side being then turned away from the ,earth4 ,from the ,full she seems to decrease gradually as she goes through the other half of her course2 shewing us less and less of her enlightened side every day1 till her next change or conjunction with the ,sun1 and then she disappears as before4 ,sidenote3 ,a proof that she shines not by her own light4 ,fig4 ,i4 #ed4 ,the continual changing of the ,moon's phases or shapes demonstrates that she shines not by any light of her own3 for if she did1 being globular1 we should always see her with a round full ,orb like the ,sun4 ,her ,orbit is represented in the ,scheme by the little circle m1 upon the ,earth's ,orbit 3 but it is drawn fifty times too large in proportion to the ,earth's2 and yet is almost too small to be seen in the ,diagram4 ,sidenote3 ,one half of her always enlightened4 #ee4 ,the ,moon has scarce any difference of seasons2 her ,axis being almost perpendicular to the ,ecliptic4 ,what is very singular1 one half of her has no darkness at all2 the ,earth constantly affording it a strong light in the ,sun's absence2 while the other half has a fortnight's darkness and a fortnight's light by turns4 ,sidenote3 ,our ,earth is her ,moon4 #ef4 ,our ,earth is a ,moon to the ,moon1 waxing and waneing regularly1 but appearing thirteen times as big1 and affording her thirteen times as much light1 as she does to us4 ,when she changes to us1 the ,earth appears full to her2 and when she is in her first quarter to us1 the ,earth is in it's third quarter to her2 and vice vers4 #eg4 ,but from one half of the ,moon1 the ,earth is never seen at all3 from the middle of the other half1 it is always seen over head2 turning round almost thirty times as quick as the ,moon does4 ,from the line which limits our view of the ,moon1 or all round what we call her edges1 only one half of the ,earth's side next her is seen2 the other half being hid below the ,horizon4 ,to her1 the ,earth seems to be the biggest ,body in the ,universe2 for it appears thirteen times as big as she does to us4 ,sidenote3 ,a ,proof of the ,moon's having no ,atmosphere2 #eh4 ,the ,moon has no such ,atmosphere1 or body of air surrounding her as we have3 for if she had1 we could never see her edge so well defined as it appears2 but there would be a sort of a mist or haziness round her1 which would make the ,stars look fainter1 when they were seen through it4 ,but observation proves1 that the ,stars which disappear behind the ,moon retain their full lustre until they seem to touch her very edge1 and then vanish in a moment4 ,this has been often observed by ,astronomers1 but particularly by ,,cassini#ac of the ,star in the breast of ,virgo1 which appears single and round to the bare eye2 but through a refracting ,telescope of #af feet appears to be two ,stars so near together1 that the distance between them seems to be but equal to one of their apparent diameters4 ,the ,moon was observed to pass over them on the #bast of ,april #agbj1 ,n4 ,s4 and as her dark edge drew near to them1 it caused no change in their colour or ,situation4 ,at #be min4 #ad sec4 past #ab at night1 the most westerly of these ,stars was hid by the dark edge of the ,moon2 and in #cj seconds afterward1 the most easterly ,star was hid3 each of them disappearing behind the ,moon in an instant1 without any preceding diminution of magnitude or brightness2 which by no means could have been the case if there were an ,atmosphere round the ,moon2 for then1 one of the ,stars falling obliquely into it before the other1 ought by refraction to have suffered some change in its colour1 or in it's distance from the other ,star which was not yet entered into the ,atmosphere4 ,but no such alteration could be perceived though the observation was performed with the utmost attention to that particular2 and was very proper to have made such a discovery4 ,the faint light1 which has been seen all around the ,moon1 in total ,eclipses of the ,sun1 has been observed1 during the time of darkness1 to have it's center coincident with the center of the ,sun2 and is therefore much more likely to arise from the ,atmosphere of the ,sun than from that of the ,moon2 for if it were the latter1 it's center would have gone along with the ,moon's4 ,sidenote3 ,nor ,seas4 ,she is full of caverns and deep pits4 #ei4 ,if there were seas in the ,moon1 she could have no clouds1 rains1 nor storms as we have2 because she has no such ,atmosphere to support the vapours which occasion them4 ,and every one knows1 that when the ,moon is above our ,horizon in the night time1 she is visible1 unless the clouds of our ,atmosphere hide her from our view2 and all parts of her appear constantly with the same clear1 serene1 and calm aspect4 ,but those dark parts of the ,moon1 which were formerly thought to be seas1 are now found to be only vast deep cavities1 and places which reflect not the ,sun's light so strongly as others1 having many caverns and pits whose shadows fall within them1 and are always dark on the sides next the ,sun2 which demonstrates their being hollow3 and most of these pits have little knobs like hillocks standing within them1 and casting shadows also2 which cause these places to appear darker than others which have fewer1 or less remarkable caverns4 ,all these appearances shew that there are no seas in the ,moon2 for if there were any1 their surfaces would appear smooth and even1 like those on the ,earth4 ,sidenote3 ,the ,stars always visible to the ,moon4 #fj4 ,there being no ,atmosphere about the ,moon1 the ,heavens in the day time have the appearance of night to a ,lunarian who turns his back toward the ,sun2 and when he does1 the ,stars appear as bright to him as they do in the night to us4 ,for1 it is entirely owing to our ,atmosphere that the ,heavens are bright about us in the day4 ,sidenote3 ,the ,earth a ,dial to the ,moon4 #fa4 ,as the ,earth turns round it's ,axis1 the several continents1 seas1 and islands appear to the ,moon's inhabitants like so many spots of different forms and brightness1 moving over it's surface2 but much fainter at some times than others1 as our clouds cover them or leave them4 ,by these spots the ,lunarians can determine the time of the ,earth's diurnal motion1 just as we do the motion of the ,sun3 and perhaps they measure their time by the motion of the ,earth's spots2 for they cannot have a truer dial4 ,sidenote3 ,,plate ,i4 ,how the ,lunarians may know the length of their year4 #fb4 ,the ,moon's ,axis is so nearly perpendicular to the ,ecliptic1 that the ,sun never removes sensibly from her ,equator3 and the#ad obliquity of her ,orbit1 which is next to nothing as seen from the ,sun1 cannot cause any sensible declination of the ,sun from her ,equator4 ,yet her inhabitants are not destitute of means for determining the length of their year1 though their method and ours must differ4 ,for we can know the length of our year by the return of our ,equinoxes2 but the ,lunarians1 having always equal day and night1 must have recourse to another method2 and we may suppose1 they measure their year by observing the ,poles of our ,earth2 as one always begins to be enlightened1 and the other disappears1 at our ,equinoxes2 they being conveniently situated for observing great tracks of land about our ,earth's ,poles1 which are entirely unknown to us4 ,hence we may conclude1 that the year is of the same absolute length both to the ,earth and ,moon1 though very different as to the number of days3 we having #cfe-a_/d natural days1 and the ,lunarians only #ab-g_/ai2 every day and night in the ,moon being as long as #bi-a_/b on the ,earth4 ,sidenote3 ,and the longitudes of their places4 #fc4 ,the ,moon's inhabitants on the side next the ,earth may as easily find the longitude of their places as we can find the latitude of ours4 ,for the ,earth keeping constantly1 or very nearly so1 over one ,meridian of the ,moon1 the east or west distances of places from that ,meridian are as easily found1 as we can find our distance from the ,equator by the ,altitude of our celestial ,poles4 ,sidenote3 ,mars4 ,fig4 ,i4 #fd4 ,the ,planet ,,mars is next in order1 being the first above the ,earth's ,orbit4 ,his distance from the ,sun is computed to be #abc millions of miles2 and by travelling at the rate of #dg thousand miles every hour1 as in the circle 1 he goes round the ,sun in #fhg of our days and #ag hours2 which is the length of his year1 and contains #ffg-a_/d of his days2 every day and night together being #dj minutes longer than with us4 ,his diameter is #dddd miles1 and by his diurnal rotation the inhabitants about his ,equator are carried #eef miles every hour4 ,his quantity of light and heat is equal but to one half of ours2 and the ,sun appears but half as big to him as to us4 ,sidenote3 ,his ,atmosphere and ,phases4 #fe4 ,this ,planet being but a fifth part so big as the ,earth1 if any ,moon attends him1 she must be very small1 and has not yet been discovered by our best telescopes4 ,he is of a fiery red colour1 and by his ,appulses to some of the fixed ,stars1 seems to be surrounded by a very gross ,atmosphere4 ,he appears sometimes gibbous1 but never horned2 which both shews that his ,orbit includes the ,earth's within it1 and that he shines not by his own light4 #ff4 ,to ,mars1 our ,earth and ,moon appear like two ,moons1 a bigger and a less2 changing places with one another1 and appearing sometimes horned1 sometimes half or three quarters illuminated1 but never full2 nor at most above a quarter of a degree from each other1 although they are #bdj thousand miles asunder4 ,sidenote3 ,,plate ,i4 ,how the other ,planets appear to ,mars4 #fg4 ,our ,earth appears almost as big to ,mars as ,venus does to us1 and at ,mars it is never seen above #dh degrees from the ,sun2 sometimes it appears to pass over the ,disc of the ,sun1 and so do ,mercury and ,venus3 but ,mercury can never be seen from ,mars by such eyes as ours1 unassisted by proper instruments2 and ,venus will be as seldom seen as we see ,mercury4 ,jupiter and ,saturn are as visible to ,mars as to us4 ,his ,axis is perpendicular to the ,ecliptic1 and his ,orbit is #b degrees inclined to it4 ,sidenote3 ,jupiter4 ,fig4 ,i4 #fh4 ,,jupiter1 the biggest of all the ,planets1 is still higher in the ,system1 being about #dbd millions of miles from the ,sun3 and going at the rate of #be thousand miles every hour in his ,orbit1 as in the circle finishes his annual period in eleven of our years #cad days and #ah hours4 ,he is above #ajjj times as big as the ,earth1 for his diameter is #ha1jjj miles2 which is more than ten times the diameter of the ,earth4 ,sidenote3 ,the number of days in his year4 #fi4 ,jupiter turns round his ,axis in #i hours #ef minutes2 so that his year contains #aj thousand #dfd days2 and the diurnal velocity of his equatoreal parts is greater than the swiftness with which he moves in his annual ,orbit2 a singular circumstance1 as far as we know4 ,by this prodigious quick ,rotation1 his equatoreal inhabitants are carried #be thousand #ibj miles every hour 7which is #ibj miles an hour more than an inhabitant of our ,earth moves in twenty-four hours7 besides the #be thousand above-mentioned1 which is common to all parts of his surface1 by his annual motion4 ,sidenote3 ,his ,belts and spots4 #gj4 ,jupiter is surrounded by faint substances1 called ,belts1 in which so many changes appear1 that they are generally thought to be clouds3 for some of them have been first interrupted and broken1 and then have vanished entirely4 ,they have sometimes been observed of different breadths1 and afterwards have all become nearly of the same breadth4 ,large spots have been seen in these ,belts2 and when a ,belt vanishes1 the contiguous spots disappear with it4 ,the broken ends of some ,belts have been generally observed to revolve in the same time with the spots2 only those nearer the ,equator in somewhat less time than those near the ,poles2 perhaps on account of the ,sun's greater heat near the ,equator1 which is parallel to the ,belts and course of the spots4 ,several large spots1 which appear round at one time1 grow oblong by degrees1 and then divide into two or three round spots4 ,the periodical time of the spots near the ,equator is #i hours #ej minutes1 but of those near the ,poles #i hours #ef minutes4 ,see ,dr4 ,,smith's ,optics1 #ajjd seq4 ,sidenote3 ,he has no change of seasons2 #ga4 ,the ,axis of ,jupiter is so nearly perpendicular to his ,orbit1 that he has no sensible change of seasons2 which is a great advantage1 and wisely ordered by the ,author of ,nature4 ,for1 if the ,axis of this ,planet were inclined any considerable number of degrees1 just so many degrees round each ,pole would in their turn be almost six of our years together in darkness4 ,and1 as each degree of a great ,circle on ,jupiter contains #gjf of our miles at a mean rate1 it is easy to judge what vast tracts of land would be rendered uninhabitable by any considerable inclination of his ,axis4 ,sidenote3 ,but has four ,moons4 #gb4 ,the ,sun appears but #a_/bh part so big to ,jupiter as to us2 and his light and heat are in the same small proportion1 but compensated by the quick returns thereof1 and by four ,moons 7some bigger and some less than our ,earth7 which revolve about him3 so that there is scarce any part of this huge ,planet but what is during the whole night enlightened by one or more of these ,moons1 except his ,poles1 whence only the farthest ,moons can be seen1 and where their light is not wanted1 because the ,sun constantly circulates in or near the ,horizon1 and is very probably kept in view of both ,poles by the ,refraction of ,jupiter's ,atmosphere1 which1 if it be like ours1 has certainly refractive power enough for that purpose4 ,sidenote3 ,their periods round ,jupiter4 ,their grand period4 #gc4 ,the ,orbits of these ,moons are represented in the ,scheme of the ,solar ,system by four small circles marked #a4 #b4 #c4 #d4 on ,jupiter's ,orbit 2 but are drawn fifty times too large in proportion to it4 ,the first ,moon1 or that nearest to ,jupiter1 goes round him in #a day #ah hours and #cf minutes of our time2 and is #bbi thousand miles distant from his center3 ,the second performs it's revolution in three days #ac hours and #ae minutes1 at #cfd thousand miles distance3 ,the third in #g days three hours and #ei minutes1 at the distance of #ehj thousand miles3 ,and the fourth1 or outermost1 in #af days #ah hours and #cj minutes1 at the distance of one million of miles from his center4 ,the ,periods of these ,moons are so incommensurate to one another1 that if ever they were all in a right line between ,jupiter and the ,sun1 it will require more than #c1jjj1jjj1jjj1jjj years from that time to bring them all into the same right line again1 as any one will find who reduces all their periods into seconds1 then multiplies them into one another1 and divides the product by #dcb2 which is the highest number that will divide the product of all their periodical times1 namely #db1jhe1cjc1cgf1ica1iid1iee1ijd seconds1 without a remainder4 ,sidenote3 ,parallax of their ,orbits1 and distances from ,jupiter4 ,,plate ,i4 ,how he appears to his nearest ,moon4 #gd4 ,the ,angles under which the ,orbits of ,jupiter's ,moons are seen from the ,earth1 at it's mean distance from ,jupiter1 are as follow3 ,the first1 #c #ee2 the second1 #f #ad2 the third1 #i #eh2 and the fourth1 #ag #cj4 ,and their distances from ,jupiter1 measured by his semidiameters1 are thus3 ,the first1 #e-b_/c2 the second1 #i2 the third4 #ad-bc_/fj2 and the fourth1 #be-ah_/fjae4 ,this ,planet1 seen from it's nearest ,moon1 appears #ajjj times as large as our ,moon does to us2 waxing and waneing in all her monthly shapes1 every #db-a_/b hours4 ,sidenote3 ,two grand discoveries made by the ,eclipse of ,jupiter's ,moons4 #ge4 ,jupiter's three nearest ,moons fall into his shadow1 and are eclipsed in every ,revolution3 but the ,orbit of the fourth ,moon is so much inclined1 that it passeth by ,jupiter1 without falling into his shadow1 two years in every six4 ,by these ,eclipses1 ,astronomers have not only discovered that the ,sun's light comes to us in eight minutes2 but have also determined the longitudes of places on this ,earth with greater certainty and facility than by any other method yet known2 as shall be explained in the eleventh ,chapter4 ,sidenote3 ,the great difference between the ,equatoreal and ,polar diameters of ,jupiter4 ,the difference little in those of our ,earth4 #gf4 ,the difference between the ,equatoreal and ,polar diameters of ,jupiter is #fbcj miles2 for his equatoreal diameter is to his polar as #ac to #ab4 ,so that his ,poles are #caae miles nearer his center than his ,equator is4 ,this results from his quick motion round his ,axis2 for the fluids1 together with the light particles1 which they can carry or wash away with them1 recede from the ,poles which are at rest1 towards the ,equator where the motion is quickest1 until there be a sufficient number accumulated to make up the deficiency of gravity occasioned by the centrifugal force1 which always arises from a quick motion round an axis3 and when the weight is made up so1 as that all parts of the surface press equally heavy toward the center1 there is an equilibrium1 and the equatoreal parts rise no higher4 ,our ,earth being but a very small ,planet1 compared to ,jupiter1 and it's motion on it's ,axis being much slower1 it is less flattened of course2 for the difference between it's equatoreal and polar diameters is only as #bcj to #bbi1 or #ce miles4 ,sidenote3 ,place of his ,nodes4 #gg4 ,jupiter's ,orbit is #a degree #bj minutes inclined to the ,ecliptic4 ,his ,north ,node is in the #gth degree of ,cancer1 and his ,south ,node in the #gth degree of ,capricorn4 ,sidenote3 ,saturn4 ,fig4 ,i4 #gh4 ,,saturn1 the remotest of all the ,planets1 is about #ggg millions of miles from the ,sun2 and1 travelling at the rate of #ah thousand miles every hour1 as in the circle marked 1 performs his annual circuit in #bi years #afg days and #e hours of our time2 which makes only one year to that ,planet4 ,his diameter is #fg1jjj miles2 and therefore he is near #fjj times as big as the ,earth4 ,sidenote3 ,fig4 ,v4 ,his ,ring4 ,,plate ,i4 #gi4 ,he is surrounded by a thin broad ,ring1 as an artificial ,globe is by its ,horizon4 ,this ,ring appears double when seen through a good telescope1 and is represented by the figure in such an oblique view as it is generally seen4 ,it is inclined #cj degrees to the ,ecliptic1 and is about #ba thousand miles in breadth2 which is equal to it's distance from ,saturn on all sides4 ,there is reason to believe that the ,ring turns round it's ,axis1 because1 when it is almost edge-wise to us1 it appears somewhat thicker on one side of the ,planet than on the other2 and the thickest edge has been seen on different sides at different times4 ,but ,saturn having no visible spots on his body1 whereby to determine the time of his turning round his ,axis1 the length of his days and nights1 and the position of his ,axis1 are unknown to us4 ,sidenote3 ,his five ,moons4 ,fig4 ,i4 #hj4 ,to ,saturn1 the ,sun appears only #a_/ijth part so big as to us2 and the light and heat he receives from the ,sun are in the same proportion to ours4 ,but to compensate for the small quantity of sun-light1 he has five ,moons1 all going round him on the outside of his ,ring1 and nearly in the same plane with it4 ,the first1 or nearest ,moon to ,saturn1 goes round him in #a day #ba hours #ai minutes2 and is #adj thousand miles from his center3 ,the second1 in two days #ag hours #dj minutes2 at the distance of #ahg thousand miles3 ,the third1 in #d days #ab hours #be minutes2 at #bfc thousand miles distance3 ,the fourth1 in #ae days #bb hours #da minutes2 at the distance of #fjj thousand miles3 ,and the fifth1 or outermost1 at one million #hjj thousand miles from ,saturn's center1 goes round him in #gi days #g hours #dh minutes4 ,their ,orbits in the ,scheme of the ,solar ,system are represented by the five small circles1 marked #a4 #b4 #c4 #d4 #e4 on ,saturn's ,orbit2 but these1 like the ,orbits of the other ,satellites1 are drawn fifty times too large in proportion to the ,orbits of their ,primary ,planets4 ,sidenote3 ,his ,axis probably inclined to his ,ring4 #ha4 ,the ,sun shines almost fifteen of our years together on one side of ,saturn's ,ring without setting1 and as long on the other in it's turn4 ,so that the ,ring is visible to the inhabitants of that ,planet for almost fifteen of our years1 and as long invisible by turns1 if it's ,axis has no ,inclination to it's ,ring3 but if the ,axis of the ,planet be inclined to the ,ring1 suppose about #cj degrees1 the ,ring will appear and disappear once every natural day to all the inhabitants within #cj degrees of the ,equator1 on both sides1 frequently eclipsing the ,sun in a ,saturnian day4 ,moreover1 if ,saturn's ,axis be so inclined to his ,ring1 it is perpendicular to his ,orbit2 and thereby the inconvenience of different seasons to that ,planet is avoided4 ,for considering the length of ,saturn's year1 which is almost equal to thirty of ours1 what a dreadful condition must the inhabitants of his ,polar regions be in1 if they be half of that time deprived of the light and heat of the ,sun8 which must not be their case alone1 if the ,axis of the ,planet be perpendicular to the ,ring1 but also the ,ring must hide the ,sun from vast tracks of land on each side of the ,equator for #ac or #ad of our years together1 on the south side and north side by turns1 as the ,axis inclines to or from the ,sun3 the reverse of which inconvenience is another good presumptive proof of the ,inclination of ,saturn's ,axis to it's ,ring1 and also of his ,axis being perpendicular to his ,orbit4 ,sidenote3 ,how the ,ring appears to ,saturn and to us4 ,in what ,signs ,saturn appears to lose his ,ring2 and in what ,signs it appears most open to us4 #hb4 ,this ,ring1 seen from ,saturn1 appears like a vast luminous ,arch in the ,heavens1 as if it did not belong to the ,planet4 ,when we see the ,ring most open1 it's shadow upon the ,planet is broadest2 and from that time the shadow grows narrower1 as the ,ring appears to do to us2 until1 by ,saturn's annual motion1 the ,sun comes to the plane of the ,ring1 or even with it's edge2 which being then directed towards us1 becomes invisible on account of it's thinness2 as shall be explained more largely in the tenth ,chapter1 and illustrated by a figure4 ,the ,ring disappears twice in every annual ,revolution of ,saturn1 namely1 when he is in the #aith degree both of ,pisces and of ,virgo4 ,and when ,saturn is in the middle between these points1 or in the #aith degree either of ,gemini or of ,sagittarius1 his ,ring appears most open to us2 and then it's longest diameter is to it's shortest as #i to #d4 ,sidenote3 ,no ,planet but ,saturn can be seen from ,jupiter2 nor any from ,jupiter besides ,saturn4 #hc4 ,to such eyes as ours1 unassisted by instruments1 ,jupiter is the only ,planet that can be seen from ,saturn2 and ,saturn the only ,planet that can be seen from ,jupiter4 ,so that the inhabitants of these two ,planets must either see much farther than we do1 or have equally good instruments to carry their sight to remote objects1 if they know that there is such a body as our ,earth in the ,universe3 for the ,earth is no bigger seen from ,jupiter than his ,moons are seen from the ,earth2 and if his large body had not first attracted our sight1 and prompted our curiosity to view him with the telescope1 we should never have known any thing of his ,moons2 unless by chance we had directed the telescope toward that small part of the ,heavens where they were at the time of observation4 ,and the like is true of the ,moons of ,saturn4 ,sidenote3 ,place of ,saturn's ,nodes4 #hd4 ,the ,orbit of ,saturn is #b-a_/b degrees inclined to the ,ecliptic1 or ,orbit of our ,earth1 and intersects it in the #bast degree of ,cancer and of ,capricorn2 so that ,saturn's ,nodes are only #ad degrees from ,jupiter's1 #gg4 ,sidenote3 ,the ,sun's light much stronger on ,jupiter and ,saturn than is generally believed4 ,all our heat depends not on the ,sun's rays4 #he4 ,the quantity of light1 afforded by the ,sun of ,jupiter1 being but #a_/bhth part1 and to ,saturn only #a_/ijth part1 of what we enjoy2 may at first thought induce us to believe that these two ,planets are entirely unfit for rational beings to dwell upon4 ,but1 that their light is not so weak as we imagine1 is evident from their brightness in the night-time2 and also1 that when the ,sun is so much eclipsed to us as to have only the #djth part of his ,disc left uncovered by the ,moon1 the decrease of light is not very sensible3 and just at the end of darkness in ,total ,eclipses1 when his western limb begins to be visible1 and seems no bigger than a bit of fine silver wire1 every one is surprised at the brightness wherewith that small part of him shines4 ,the ,moon when ,full affords travellers light enough to keep them from mistaking their way2 and yet1 according to ,dr4 ,,smith#af1 it is equal to no more than a #ij thousandth part of the light of the ,sun3 that is1 the ,sun's light is #ij thousand times as strong as the light of the ,moon when ,full4 ,consequently1 the ,sun gives a thousand times as much light to ,saturn as the ,full ,moon does to us2 and above three thousand times as much to ,jupiter4 ,so that these two ,planets1 even without any ,moons1 would be much more enlightened than we at first imagine2 and by having so many1 they may be very comfortable places of residence4 ,their heat1 so far as it depends on the force of the ,sun's rays1 is certainly much less than ours2 to which no doubt the bodies of their inhabitants are as well adapted as ours are to the seasons we enjoy4 ,and if we consider1 that ,jupiter never has any winter1 even at his ,poles2 which probably is also the case with ,saturn1 the cold cannot be so intense on these two ,planets as is generally imagined4 ,besides1 there may be something in their nature or soil much warmer than in that of our ,earth3 and we find that all our heat depends not on the rays of the ,sun2 for if it did1 we should always have the same months equally hot or cold at their annual returns4 ,but it is far otherwise1 for ,february is sometimes warmer than ,may1 which must be owing to vapours and exhalations from the ,earth4 ,sidenote3 ,it is highly probable that all the ,planets are inhabited4 ,,plate ,i4 #hf4 ,every person who looks upon1 and compares the ,systems of ,moons together1 which belong to ,jupiter and ,saturn1 must be amazed at the vast magnitude of these two ,planets1 and the noble attendance they have in respect of our little ,earth3 and can never bring himself to think1 that an infinitely wise ,creator should dispose of all his animals and vegetables here1 leaving the other ,planets bare and destitute of rational creatures4 ,to suppose that he had any view to our ,benefit1 in creating these ,moons and giving them their motions round ,jupiter and ,saturn2 to imagine that he intended these vast ,bodies for any advantage to us1 when he well knew that they could never be seen but by a few ,astronomers peeping through telescopes2 and that he gave to the ,planets regular returns of days and nights1 and different seasons to all where they would be convenient2 but of no manner of service to us1 except only what immediately regards our own ,planet the ,earth2 to imagine1 ,i say1 that he did all this on our account1 would be charging him impiously with having done much in vain3 and as absurd1 as to imagine that he has created a little ,sun and a ,planetary ,system within the shell of our ,earth1 and intended them for our use4 ,these considerations amount to little less than a positive proof that all the ,planets are inhabited3 for if they are not1 why all this care in furnishing them with so many ,moons1 to supply those with light which are at the greater distances from the ,sun8 ,do we not see1 that the farther a ,planet is from the ,sun1 the greater ,apparatus it has for that purpose8 save only ,mars1 which being but a small ,planet1 may have ,moons too small to be seen by us4 ,we know that the ,earth goes round the ,sun1 and turns round it's own ,axis1 to produce the vicissitudes of summer and winter by the former1 and of day and night by the latter motion1 for the benefit of its inhabitants4 ,may we not then fairly conclude1 by parity of reason1 that the end and design of all the other ,planets is the same8 and is not this agreeable to that beautiful harmony which reigns over the ,universe8 ,surely it is3 and raises in us the most magnificent ideas of the ,,supreme ,,being1 who is every where1 and at all times present2 displaying his power1 wisdom1 and goodness among all his creatures6 and distributing happiness to innumerable ranks of various beings6 ,sidenote3 ,fig4 ,,ii4 ,how the ,sun appears to the different ,planets4 #hg4 ,in ,fig4 #b;d1 we have a view of the proportional breadth of the ,sun's face or disc1 as seen from the different ,planets4 ,the ,sun is represented ,no #a1 as seen from ,mercury2 ,no #b1 as seen from ,venus2 ,no #c1 as seen from the ,earth2 ,no #d1 as seen from ,mars2 ,no #e1 as seen from ,jupiter2 and ,no #f1 as seen from ,saturn4 ,sidenote3 ,fig4 ,,iii4 ,fig4 ,,iv4 ,let the circle ,b be the ,sun as seen from any ,planet1 at a given distance2 to another ,planet1 at double that distance1 the ,sun will appear just of half that breadth1 as ,a2 which contains only one fourth part of the area or surface of ,b4 ,for1 all circles1 as well as square surfaces1 are to one another as the squares of their diameters4 ,thus1 the square ,a is just half as broad as the square ,b2 and yet it is plain to sight1 that ,b contains four times as much surface as ,a4 ,hence1 in round numbers1 the ,sun appears #g times larger to ,mercury than to us1 #ij times larger to us than to ,saturn1 and #fcj times as large to ,mercury as to ,saturn4 ,sidenote3 ,fig4 ,v4 ,proportional bulks and distances of the ,planets4 ,,plate ,i4 #hh4 ,in ,fig4 #eth1 we have a view of the bulks of the ,planets in proportion to each other1 and to a supposed globe of two foot diameter for the ,sun4 ,the ,earth is #bg times as big as ,mercury1 very little bigger than ,venus1 #e times as big as ,mars2 but ,jupiter is #ajdi times as big as the ,earth1 ,saturn #ehf times as big1 exclusive of his ,ring2 and the ,sun is #hgg thousand #fej times as big as the ,earth4 ,if the ,planets in this ,figure were set at their due distances from a ,sun of two feet diameter1 according to their proportional bulks1 as in our ,system1 ,mercury would be #bh yards from the ,sun's center2 ,venus #ea yards #a foot2 the ,earth #gj yards #b feet2 ,mars #ajg yards #b feet2 ,jupiter #cgj yards #b feet2 and ,saturn #gfj yards two feet4 ,the ,comet of the year #afhj1 at it's greatest distance1 #aj thousand #gfj yards4 ,in this proportion1 the ,moon's distance from the center of the ,earth would be only #g-a_/b inches4 ,sidenote3 ,an idea of their distances4 #hi4 ,to assist the imagination in conceiving an idea of the vast distances of the ,sun1 ,planets1 and ,stars1 let us suppose1 that a body projected from the ,sun should continue to fly with the swiftness of a cannon ball2 i4 e4 #dhj miles every hour2 this body would reach the ,orbit of ,mercury1 in #g years #bba days2 of ,venus1 in #ad years #h days2 of the ,earth1 in #ai years #ia days2 of ,mars1 in #bi years #he days2 of ,jupiter1 in #ajj years #bhj days2 of ,saturn1 in #ahd years #bdj days2 to the ,comet of #afhj1 at it's greatest distance from the ,sun1 in #bffj years2 and to the nearest fixed ,stars in about #g million #fjj thousand years4 ,sidenote3 ,why the ,planets appear bigger and less at different times4 #ij4 ,as the ,earth is not the center of the ,orbits in which the ,planets move1 they come nearer to it and go farther from it and at different times2 on which account they appear bigger and less by turns4 ,hence1 the apparent magnitudes of the ,planets are not always a certain rule to know them by4 ,sidenote3 ,fig4 ,i4 #ia4 ,under ,fig4 #c1 are the names and characters of the twelve ,signs of the ,zodiac1 which the ,reader should be perfectly well acquainted with2 so as to know the characters without seeing the names4 ,every ,sign contains #cj degrees1 as in the ,circle bounding the ,solar ,system2 to which the characters of the ,signs are set in their proper places4 ,sidenote3 ,the ,comets4 #ib4 ,the ,,comets are solid opaque bodies1 with long transparent trains or tails1 issuing from that side which is turned away from the ,sun4 ,they move about the ,sun1 in very excentric ellipses2 and are of a much greater density than the ,earth2 for some of them are heated in every ,period to such a degree1 as would vitrify or dissipate any substance known to us4 ,sir ,,isaac ,,newton computed the heat of the ,comet which appeared in the year #afhj1 when nearest the ,sun1 to be #bjjj times hotter than red-hot iron1 and that being thus heated1 it must retain it's heat until it comes round again1 although it's ,period should be more than twenty thousand years2 and it is computed to be only #ege4 ,the method of computing the heat of bodies1 keeping at any known distance from the ,sun1 so far as their heat depends on the force of the ,sun's rays1 is very easy2 and shall be explained in the eighth ,chapter4 ,sidenote3 ,,plate ,i4 ,fig4 ,i4 ,they prove that the ,orbits of the ,planets are not solid4 ,the ,periods only of three are known4 ,they prove the ,stars to be at immense distances4 #ic4 ,part of the ,paths of three ,comets are delineated in the ,scheme of the ,solar ,system1 and the years marked in which they made their appearance4 ,it is believed1 that there are at least #ba ,comets belonging to our ,system1 moving in all sorts of directions3 and all those which have been observed1 have moved through the ethereal ,regions and the ,orbits of the ,planets without suffering the least sensible resistance in their motions2 which plainly proves that the ,planets do not move in solid ,orbs4 ,of all the ,comets1 the ,periods of the above-mentioned three only are known with any degree of certainty4 ,the first of these ,comets appeared in the years #aeca1 #afjg1 and #afhb2 and is expected to appear again in the year #ageh1 and every #geth year afterwards4 ,the second of them appeared in #aecb and #affa1 and may be expected to return in #aghi and every #abith year afterwards4 ,the third1 having last appeared in #afhj1 and it's ,period being no less than #ege years1 cannot return until the year #bbbe4 ,this ,comet1 at it's greatest distance1 is about #aa thousand two hundred millions of miles from the ,sun2 and at it's least distance from the ,sun's center1 which is #dij1jjj miles1 is within less than a third part of the ,sun's semi-diameter from his surface4 ,in that part of it's ,orbit which is nearest the ,sun1 it flies with the amazing swiftness of #hhj1jjj miles in an hour2 and the ,sun1 as seen from it1 appears an hundred degrees in breadth2 consequently1 #dj thousand times as large as he appears to us4 ,the astonishing length that this ,comet runs out into empty ,space1 suggests to our minds an idea of the vast distance between the ,sun and the nearest fixed ,stars2 of whose ,attractions all the ,comets must keep clear1 to return periodically1 and go round the ,sun2 and it shews us also1 that the nearest ,stars1 which are probably those that seem the largest1 are as big as our ,sun1 and of the same nature with him2 otherwise1 they could not appear so large and bright to us as they do at such an immense distance4 ,sidenote3 ,inferences drawn from the above phenomena4 #id4 ,the extreme heat1 the dense atmosphere1 the gross vapours1 the chaotic state of the ,comets1 seem at first sight to indicate them altogether unfit for the purposes of animal life1 and a most miserable habitation for rational beings3 and therefore #agsome are of opinion that they are so many hells for tormenting the damned with perpetual vicissitudes of heat and cold4 ,but1 when we consider1 on the other hand1 the infinite power and goodness of the ,deity2 the latter inclining1 and the former enabling him to make creatures suited to all states and circumstances2 that matter exists only for the sake of intelligence2 and that wherever we find it1 we always find it pregnant with life1 or necessarily subservient thereto2 the numberless species1 the astonishing diversity of animals in earth1 air1 water1 and even on other animals2 every blade of grass1 every tender leaf1 every natural fluid1 swarming with life2 and every one of these enjoying such gratifications as the nature and state of each requires3 when we reflect moreover that some centuries ago1 till experience undeceived us1 a great part of the ,earth was judged uninhabitable2 the ,torrid ,zone by reason of excessive heat1 and the two ,frigid ,zones because of their intollerable cold2 it seems highly probable1 that such numerous and large masses of durable matter as the ,comets are1 however unlike they be to our ,earth1 are not destitute of beings capable of contemplating with wonder1 and acknowledging with gratitude the wisdom1 symmetry1 and beauty of the ,creation2 which is more plainly to be observed in their extensive ,tour through the ,heavens1 than in our more confined ,circuit4 ,if farther conjecture is permitted1 may we not suppose them instrumental in recruiting the expended fuel of the ,sun2 and supplying the exhausted moisture of the ,planets8 ,however difficult it may be1 circumstanced as we are1 to find out their particular destination1 this is an undoubted truth1 that wherever the ,deity exerts his power1 there he also manifests his wisdom and goodness4 ,sidenote3 ,this ,system very ancient1 and demonstrable4 #ie4 ,,the ,,solar ,,system here described is not a late invention2 for it was known and taught by the wise ,samian philosopher ,,pythagoras1 and others among the ancients2 but in latter times was lost1 'till the #aeth century1 when it was again restored by the famous ,polish philosopher ,,nicholaus ,,copernicus1 who was born at ,thorn in the year #adgc4 ,in this1 he was followed by the greatest mathematicians and philosophers that have since lived2 as ,,kepler1 ,,galileo1 ,,descartes1 ,,gassendus1 and ,sir ,,isaac ,,newton2 the last of whom has established this ,system on such an everlasting foundation of mathematical and physical demonstration1 as can never be shaken3 and none who understand him can hesitate about it4 ,sidenote3 ,the ,ptolemean ,system absurd4 #if4 ,in the ,ptolemean ,system the ,earth was supposed to be fixed in the ,center of the ,universe2 and that the ,moon1 ,mercury1 ,venus1 the ,sun1 ,mars1 ,jupiter1 and ,saturn moved round the ,earth3 above the ,planets1 this ,hypothesis placed the ,firmament of ,stars1 and then the two ,crystalline ,spheres2 all which were included in and received motion from the ,primum ,mobile1 which constantly revolved about the ,earth in #bd hours1 from ,east to ,west4 ,but as this rude ,scheme was found incapable to stand the test of art and observation1 it was soon rejected by all true philosophers2 notwithstanding the opposition and violence of blind and zealous bigots4 ,sidenote3 ,the ,tychonic ,system1 partly true and partly false4 #ig4 ,the ,tychonic ,system succeeded the ,ptolemean1 but was never so generally received4 ,in this the ,earth was supposed to stand still in the ,center of the ,universe or ,firmament of ,stars1 and the ,sun to revolve about it every #bd hours2 the ,planets1 ,mercury1 ,venus1 ,mars1 ,jupiter1 and ,saturn1 going round the ,sun in the times already mentioned4 ,but some of ,,tycho's disciples supposed the ,earth to have a diurnal motion round it's ,axis1 and the ,sun with all the above ,planets to go round the ,earth in a year2 the ,planets moving round the ,sun in the foresaid times4 ,this hypothesis1 being partly true and partly false1 was embraced by few2 and soon gave way to the only true and rational ,system1 restored by ,,copernicus and demonstrated by ,sir ,,isaac ,,newton4 #ih4 ,to bring the foregoing particulars at once in view1 with several others which follow1 concerning the ,periods1 ,distances1 ,bulks1 c4 of the ,planets1 the following ,table is inserted4 ,a ,,table ,of the ,,periods1 ,,revolutions1 ,,magnitudes1 c4 of the ,,planets4 ---------------------------------------- ---------------------- ,sun and ,annual ,diurnal ,diameter ,mean ,mean distance ,planets4period rotation in diam4 asfrom the ,sun round on it's ,english seen fr4 in ,english the ,sun4 ,axis4 miles4 the ,sun4 miles4 ---------------------------------------- ---------------------- ,sun ---- #be;d4 #f;h4 #gfcjjj ---- ---- ,mercury #hg;d #bc;h,unknown4 #bfjj #bj #cb1jjj1jjj ,venus #bbd;d #ag;h#bd;d4 #h;h4 #gijf #cj #ei1jjj1jjj ,earth #cfe;d #f;h #a;d4 #j;h4 #gigj #ba #ha1jjj1jjj ,moon #cfe;d #f;h#bi;d4 #ab-c_/d;h4 #bahj #f #ha1jjj1jjj ,mars #fhf;d #bc;h#bd;h4 #djm4 #dddd #aa #abc1jjj1jjj ,jupiter #dccb;d #ab;h #i;h4 #efm4 #hajjj #cg #dbd1jjj1jjj ,saturn #ajgei;d #g;h,unknown4 #fgjjj #af #ggg1jjj1jjj ---------------------------------------- ---------------------- ---------------------------------------- ------------------------- ,sun and ,excentricity ,axis ,orbit ,place of ,place of ,proportion ,planets4 of it's inclinedinclined it's it's of ,orbit to to ,aphelion4,ascending,diameters4 in miles4 ,orbit4 ,ecliptic4 ,node4 ---------------------------------------- ------------------------- ,sun ---- #h #j ---- ---- ---- #ajjjj ,mercury #f1gbj1jjj ,unkn4 #f #ed #ac #h #ad #dc #cd-a_/aj ,venus #dac1jjj #ge #j #c #bj #d #bj #ac #ei #ajc-a_/b ,earth #a1cgg1jjj #bc #bi #j #j #h #a ---- #ajd-a_/b ,moon #ac1jjj #b #aj #e #h ---- ,variable4 #bh-a_/b ,mars #aa1dci1jjj #j #j #a #eb #j #cb #ag #ag #eh-a_/f ,jupiter #bj1ceb1jjj #j #j #a #bj #i #aj #g #biajfa-b_/c ,saturn #db1gce1jjj ,unkn4 #b #cj #bg #ej #ba #ac #hgh-a_/i ---------------------------------------- ------------------------- ---------------------------------------- ----------------------------- ,sun and ,proportion,prop4 of,proportion,proportion,propor4 ,hourly ,hourly ,planets4of ,gravity of of quantitymotion motion ,bulk4 on the ,density4 ,light of in it'sof it's surface4 ,heat4 ,matter4 ,orbit4 ,equator4 ---------------------------------------- ----------------------------- ,sun #hggfej #bd #be-a_/b #dejjj #bbgejj ---- #chah ,mercury #a_/bg ,unkn4 ,unkn4 #f-a_/b ,unkn4 #iejjj ,unkn4 ,venus #a ,unkn4 ,unkn4 #a-c_/d ,unkn4 #fijjj #dc ,earth #a #a #ajj #a #a #ehjjj #ajdb ,moon #a_/ej #cd_/ajj #abc-a_/b #a #a_/dj #bbij #i-a_/b ,mars #a_/e ,unkn4 ,unkn4 #c_/g ,unkn4 #dgjjj #eef ,jupiter #ajdi #b #ai #a_/bh #bbj #bejjj #beibj ,saturn #ehf #a-a_/b #ae #a_/ij #id #ahjjj ,unkn4 ---------------------------------------- ----------------------------- ---------------------------------------- ----------------------- ,sun and ,square miles in ,cubic miles in solidity4,would fall to ,planets4 surface4 the ,sun in ---------------------------------------- ----------------------- ,sun #a1hbh1iaa1jjj1jjjbcb1egg1aae1acg1jjj1jj j days h4 ,mercury #ba1bcf1hjj #i1aie1ecd1ejj #ae #ac ,venus #fia1cfa1cjj #beh1ejg1hcb1bjj #ci #ag ,earth #aii1heb1hfj #bfe1djd1eih1jhj #ad #aj ,moon #ad1hih1gej #e1djh1bdf1jjj #fd #aj ,mars #fb1jch1bdj #de1ifi1cce1hdj #aba #j ,jupiter #bj1fjc1igj1jjj #bgh1aec1eie1jjj1jjj #bij #j ,saturn #ad1ajb1efb1jjj #aee1abh1ahb1jjj1jjj #gfg #j ,if the projectile force was destroyed4 ---------------------------------------- ----------------------- ,if the ,moon's projectile force was destroyed1 she would fall to the ,earth in #d days #ba hours4 ---------------------------------------- ------ ,jupiter's,periods round ,saturn's,periods round ,moons4 ,jupiter4 ,moons4 ,saturn4 ---------------------------------------- ------ ,no ,d4 ,h4 ,m4 ,no ,d4 ,h4 ,m4 ---------------------------------------- ------ #a #a #ah #cf #a #a #ba #ai #b #c #ac #ae #b #b #ag #dj #c #g #c #ei #c #d #ab #be #d #af #ah #cj #d #ae #bb #da ----------------------- #e #gi #g #dh ----------------------- ,,chap4 ,,iii4 ,the ,,copernican ,,system demonstrated to be true4 ,sidenote3 ,of matter and motion4 #ii4 ,matter is of itself inactive1 and indifferent to motion or rest4 ,a body at rest can never put itself in motion2 a body in motion can never stop nor move slower of itself4 ,hence1 when we see a body in motion we conclude some other substance must have given it that motion2 when we see a body fall from motion to rest we conclude some other body or cause stopt it4 #ajj4 ,all motion is naturally rectilineal4 ,a bullet thrown by the hand1 or discharged from a cannon would continue to move in the same direction it received at first1 if no other power diverted its course4 ,therefore1 when we see a body moving in a curve of whatever kind1 we conclude it must be acted upon by two powers at least3 one to put it in motion1 and another drawing it off from the rectilineal course which it would otherwise have continued to move in4 ,sidenote3 ,gravity demonstrable4 #aja4 ,the power by which bodies fall towards the ,earth is called ,gravity or ,attraction4 ,by this power in the ,earth it is1 that all bodies1 on whatever side1 fall in lines perpendicular to it's surface4 ,on opposite parts of the ,earth bodies fall in opposite directions1 all towards the centre where the force of gravity is as it were accumulated4 ,by this power constantly acting on bodies near the ,earth they are kept from leaving it altogether2 and those on its surface are kept thereto on all sides1 so that they cannot fall from it4 ,bodies thrown with any obliquity are drawn by this power from a straight line into a curve1 until they fall to the ,ground3 the greater the force by which they are thrown1 the greater is the distance they are carried before they fall4 ,if we suppose a body carried several miles above the ,earth1 and there projected in an horizontal direction1 with so great a velocity that it would move more than a semidiameter of the ,earth1 in the time it would take to fall to the ,earth by gravity2 in that case1 if there were no resisting medium in the way1 the body would not fall to the ,earth at all2 but continue to circulate round the ,earth1 keeping always the same path1 and returning to the point from whence it was projected1 with the same velocity as at first4 ,sidenote3 ,projectile force demonstrable4 #ajb4 ,we find the ,moon moves round the ,earth in an ,orbit nearly circular4 ,the ,moon therefore must be acted on by two powers or forces2 one which would cause her to move in a right line1 another bending her motion from that line into a curve4 ,this attractive power must be seated in the ,earth2 for there is no other body within the ,moon's ,orbit to draw her4 ,the attractive power of the ,earth therefore extends to the ,moon2 and1 in combination with her projectile force1 causes her to move round the ,earth in the same manner as the circulating body above supposed4 ,sidenote3 ,the ,sun and ,planets attract each other4 #ajc4 ,the ,moons of ,jupiter and ,saturn are observed to move round their primary ,planets3 therefore there is such a power as gravity in these ,planets4 ,all the ,planets move round the ,sun1 and respect it for their centre of motion3 therefore the ,sun must be endowed with attracting force1 as well as the ,earth and ,planets4 ,the like may be proved of the ,comets4 ,so that all the bodies or matter in the ,solar ,system are possessed of this power2 and perhaps so is all matter whatsoever4 #ajd4 ,as the ,sun attracts the ,planets with their ,satellites1 and the ,earth the ,moon1 so the ,planets and ,satellites re-attract the ,sun1 and the ,moon the ,earth3 action and re-action being always equal4 ,this is also confirmed by observation2 for the ,moon raises tides in the ocean1 the ,satellites and ,planets disturb one another's motions4 #aje4 ,every particle of matter being possessed of an attracting power1 the effect of the whole must be in proportion to the number of attracting particles3 that is1 to the quantity of matter in the body4 ,this is demonstrated from experiments on pendulums3 for1 if they are of equal lengths1 whatever their weights be1 they always vibrate in equal times4 ,now1 if one be double the weight of another1 the force of gravity or attraction must be double to make it oscillate with the same celerity3 if one is thrice the weight or quantity of matter of another1 it requires thrice the force of gravity to make it move with the same celerity4 ,hence it is certain1 that the power of gravity is always proportional to the quantity of matter in bodies1 whatever their bulks or figures are4 #ajf4 ,gravity also1 like all other virtues or emanations issuing from a centre1 decreases as the square of the distance increases3 that is1 a body at twice the distance attracts another with only a fourth part of the force2 at four times the distance1 with a sixteenth part of the force4 ,this too is confirmed from observation1 by comparing the distance which the ,moon falls in a minute from a right line touching her ,orbit1 with the space which bodies near the ,earth fall in the same time3 and also by comparing the forces which retain ,jupiter's ,moons in their ,orbits4 ,this will be more fully explained in the seventh ,chapter4 ,sidenote3 ,gravitation and projection exemplified4 #ajg4 ,the mutual attraction of bodies may be exemplified by a boat and a ship on the ,water1 tied by a rope4 ,let a man either in ship or boat pull the rope 7it is the same in effect at which end he pulls1 for the rope will be equally stretched throughout17 the ship and boat will be drawn towards one another2 but with this difference1 that the boat will move as much faster than the ship as the ship is heavier than the boat4 ,suppose the boat as heavy as the ship1 and they will draw one another equally 7setting aside the greater resistance of the ,water on the bigger body7 and meet in the middle of the first distance between them4 ,if the ship is a thousand or ten thousand times heavier than the boat1 the boat will be drawn a thousand or ten thousand times faster than the ship2 and meet proportionably nearer the place from which the ship set out4 ,now1 whilst one man pulls the rope1 endeavouring to bring the ship and boat together1 let another man1 in the boat1 endeavour to row her off sidewise1 or at right ,angles to the rope2 and the former1 instead of being able to draw the boat to the ship1 will find it enough for him to keep the boat from going further off2 whilst the latter1 endeavouring to row off the boat in a straight line1 will1 by means of the other's pulling it towards the ship1 row the boat round the ship at the rope's length from her4 ,here1 the power employed to draw the ship and boat to one another represents the mutual attraction of the ,sun and ,planets1 by which the ,planets would fall freely towards the ,sun with a quick motion2 and would also in falling attract the ,sun towards them4 ,and the power employed to row off the boat represents the projectile force impressed on the ,planets at right ,angles1 or nearly so1 to the ,sun's attraction2 by which means the ,planets move round the ,sun1 and are kept from falling to it4 ,on the other hand1 if it be attempted to make a heavy ship go round a light boat1 they will meet sooner than the ship can get round2 or the ship will drag the boat after it4 #ajh4 ,let the above principles be applied to the ,sun and ,earth2 and they will evince1 beyond a possibility of doubt1 that the ,sun1 not the ,earth1 is the center of the ,system2 and that the ,earth moves round the ,sun as the other ,planets do4 ,sidenote3 ,the absurdity of supposing the ,earth at rest4 ,for1 if the ,sun moves about the ,earth1 the ,earth's attractive power must draw the ,sun towards it from the line of projection so1 as to bend it's motion into a curve2 and the ,earth being at least #afi thousand times lighter than the ,sun1 by being so much less as to it's quantity of matter1 must move #afi thousand times faster toward the ,sun than the ,sun does toward the ,earth2 and consequently would fall to the ,sun in a short time if it had not a very strong projectile motion to carry it off4 ,the ,earth therefore1 as well as every other ,planet in the ,system1 must have a rectilineal impulse to prevent its falling into the ,sun4 ,to say1 that gravitation retains all the other ,planets in their ,orbits without affecting the ,earth1 which is placed between the ,orbits of ,mars and ,venus1 is as absurd as to suppose that six cannon bullets might be projected upwards to different heights in the ,air1 and that five of them should fall down to the ground2 but the sixth1 which is neither the highest nor the lowest1 should remain suspended in the ,air without falling2 and the ,earth move round about it4 #aji4 ,there is no such thing in nature as a heavy body moving round a light one as its centre of motion4 ,a pebble fastened to a mill-stone by a string1 may by an easy impulse be made to circulate round the mill-stone3 but no impulse can make a mill-stone circulate round a loose pebble1 for the heaviest would undoubtedly carry the lightest along with it wherever it goes4 #aaj4 ,the ,sun is so immensely bigger and heavier than the ,earth#ah1 that if he was moved out of his place1 not only the ,earth1 but all the other ,planets if they were united into one mass1 would be carried along with the ,sun as the pebble would be with the mill-stone4 ,sidenote3 ,the harmony of the celestial motions4 ,the absurdity of supposing the ,stars and ,planets to move round the ,earth4 #aaa4 ,by considering the law of gravitation1 which takes place throughout the ,solar ,system1 in another light1 it will be evident that the ,earth moves round the ,sun in a year2 and not the ,sun round the ,earth4 ,it has been shewn 7 #ajf7 that the power of gravity decreases as the square of the distance increases3 and from this it follows with mathematical certainty1 that when two or more bodies move round another as their centre of motion1 the squares of their periodic times will be to one another in the same proportion as the cubes of their distances from the central body4 ,this holds precisely with regard to the ,planets round the ,sun1 and the ,satellites round the ,planets2 the relative distances of all which1 are well known4 ,but1 if we suppose the ,sun to move round the ,earth1 and compare its period with the ,moon's by the above rule1 it will be found that the ,sun would take no less than #agc1eaj days to move round the ,earth1 in which case our year would be #dge times as long as it now is4 ,to this we may add1 that the aspects of increase and decrease of the ,planets1 the times of their seeming to stand still1 and to move direct and retrograde1 answer precisely to the ,earth's motion2 but not at all to the ,sun's without introducing the most absurd and monstrous suppositions1 which would destroy all harmony1 order1 and simplicity in the ,system4 ,moreover1 if the ,earth is supposed to stand still1 and the ,stars to revolve in free spaces about the ,earth in #bd hours1 it is certain that the forces by which the ,stars revolve in their ,orbits are not directed to the ,earth1 but to the centres of the several ,orbits3 that is1 of the several parallel ,circles which the ,stars on different sides of the ,equator describe every day3 and the like inferences may be drawn from the supposed diurnal motion of the ,planets1 since they are never in the ,equinoctial but twice1 in their courses with regard to the starry ,heavens4 ,but1 that forces should be directed to no central body1 on which they physically depend1 but to innumerable imaginary points in the axe of the ,earth produced to the ,poles of the ,heavens1 is an hypothesis too absurd to be allowed of by any rational creature4 ,and it is still more absurd to imagine that these forces should increase exactly in proportion to the distances from this axe2 for this is an indication of an increase to infinity3 whereas the force of attraction is found to decrease in receding from the fountain from whence it flows4 ,but1 the farther that any ,star is from the quiescent ,pole the greater must be the ,orbit which it describes2 and yet it appears to go round in the same time as the nearest ,star to the ,pole does4 ,and if we take into consideration the two-fold motion observed in the ,stars1 one diurnal round the ,axis of the ,earth in #bd hours1 and the other round the ,axis of the ,ecliptic in #beibj years #bea1 it would require an explication of such a perplexed composition of forces1 as could by no means be reconciled with any physical ,theory4 ,sidenote3 ,objections against the ,earth's motion answered4 #aab4 ,there is but one objection of any weight that can be made to the ,earth's motion round the ,sun2 which is1 that in opposite points of the ,earth's ,orbit1 it's ,axis which always keeps a parallel direction would point to different fixed ,stars2 which is not found to be fact4 ,but this objection is easily removed by considering the immense distance of the ,stars in respect of the diameter of the ,earth's ,orbit2 the latter being no more than a point when compared to the former4 ,if we lay a ruler on the side of a table1 and along the edge of the ruler view the top of a spire at ten miles distance2 then lay the ruler on the opposite side of the table in a parallel situation to what it had before1 and the spire will still appear along the edge of the ruler2 because our eyes1 even when assisted by the best instruments are incapable of distinguishing so small a change4 #aac4 ,dr4 ,,bradley1 our present ,astronomer ,royal1 has found by a long series of the most accurate observations1 that there is a small apparent motion of the fixed ,stars1 occasioned by the aberration of their light1 and so exactly answering to an annual motion of the ,earth1 as evinces the same1 even to a mathematical demonstration4 ,those who are qualified to read the ,doctor's modest ,account of this great discovery may consult the ,philosophical ,transactions1 ,no #djf4 ,or they may find it treated of at large by ,drs4 ,,smith#ai1 ,,long#bj1 ,,desaguliers#ba1 ,,rutherfurth1 ,mr4 ,,maclaurin#bb1 and ,m4 ,,de ,,la ,,caille#bc4 ,sidenote3 ,why the ,sun appears to change his place4 #aad4 ,it is true that the ,sun seems to change his place daily1 so as to make a tour round the starry ,heavens in a year4 ,but whether the ,earth or ,sun moves1 this appearance will be the same2 for1 when the ,earth is in any part of the ,heavens1 the ,sun will appear in the opposite4 ,and therefore1 this appearance can be no objection against the motion of the ,earth4 #aae4 ,it is well known to every person who has sailed on smooth ,water1 or been carried by a stream in a calm1 that however fast the vessel goes he does not feel its progressive motion4 ,the motion of the ,earth is incomparably more smooth and uniform than that of a ship1 or any machine made and moved by human art3 and therefore it is not to be imagined that we can feel it's motion4 ,sidenote3 ,the ,earth's motion on it's ,axis demonstrated4 #aaf4 ,we find that the ,sun1 and those ,planets on which there are visible spots1 turn round their ,axes3 for the spots move regularly over their ,disks#bd4 ,from hence we may reasonably conclude that the other ,planets on which we see no spots1 and the ,earth which is likewise a ,planet1 have such rotations4 ,but being incapable of leaving the ,earth1 and viewing it at a distance2 and it's rotation being smooth and uniform1 we can neither see it move on it's ,axis as we do the ,planets1 nor feel ourselves affected by it's motion4 ,yet there is one effect of such a motion which will enable us to judge with certainty whether the ,earth revolves on it's ,axis or not4 ,all ,globes which do not turn round their ,axes will be perfect spheres1 on account of the equality of the weight of bodies on their surfaces2 especially of the fluid parts4 ,but all ,globes which turn on their ,axes will be oblate spheroids2 that is1 their surfaces will be higher1 or farther from the centre1 in the equatoreal than in the polar ,regions3 for1 as the equatoreal parts move quickest1 they will recede farther from the ,axis of motion1 and enlarge the equatoreal diameter4 ,that our ,earth is really of this figure is demonstrable from the unequal vibrations of a pendulum1 and the unequal lengths of degrees in different latitudes4 ,since then1 the ,earth is higher at the ,equator than at the ,poles1 the sea1 which naturally runs downward1 or towards the places which are nearest the centre1 would run towards the polar ,regions1 and leave the equatoreal parts dry1 if the centrifugal force of these parts did not raise and carry the waters thither4 ,the ,earth's equatoreal diameter is #ce miles longer than its ,axis4 ,sidenote3 ,all bodies heavier at the ,poles than they would be at the ,equator4 #aag4 ,bodies near the ,poles are heavier than those towards the ,equator1 because they are nearer the ,earth's centre1 where the whole force of the ,earth's attraction is accumulated4 ,they are also heavier because their centrifugal force is less on account of their diurnal motion being slower4 ,for both these reasons1 bodies carried from the ,poles toward the ,equator1 gradually lose of their weight4 ,experiments prove that a pendulum1 which vibrates seconds near the ,poles vibrates slower near the ,equator1 which shews that it is lighter or less attracted there4 ,to make it oscillate in the same time1 'tis found necessary to diminish it's length4 ,by comparing the different lengths of pendulums swinging seconds at the ,equator and at ,london1 it is found that a pendulum must be #b-afi_/ajjj lines shorter at the ,equator than at the ,poles4 ,a line is a twelfth part of an inch4 ,sidenote3 ,how they might lose all their weight4 #aah4 ,if the ,earth turned round it's ,axis in #hd minutes #dc seconds1 the centrifugal force would be equal to the power of gravity at the ,equator2 and all bodies there would entirely lose their weight4 ,if the ,earth revolved quicker they would all fly off1 and leave it4 ,sidenote3 ,the ,earth's motion cannot be felt4 #aai4 ,one on the ,earth can no more be sensible of it's undisturbed motion on it's ,axis1 than one in the cabin of a ship on smooth ,water can be sensible of her motion when she turns gently and uniformly round4 ,it is therefore no argument against the ,earth's diurnal motion that we do not feel it3 nor is the apparent revolutions of the celestial bodies every day a proof of the reality of these motions2 for whether we or they revolve1 the appearance is the very same4 ,a person looking through the cabin windows of a ship as strongly fancies the objects on land to go round when the ship turns1 as if they were actually in motion4 ,sidenote3 ,to the different ,planets the ,heavens appear to turn round on different ,axes4 #abj4 ,if we could translate ourselves from ,planet to ,planet1 we should still find that the ,stars would appear of the same magnitudes1 and at the same distances from each other1 as they do to us here2 because the width of the remotest ,planet's ,orbit bears no sensible proportion to the distance of the ,stars4 ,but then1 the ,heavens would seem to revolve about very different ,axes2 and consequently1 those quiescent ,points which are our ,poles in the ,heavens would seem to revolve about other points1 which1 though apparently in motion to us on ,earth would be at rest as seen from any other ,planet4 ,thus1 the ,axis of ,venus1 which lies almost at right ,angles to the ,axis of the ,earth1 would have it's motionless ,poles in two opposite points of the ,heavens lying almost in our ,equinoctial1 where the motion appears quickest because it is performed in the greatest ,circle4 ,and the very ,poles1 which are at rest to us1 have the quickest motion of all as seen from ,venus4 ,to ,mars and ,jupiter the ,heavens appear to turn round with very different velocities on the same ,axis1 whose ,poles are about #bc-a_/b degrees from ours4 ,were we on ,jupiter we should be at first amazed at the rapid motion of the ,heavens2 the ,sun and ,stars going round in #i hours #ef minutes4 ,could we go from thence to ,venus we should be as much surprised at the slowness of the heavenly motions3 the ,sun going but once round in #ehd hours1 and the ,stars in #edj4 ,and could we go from ,venus to the ,moon we should see the ,heavens turn round with a yet slower motion2 the ,sun in #gjh hours1 the ,stars in #fee4 ,as it is impossible these various circumvolutions in such different times and on such different ,axes can be real1 so it is unreasonable to suppose the ,heavens to revolve about our ,earth more than it does about any other ,planet4 ,when we reflect on the vast distance of the fixed ,stars1 to which #afb1jjj1jjj of miles is but a point1 we are filled with amazement at the immensity of their distance4 ,but if we try to frame an idea of the extreme rapidity with which the ,stars must move1 if they move round the ,earth in #bd hours1 the thought becomes so much too big for our imagination1 that we can no more conceive it than we do infinity or eternity4 ,if the ,sun was to go round the ,earth in a day1 he must travel upwards of #cjj1jjj miles in a minute3 but the ,stars being at least #aj1jjj times as far as the ,sun from us1 those about the ,equator must move #aj1jjj times as quick4 ,and all this to serve no other purpose than what can be as fully and much more simply obtained by the ,earth's turning round eastward as on an ,axis1 every #bd hours1 causing thereby an apparent diurnal motion of the ,sun westward1 and bringing about the alternate returns of day and night4 ,illustration3 ,pl4 ,,ii4 ,sidenote3 ,objections against the ,earth's diurnal motion answered4 #aba4 ,as to the common objections against the ,earth's motion on it's ,axis1 they are all easily answered and set aside4 ,that it may turn without being seen or felt to do so1 has been already shewn1 #aai4 ,but some are apt to imagine that if the ,earth turns eastward 7as it certainly does if it turns at all7 a ball fired perpendicularly upward in the air must fall considerably westward of the place it was projected from4 ,this objection1 which at first seems to have some weight1 will be found to have none at all when we consider that the gun and ball partake of the ,earth's motion2 and therefore the ball being carried forward with the air as quick as the ,earth and air turn1 must fall down again on the same place4 ,a stone let fall from the top of a main-mast1 if it meets with no obstacle1 falls on the deck as near the foot of the mast when the ship sails as when it does not4 ,and if an inverted bottle1 full of liquor1 be hung up to the cieling of the cabin1 and a small hole be made in the cork to let the liquor drop through on the floor1 the drops will fall just as far forward on the floor when the ship sails as when it is at rest4 ,and gnats or flies can as easily dance among one another in a moving cabin as in a fixed chamber4 ,as for those scripture expressions which seem to contradict the ,earth's motion1 this general answer may be made to them all1 viz4 'tis plain from many instances that the ,scriptures were never intended to instruct us in ,philosophy or ,astronomy2 and therefore1 on those subjects1 expressions are not always to be taken in the strictest sense2 but for the most part as accommodated to the common apprehensions of mankind4 ,men of sense in all ages1 when not treating of the sciences purposely1 have followed this method3 and it would be in vain to follow any other in addressing ourselves to the vulgar1 or bulk of any community4 ,moses calls the ,moon ,a ,,great ,,luminary 7as it is in the ,hebrew7 as well as the ,sun3 but the ,moon is known to be an opaque body1 and the smallest that ,astronomers have observed in the ,heavens and shines upon us not by any inherent light of it's own1 but by reflecting the light of the ,sun4 ,if ,moses had known this1 and told the ,israelites so1 they would have stared at him2 and considered him rather as a madman than as a person commissioned by the ,almighty to be their leader4 ,,chap4 ,,iv4 ,the ,phenomena of the ,heavens as seen from different parts of the ,earth4 ,sidenote3 ,we are kept to the ,earth by gravity4 ,,plate ,,ii4 ,fig4 ,i4 ,antipodes4 ,axis of the ,world4 ,it's ,poles4 ,fig4 ,,ii4 #abb4 ,we are kept to the ,earth's surface on all sides by the power of it's central attraction2 which1 laying hold of all bodies according to their densities or quantities of matter without regard to their bulks1 constitutes what we call their weight4 ,and having the sky over our heads1 go where we will1 and our feet towards the centre of the ,earth1 we call it up over our heads1 and down under our feet3 although the same right line which is down to us1 if continued through and beyond the opposite side of the ,earth1 would be up to the inhabitants on the opposite side4 ,for1 the inhabitants n1 i1 e1 m1 s1 o1 q1 l stand with their feet toward the ,earth's centre ,c2 and have the same figure of sky ,n1 l1 ,e1 ,m1 ,s1 ,o1 ,q1 ,l over their heads4 ,therefore1 the point ,s is as directly upward to the inhabitant s on the south ,pole as ,n is to the inhabitant n on the ,north ,pole3 so is ,e to the inhabitant e1 supposed to be on the north end of ,peru2 and ,q to the opposite inhabitant q on the middle of the island ,sumatra4 ,each of these observers is surprised that his opposite or ,antipode can stand with his head hanging downwards4 ,but let either go to the other1 and he will tell him that he stood as upright and firm on the place where he was as he now stands where he is4 ,to all these observers the ,sun1 ,moon1 and ,stars seem to turn round the points ,n and ,s as the ,poles of the fixed ,axis ,,ncs2 because the ,earth does really turn round the mathematical line n,cs as round an ,axis of which n is the ,north ,pole and s the ,south ,pole4 ,the ,inhabitant ,u 7,fig4 ,,ii47 affirms that he is on the uppermost side of the ,earth1 and wonders how another at ,l can stand on the undermost side with his head hanging downwards4 ,but ,u in the mean time forgets that in twelve hours time he will be carried half round with the ,earth2 and then be in the very situation that ,l now is1 although as far from him as before4 ,and yet1 when ,u comes there1 he will find no difference as to his manner of standing2 only he will see the opposite half of the ,heavens1 and imagine the ,heavens to have gone half round him4 ,sidenote3 ,how our ,earth might have an upper and an under side4 #abc4 ,when we see a globe hung up in a room we cannot help imagining it to have an upper and an under side1 and immediately form a like idea of the ,earth2 from whence we conclude1 that it is as impossible for persons to stand on the under side of the ,earth as for pebbles to lie on the under side of a common ,globe1 which instantly fall down from it to the ground2 and well they may1 because the attraction of the ,earth1 being too strong for the attraction of the ,globe1 pulls them away4 ,just so would be the case with our ,earth1 if it were placed near a ,globe much bigger than itself1 such as ,jupiter3 for then it would really have an upper and an under side with respect to that large ,globe2 which1 by it's ,attraction1 would pull away every thing from the side of the ,earth next to it2 and only those on the top of the opposite or upper side could keep upon it4 ,but there is no larger ,globe near enough our ,earth to overcome it's central attraction2 and therefore it has no such thing as an upper and an under side3 for all bodies on or near it's surface1 even to the ,moon1 gravitate towards it's center4 ,sidenote3 ,,plate ,,ii4 #abd4 ,let any man imagine that the ,earth and every thing but himself is taken away1 and he left alone in the midst of indefinite ,space2 he could then have no idea of up or down2 and were his pockets full of gold1 he might take the pieces one by one1 and throw them away on all sides of him1 without any danger of losing them2 for the attraction of his body would bring them all back by the ways they went1 and he would be down to every one of them4 ,but then1 if a ,sun or any other large body were created1 and placed in any part of ,space several millions of miles from him1 he would be attracted towards it1 and could not save himself from falling down to it4 ,sidenote3 ,fig4 ,i4 ,one half of the ,heavens visible to an inhabitant on any part of the ,earth4 ,phenomena at the ,poles4 ,,plate ,,ii4 #abe4 ,the ,earth's bulk is but a point1 as that at ,c1 compared to the ,heavens2 and therefore every inhabitant upon it1 let him be where he will1 as at n1 e1 m1 s1 c4 sees one half of the ,heavens4 ,the inhabitant n1 on the ,north ,pole of the ,earth1 constantly sees the ,hemisphere ,,enq2 and having the ,north ,pole ,n of the ,heavens just over his head1 his #be;,horizon coincides with the ,celestial ,equator ,,ecq4 ,therefore all the ,stars in the ,northern ,hemisphere ,,enc1 between the ,equator and ,north ,pole1 appear to turn round the line ,,nc1 moving parallel to the ,horizon4 ,the ,equatoreal ,stars keep in the ,horizon1 and all those in the ,southern ,hemisphere ,,esq are invisible4 ,the like ,phenomena are seen by the observer s on the ,south ,pole1 with respect to the ,hemisphere ,,esq2 and to him the opposite ,hemisphere is always invisible4 ,hence1 under either ,pole1 only one half of the ,heavens is seen2 for those parts which are once visible never set1 and those which are once invisible never rise4 ,but the ,ecliptic ,,ycx or ,orbit which the ,sun appears to describe once a year by the ,earth's annual motion1 has the half ,,yc constantly above the ,horizon ,,ecq of the ,north ,pole n2 and the other half ,,cx always below it4 ,therefore whilst the ,sun describes the northern half ,,yc of the ,ecliptic he neither sets to the ,north ,pole nor rises to the ,south2 and whilst he describes the southern half ,,cx he neither sets to the ,south ,pole nor rises to the ,north4 ,the same things are true with respect to the ,moon2 only with this difference1 that as the ,sun describes the ,ecliptic but once a year1 he is for half that time visible to each ,pole in it's turn1 and as long invisible2 but as the ,moon goes round the ,ecliptic in #bg days #h hours1 she is only visible for #ac days #af hours1 and as long invisible to each ,pole by turns4 ,all the ,planets likewise rise and set to the ,poles1 because their ,orbits are cut obliquely in halves by the ,horizon of the ,poles4 ,when the ,sun 7in his apparent way from ,x7 arrives at ,c1 which is on the #bjth of ,march1 he is just rising to an observer at n on the ,north ,pole1 and setting to another at s on the ,south ,pole4 ,from ,c he rises higher and higher in every apparent ,diurnal revolution 'till he comes to the highest point of the ,ecliptic y1 on the #bast of ,june1 and then he is at his greatest ,altitude1 which is #bc-a_/b degrees1 or the ,arc ,ey1 equal to his greatest ,north declination2 and from thence he seems to descend gradually in every apparent ,circumvolution1 'till he sets at ,c on the #bc;d of ,september2 and then he goes to exhibit the like ,appearances at the ,south ,pole for the other half of the year4 ,hence the ,sun's apparent motion round the ,earth is not in parallel ,circles1 but in ,spirals2 such as might be represented by a thread wound round a ,globe from ,tropic to ,tropic2 the ,spirals being at some distance from one another about the ,equator1 but gradually nearer to each other as they approach nearer to the ,tropics4 ,sidenote3 ,phenomena at the ,equator4 ,fig4 ,i4 #abf4 ,if the observer be any where on the ,terrestrial ,equator e,cq1 as suppose at e1 he is in the ,plane of the ,celestial ,equator2 or under the ,equinoctial ,,ecq2 and the ,axis of the ,earth n,cs is coincident with the ,plane of his ,horizon1 extended out to ,n and ,s1 the ,north and ,south ,poles of the ,heavens4 ,as the ,earth turns round the line ,,ncs1 the whole ,heavens ,m,o,ll seem to turn round the same line1 but the contrary way4 ,it is plain that this observer has the ,poles constantly in his ,horizon1 and that his ,horizon cuts the ,diurnal paths of all the ,celestial bodies perpendicularly and in halves4 ,therefore the ,sun1 ,planets1 and ,stars rise every day1 and ascend perpendicularly above the ,horizon for six hours1 and passing over the ,meridian1 descend in the same manner for the six following hours2 then set in the ,horizon1 and continue twelve hours below it4 ,consequently at the ,equator the days and nights are equally long throughout the year4 ,when the observer is in the situation e1 he sees the ,hemisphere ,,sen2 but in twelve hours after1 he is carried half round the ,earth's ,axis to q1 and then the ,hemisphere ,,sqn becomes visible to him2 and ,,sen disappears1 being hid by the ,convexity of the ,earth4 ,thus we find that to an observer at either of the ,poles one half of the ,sky is always visible1 and the other half never seen2 but to an observer on the ,equator the whole ,sky is seen every #bd hours4 ,the ,figure here referred to1 represents a ,celestial globe of glass1 having a ,terrestrial globe within it2 after the manner of the ,glass ,sphere invented by my generous friend ,dr4 ,,long1 ,lowndes's ,professor of ,astronomy in ,cambridge4 ,sidenote3 ,remark4 #abg4 ,if a ,globe be held sidewise to the eye1 at some distance1 and so that neither of it's ,poles can be seen1 the ,equator ,,ecq and all ,circles parallel to it1 as ,,dl1 yzx1 ab,x1 ,,mo1 c4 will appear to be straight lines1 as projected in this ,figure2 which is requisite to be mentioned here1 because we shall have occasion to call them ,circles in the following ,article#bf4 ,sidenote3 ,phenomena between the ,equator and ,poles4 ,the ,circles of perpetual ,apparition and ,occultation4 #abh4 ,let us now suppose that the observer has gone from the ,equator e towards the ,north ,pole n1 and that he stops at i1 from which place he then sees the ,hemisphere ,m,el,n,l2 his ,horizon ,,mcl having shifted as many #bg;,degrees from the ,celestial poles ,n and ,s as he has travelled from under the ,equinoctial ,e4 ,and as the ,heavens seem constantly to turn round the line ,,ncs as an ,axis1 all those ,stars which are as far from the ,north ,pole ,n as the observer is from under1 the ,equinoctial1 namely the ,stars north of the dotted parallel ,,dl1 never set below the ,horizon2 and those which are south of the dotted parallel ,,mo never rise above it4 ,hence1 the former of these two parallel ,circles is called the ,circle of perpetual ,apparition1 and the latter the ,circle of perpetual ,occultation3 but all the ,stars between these two ,circles rise and set every day4 ,let us imagine many ,circles to be drawn between these two1 and parallel to them2 those which are on the north side of the ,equinoctial will be unequally cut by the ,horizon ,,mcl1 having larger portions above the ,horizon than below it2 and the more so1 as they are nearer to the ,circle of perpetual ,apparition2 but the reverse happens to those on the south side of the ,equinoctial1 whilst the ,equinoctial is divided in two equal parts by the ,horizon4 ,hence1 by the apparent turning of the ,heavens1 the northern ,stars describe greater ,arcs or ,portions of ,circles above the ,horizon than below it2 and the greater as they are farther from the ,equinoctial towards the ,circle of perpetual ,apparition2 whilst the contrary happens to all ,stars south of the ,equinoctial3 but those upon it describe equal ,arcs both above and below the ,horizon1 and therefore they are just as long above as below it4 ,sidenote3 ,,plate ,,ii4 #abi4 ,an observer on the ,equator has no ,circle of perpetual ,apparition or ,occultation1 because all the ,stars1 together with the ,sun and ,moon1 rise and set to him every day4 ,but1 as a bare view of the ,figure is sufficient to shew that these two ,circles ,,dl and ,,mo are just as far from the ,poles ,n and ,s as the observer at i 7or one opposite to him at o7 is from the ,equator ,,ecq2 it is plain1 that if an observer begins to travel from the ,equator towards either ,pole1 his ,circle of perpetual ,apparition rises from that ,pole as from a ,point1 and his ,circle of perpetual ,occultation from the other4 ,as the observer advances toward the nearer ,pole1 these two ,circles enlarge their diameters1 and come nearer one another1 until he comes to the ,pole2 and then they meet and coincide in the ,equator4 ,on different sides of the ,equator1 to observers at equal distances from it1 the ,circle of perpetual ,apparition to one is the ,circle of perpetual ,occultation to the other4 ,sidenote3 ,why the ,stars always describe the same parallel of motion1 and the ,sun a different4 #acj4 ,because the ,stars never vary their distances from the ,equinoctial1 so as to be sensible in an age1 the lengths of their diurnal and nocturnal ,arcs are always the same to the same places on the ,earth4 ,but as the ,earth goes round the ,sun every year in the ,ecliptic1 one half of which is on the north side of the ,equinoctial and the other half on it's south side1 the ,sun appears to change his place every day1 so as to go once round the ,circle ,,ycx every year #aad4 ,therefore whilst the ,sun appears to advance northward1 from having described the ,parallel ab,x touching the ,ecliptic in ,x the days continually lengthen and the nights shorten1 until he comes to y and describes the ,parallel yzx1 when the days are at the longest and the nights at the shortest3 for then1 as the ,sun goes no farther northward1 the greatest portion that is possible of the diurnal ,arc yz is above the ,horizon of the inhabitant i2 and the smallest portion zx below it4 ,as the ,sun declines southward from y he describes smaller diurnal and greater nocturnal ,arcs1 or ,portions of ,circles1 every day2 which causeth the days to shorten and nights to lengthen1 until he arrives again at the ,parallel ab,x2 which having only the small part ab above the ,horizon ,,mcl1 and the great part b,x below it1 the days are at the shortest and the nights at the longest2 because the ,sun recedes no farther south1 but returns northward as before4 ,it is easy to see that the ,sun must be in the ,equinoctial ,,ecq twice every year1 and then the days and nights are equally long2 that is1 #ab hours each4 ,these hints serve at present to give an idea of some of the ,appearances resulting from the motions of the ,earth2 which will be more particularly described in the tenth ,chapter4 ,sidenote3 ,fig4 ,i4 ,parallel1 ,oblique1 and ,right sphere1 what4 #aca4 ,to an observer at either ,pole1 the ,horizon and ,equinoctial are coincident2 and the ,sun and ,stars seem to move parallel to the ,horizon3 therefore1 such an observer is said to have a ,parallel position of the ,sphere4 ,to an observer any where between the ,poles and ,equator1 the ,parallels described by the ,sun and ,stars are cut obliquely by the ,horizon1 and therefore he is said to have an ,oblique position of the ,sphere4 ,to an observer any where on the ,equator1 the ,parallels of ,motion1 described by the ,sun and ,stars are cut perpendicularly1 or at ,right angles1 by the ,horizon2 and therefore he is said to have a ,right position of the ,sphere4 ,and these three are all the different ways that the ,sphere can be posited to all people1 on the ,earth4 ,,chap4 ,v4 ,the ,phenomena of the ,heavens as seen from different ,parts of the ,solar ,system4 #acb4 ,so vastly great is the distance of the starry ,heavens1 that if viewed from any part of the ,solar ,system1 or even many millions of miles beyond it1 its appearance would be the very same to us4 ,the ,sun and ,stars would all seem to be fixed on one concave surface1 of which the ,spectator's eye would be the centre4 ,but the ,planets1 being much nearer than the ,stars1 their appearances will vary considerably with the place from which they are viewed4 #acc4 ,if the spectator is at rest without their ,orbits1 the ,planets will seem to be at the same distance as the ,stars2 but continually changing their places with respect to the ,stars1 and to one another3 assuming various phases of increase and decrease like the ,moon4 ,and1 notwithstanding their regular motions about the ,sun1 will sometimes appear to move quicker1 sometimes slower1 be as often to the west as to the east of the ,sun2 and at their greatest distances seem quite stationary4 ,the duration1 extent1 and points in the ,heavens where these digressions begin and end1 would be more or less according to the respective distances of the several ,planets from the ,sun3 but in the same ,planet they would continue invariably the same at all times2 like pendulums of unequal lengths oscillating together1 the shorter move quick and go over a small space1 the longer move slow and go over a large space4 ,if the observer is at rest within the ,orbits of the ,planets1 but not near the common center1 their apparent motions will be irregular1 but less so than in the former case4 ,each of the several ,planets will appear bigger and less by turns1 as they approach nearer or recede farther from the observer2 the nearest varying most in their size4 ,they will also move quicker or slower with regard to the fixed ,stars1 but will never be retrograde or stationary4 #acd4 ,next1 let a spectator in motion view the ,heavens3 the same apparent irregularities will be observed1 but with some variation resulting from his own motion4 ,if he is on a ,planet which has a rotation on it's ,axis1 not being sensible of his own motion he will imagine the whole ,heavens1 ,sun1 ,planets1 and ,stars to revolve about him in the same time that his ,planet turns round1 but the contrary way2 and will not be easily convinced of the deception4 ,if his ,planet moves round the ,sun1 the same irregularities and aspects as above will appear in the motions of the ,planets3 only1 the times of their being direct1 stationary and retrograde will be accelerated or retarded as they concur with1 or are contrary to his motion3 and the ,sun will seem to move among the fixed ,stars or ,signs1 directly opposite to those in which his ,planet moves2 changing it's place every day as he does4 ,in a word1 whether our observer be in motion or at rest1 whether within or without the ,orbits of the ,planets1 their motions will seem irregular1 intricate and perplexed1 unless he is in the center of the ,system2 and from thence1 the most beautiful order and harmony will be observed4 ,sidenote3 ,the ,sun's center the only point from which the true motions and places of the ,planets could be seen4 #ace4 ,the ,sun being the center of all the ,planets motions1 the only place from which their motions could be truly seen1 is the ,sun's center2 where the observer being supposed not to turn round with the ,sun 7which1 in this case1 we must imagine to be a transparent body7 would see all the ,stars at rest1 and seemingly equidistant from him4 ,to such an observer the ,planets would appear to move among the fixed ,stars1 in a simple1 regular1 and uniform manner2 only1 that as in equal times they describe equal ,areas1 they would describe spaces somewhat unequal1 because they move in elliptic ,orbits #aee4 ,their motions would also appear to be what they are in fact1 the same way round the ,heavens2 in paths which cross at small ,angles in different parts of the ,heavens1 and then separate a little from one another #bj4 ,so that1 if the solar ,astronomer should make the ,path or ,orbit of any one ,planet a standard1 and consider it as having no obliquity #bja1 he would judge the paths of all the rest to be inclined to it2 each ,planet having one half of it's path on one side1 and the other half on the opposite side of the standard ,path or ,orbit4 ,and if he should ever see all the ,planets start from a conjunction with each other#bh2 ,mercury would move so much faster than ,venus as to overtake her again 7though not in the same point of the ,heavens7 in a quantity of time almost equal to #ade of our days and nights2 or1 as we commonly call them1 ,natural ,days1 which include both the days and nights3 ,venus would move so much faster than the ,earth as to overtake it again in #ehe natural days3 the ,earth so much faster than ,mars as to overtake him again in #ggh such days3 ,mars is much faster than ,jupiter as to overtake him again in #hag such days3 and ,jupiter so much faster than ,saturn as to overtake him again in #gbcf days1 all of our time4 ,sidenote3 ,the judgment that a solar ,astronomer would probably make concerning the distances and bulks of the ,planets4 #acf4 ,but as our solar ,astronomer could have no idea of measuring the courses of the ,planets by our days1 he would very probably take the period of ,mercury1 which is the quickest moving ,planet1 for a measure to compare the periods of the others by4 ,as all the ,stars would appear quiescent to him1 he would never think that they had any dependance upon the ,sun2 but could naturally imagine that the ,planets have1 because they move round the ,sun4 ,and it is by no means improbable1 that he would conclude those ,planets whose periods are quickest to move in ,orbits proportionably less than those do which make slower circuits4 ,but being destitute of a method for finding their ,parallaxes1 or1 more properly speaking1 as they could have no ,parallax to him1 he could never know any thing of their real distances or magnitudes4 ,their relative distances he might perhaps guess at by their periods1 and from thence infer something of truth concerning their relative bulks1 by comparing their apparent bulks with one another4 ,for example1 ,jupiter appearing bigger to him than ,mars1 he would conclude it to be much bigger in fact2 because it appears so1 and must be farther from him1 on account of it's longer period4 ,mercury would seem bigger than the ,earth2 but by comparing it's period with the ,earth's1 he would conclude that the ,earth is much farther from him than ,mercury1 and consequently that it must be really bigger though apparently less2 and so of the rest4 ,and1 as each ,planet would appear somewhat bigger in one part of it's ,orbit than in the opposite1 and to move quickest when it seems biggest1 the observer would be at no loss to determine that all the ,planets move in ,orbits of which the ,sun is not precisely in the center4 ,sidenote3 ,the ,planetary motions very irregular as seen from the ,earth4 ,,plate ,,iii4 #acg4 ,the apparent magnitudes of the ,planets continually change as seen from the ,earth1 which demonstrates that they approach nearer to it1 and recede farther from it by turns4 ,from these ,phenomena1 and their apparent motions among the ,stars1 they seem to describe looped curves which never return into themselves1 ,venus's path excepted4 ,and if we were to trace out all their apparent paths1 and put the figures of them together in one diagram1 they would appear so anomalous and confused1 that no man in his senses could believe them to be representations of their real paths2 but would immediately conclude1 that such apparent irregularities must be owing to some ,optic illusions4 ,and after a good deal of enquiry1 he might perhaps be at a loss to find out the true cause of these inequalities2 especially if he were one of those who would rather1 with the greatest justice1 charge frail man with ignorance1 than the ,almighty with being the author of such confusion4 ,sidenote3 ,those of ,mercury and ,venus represented4 ,fig4 ,i4 #ach4 ,dr4 ,,long1 in his first volume of ,astronomy1 has given us figures of the apparent paths of all the ,planets separately from ,,cassini2 and on seeing them ,i first thought of attempting to trace some of them by a machine#bi that shews the motions of the ,sun1 ,mercury1 ,venus1 the ,earth and ,moon1 according to the ,copernican ,system4 ,having taken off the ,sun1 ,mercury1 and ,venus1 ,i put black-lead pencils in their places1 with the points turned upward2 and fixed a circular sheet of paste-board so1 that the ,earth kept constantly under it's center in going round the ,sun2 and the paste-board kept its parallelism4 ,then1 pressing gently with one hand upon the paste-board to make it touch the three pencils1 with the other hand ,i turned the winch which moves the whole machinery3 and as the ,earth1 together with the pencils in the places of ,mercury and ,venus1 had their proper motions round the ,sun's pencil1 which kept at rest in the center of the machine1 all the three pencils described a diagram from which the first ,figure of the third ,plate is truly copied in a smaller size4 ,as the ,earth moved round the ,sun1 the ,sun's pencil described the dotted ,circle of ,months1 whilst ,mercury's pencil drew the curve with the greatest number of loops1 and ,venus's that with the fewest4 ,in their inferiour conjunctions they come as much nearer the ,earth1 or within the ,circle of the ,sun's apparent motion round the ,heavens1 as they go beyond it in their superiour conjunctions4 ,on each side of the loops they appear ,stationary2 in that part of each loop next the ,earth retrograde2 and in all rest of their paths direct4 ,illustration3 ,plate ,,iii4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sc4 ,sidenote3 ,,plate ,,iii4 ,if ,cassini's ,figures of the paths of the ,sun1 ,mercury and ,venus were put together1 the ,figure as above traced out1 would be exactly like them4 ,it represents the ,sun's apparent motion round the ,ecliptic1 which is the same every year2 ,mercury's motion for seven years2 and ,venus's for eight2 in which time ,mercury's path makes #bc loops1 crossing itself so many times1 and ,venus's only five4 ,in eight years ,venus falls so nearly into the same apparent path again1 as to deviate very little from it in some ages2 but in what number of years ,mercury and the rest of the ,planets would describe the same visible paths over again1 ,i cannot at present determine4 ,having finished the above ,figure of the paths of ,mercury and ,venus1 ,i put the ,ecliptic round them as in the ,doctor's ,book2 and added the dotted lines from the ,earth to the ,ecliptic for shewing ,mercury's apparent or geocentric motion therein for one year2 in which time his path makes three loops1 and goes on a little farther2 which shews that he has three inferiour1 and as many superiour conjunctions with the ,sun in that time1 and also that he is six times ,stationary1 and thrice ,retrograde4 ,let us now trace out his motion for one year in the ,figure4 ,sidenote3 ,fig4 ,i4 ,suppose ,mercury to be setting out from ,a towards ,b 7between the ,earth and left-hand corner of the ,plate7 and as seen from the ,earth his motion will then be direct1 or according to the order of the ,signs4 ,but when he comes to ,b1 he appears to stand still in the #bc;d degree of at ,f1 as shewn by the line ,,bf4 ,whilst he goes from ,b to ,c1 the line ,,bf goes backward from ,f to ,e1 or contrary to the order of ,signs2 and when he is at ,c he appears ,stationary at ,e2 having gone back #aa-a_/b degrees4 ,now1 suppose him ,stationary on the first of ,january at ,c1 on the tenth thereof he will appear in the ,heavens as at #bj1 near ,f2 on the #bjth he will be seen as at ,g2 on the #cast at ,h2 on the #ajth of ,february at ,i2 on the #bjth at ,k2 and on the #bhth at ,l2 as the dotted lines shew1 which are drawn through every tenth day's motion in his looped path1 and continued to the ,ecliptic4 ,on the #ajth of ,march he appears at ,m2 on the #bjth at ,n2 and on the #cast at ,o4 ,on the #ajth of ,april he appears ,stationary at ,p2 on the #bjth he seems to have gone back again to ,o2 and on the #cjth he appears ,stationary at ,q having gone back #aa-a_/b degrees4 ,thus ,mercury seems to go forward #d ,signs #aa ,degrees1 or #aca ,degrees2 and to go back only #aa or #ab ,degrees1 at a mean rate4 ,from the #cjth of ,april to the #ajth of ,may1 he seems to move from ,q to ,r2 and on the #bjth he is seen at ,s1 going forward in the same manner again1 according to the order of letters2 and backward when they go back2 which1 'tis needless to explain any farther1 as the reader can trace him out so easily through the rest of the year4 ,the same appearances happen in ,venus's motion2 but as she moves slower than ,mercury1 there are longer intervals of time between them4 ,having already #abj4 given some account of the apparent diurnal motions of the ,heavens as seen from the different ,planets1 we shall not trouble the reader any more with that subject4 ,,chap4 ,,vi4 ,the ,ptolemean ,system refuted4 ,the ,motions and ,phases of ,mercury and ,venus explained4 #aci4 ,the ,tychonic ,system #ig1 being sufficiently refuted by the #ajith ,article1 we shall say nothing more about it4 #adj4 ,the ,ptolemean ,system #if1 which asserts the ,earth to be at rest in the ,center of the ,universe1 and all the ,planets with the ,sun and ,stars to move round it1 is evidently false and absurd4 ,for if this hypothesis were true1 ,mercury and ,venus could never be hid behind the ,sun1 as their ,orbits are included within the ,sun's3 and again1 these two ,planets would always move direct1 and be as often in ,opposition to the ,sun as in ,conjunction with him4 ,but the contrary of all this is true3 for they are just as often behind the ,sun as before him1 appear as often to move backwards as forwards1 and are so far from being seen at any time in the side of the ,heavens opposite to the ,sun1 that they were never seen a quarter of a circle in the ,heavens distant from him4 ,sidenote3 ,appearances of ,mercury and ,venus4 #ada4 ,these two ,planets1 when viewed with a good telescope1 appear in all the various shapes of the ,moon2 which is a plain proof that they are enlightened by the ,sun1 and shine not by any light of their own3 for if they did1 they would constantly appear round as the ,sun does2 and could never be seen like dark spots upon the ,sun when they pass directly between him and us4 ,their regular ,phases demonstrate them to be ,spherical bodies2 as may be shewn by the following experiment4 ,sidenote3 ,experiment to prove they are round4 ,hang an ivory ball by a thread1 and let any ,person move it round the flame of a candle1 at two or three yards distance from your ,eye3 when the ball is beyond the candle1 so as to be almost hid by the flame1 it's enlightened side will be towards you1 and appear round like the ,full ,moon3 ,when the ball is between you and the candle1 it's enlightened side will disappear1 as the ,moon does at the ,change3 ,when it is half way between these two positions1 it will appear half illuminated1 like the ,moon in her ,quarters3 ,but in every other place between these positions1 it will appear more or less horned or gibbous4 ,if this experiment be made with a circular plate which has a flat surface1 you may make it appear fully enlightened1 or not enlightened at all2 but can never make it seem either horned or gibbous4 ,sidenote3 ,,plate ,,ii4 ,experiment to represent the motions of ,mercury and ,venus4 #adb4 ,if you remove about six or seven yards from the candle1 and place yourself so that it's flame may be just about the height of your eye1 and then desire the other person to move the ball slowly round the candle as before1 keeping it as near of an equal height with the flame as he possibly can1 the ball will appear to you not to move in a circle1 but rather to vibrate backward and forward like a pendulum2 moving quickest when it is directly between you and the candle1 and when directly beyond it2 and gradually slower as it goes farther to the right or left side of the flame1 until it appears at the greatest distance from the flame2 and then1 though it continues to move with the same velocity1 it will seem to stand still for a moment4 ,in every ,revolution it will shew all the above ,phases #ada2 and if two balls1 a smaller and a greater1 be moved in this manner round the candle1 the smaller ball being kept nearest the flame1 and carried round almost three times as often as the greater1 you will have a tolerably good representation of the apparent ,motions of ,mercury and ,venus2 especially1 if the bigger ball describes a circle almost twice as large in diameter as the circle described by the lesser4 ,sidenote3 ,fig4 ,,iii4 ,the elongations or digressions of ,mercury from the ,sun4 ,,plate ,,ii4 #adc4 ,let ,,abcde be a part or segment of the visible ,heavens1 in which the ,sun1 ,moon1 ,planets1 and ,stars appear to move at the same distance from the ,earth ,e4 ,for there are certain limits1 beyond which the eye cannot judge of different distances2 as is plain from the ,moon's appearing to be no nearer to us than the ,sun and ,stars are4 ,let the circle fghiklmno be the ,orbit in which ,mercury m moves round the ,sun ,s1 according to the order of the letters4 ,when ,mercury is at f1 he disappears to the ,earth at ,e1 because his enlightened side is turned from it2 unless he be then in one of his ,nodes #bj1 #be2 in which case1 he will appear like a dark spot upon the ,sun4 ,when he is at g in his ,orbit1 he appears at ,b in the ,heavens1 westward of the ,sun ,s1 which is seen at ,c3 when at h1 he appears at ,a1 at his greatest western elongation or distance from the ,sun2 and then seems to stand still4 ,but1 as he moves from h to i1 he appears to go from ,a to ,b2 and seems to be in the same place when at i as when he was at g1 only not near so big3 at k he is hid from the ,earth ,e by the ,sun ,s2 being then in his superiour ,conjunction4 ,in going from k to l1 he appears to move from ,c to ,d2 and when he is at n1 he appears stationary at ,e2 being seen as far east from the ,sun then1 as he was west from him at ,a4 ,in going from n to o in his ,orbit1 he seems to go back again in the ,heavens1 from ,e to ,d2 and is seen in the same place 7with respect to the ,sun7 at o as when he was at l2 but of a larger diameter at o1 because he is then nearer the ,earth ,e3 and when he comes to f1 he again passes by the ,sun1 and disappears as before4 ,in going from n to h in his ,orbit1 he seems to go backward in the ,heavens from ,e to ,a2 and in going from h to n1 he seems to go forward from ,a to ,e4 ,as he goes on from f a little of his enlightened side at g is seen from ,e2 at h he appears half full1 because half of his enlightened side is seen2 at i1 gibbous1 or more than half full2 and at k he would appear quite full1 were he not hid from the ,earth ,e by the ,sun ,s4 ,at l he appears gibbous again2 at n half decreased1 at o horned1 and at f new like the ,moon at her ,change4 ,he goes sooner from his eastern station at n to his western station at h than from h to n again2 because he goes through less than half his ,orbit in the former case1 and more in the latter4 ,sidenote3 ,fig4 ,,iii4 ,the ,elongations and ,phases of ,venus4 ,the greatest ,elongations of ,mercury and ,venus4 #add4 ,in the same ,figure1 let ,,fghiklmn be the ,orbit in which ,venus v moves round the ,sun ,s1 according to the order of the letters3 and let ,e be the ,earth as before4 ,when ,venus is at ,f she is in her inferiour ,conjunction2 and disappears like the ,new ,moon because her dark side is toward the ,earth4 ,at ,g she appears half enlightened to the ,earth1 like the ,moon in her first quarter3 at h she appears gibbous2 at ,i1 almost full2 her enlightened side being then nearly towards the ,earth3 at ,k1 she would appear quite full to the ,earth ,e2 but is hid from it by the ,sun ,s3 at ,l1 she appears upon the decrease1 or gibbous2 at ,m1 more so2 at ,n1 only half enlightened2 and at ,f she disappears again4 ,in moving from ,n to ,g1 she seems to go backward in the ,heavens2 and from ,g to ,n1 forward3 but1 as she describes a much greater portion of her ,orbit in going from ,g to ,n than from ,n to ,g1 she appears much longer direct than retrograde in her motion4 ,at ,n and ,g she appears stationary2 as ,mercury does at n and h4 ,mercury1 when stationary seems to be only #bh degrees from the ,sun2 and ,venus when so1 #dg2 which is a demonstration that ,mercury's ,orbit is included within ,venus's1 and ,venus's within the ,earth's4 ,sidenote3 ,morning and ,evening ,star1 what4 #ade4 ,venus1 from her superiour ,conjunction at ,k to her inferiour ,conjunction at ,f is seen on the east side of the ,sun ,s from the ,earth4 ,e2 and therefore she shines in the ,evening after the ,sun sets1 and is called the ,evening ,star3 for1 the ,sun being then to the westward of ,venus1 he must set first4 ,from her inferiour ,conjunction to her superiour1 she appears on the west side of the ,sun2 and therefore rises before him1 for which reason she is called the ,morning ,star4 ,when she is about ,n or ,g1 she shines so bright1 that bodies cast shadows in the night-time4 ,sidenote3 ,,plate ,,ii4 ,the stationary places of the ,planets variable4 #adf4 ,if the ,earth kept always at ,e1 it is evident that the ,stationary places of ,mercury and ,venus would always be in the same points of the ,heavens where they were before4 ,for example2 whilst ,mercury m goes from h to n1 according to the order of the letters1 he appears to describe the arc ,,abcde in the ,heavens1 direct3 and whilst he goes from n to h1 he seems to describe the same arc back again1 from ,e to ,a1 retrograde3 always at n and h he appears stationary at the same points ,e and ,a as before4 ,but ,mercury goes round his ,orbit1 from f to f again1 in #hh days2 and yet there are #aaf days from any one of his ,conjunctions1 or apparent ,stations1 to the same again3 and the places of these ,conjunctions and ,stations are found to be about #aad degrees eastward from the points of the ,heavens where they were last before2 which proves1 that the ,earth has not kept all that time at ,e1 but has had a progressive motion in it's ,orbit from ,e to t4 ,venus also differs every time in the places of her ,conjunctions and ,stations2 but much more than ,mercury2 because1 as ,venus describes a much larger ,orbit than ,mercury does1 the ,earth advances so much the farther in it's annual path before ,venus comes round again4 ,sidenote3 ,the ,elongations of all ,saturn's inferiour ,planets as seen from him4 #adg4 ,as ,mercury and ,venus1 seen from the ,earth1 have their respective ,elongations from the ,sun1 and ,stationary places2 so has the ,earth1 seen from ,mars2 and ,mars1 seen from ,jupiter2 and ,jupiter1 seen from ,saturn4 ,that is1 to every superiour ,planet1 all the inferiour ones have their ,stations and ,elongations2 as ,venus and ,mercury have to the ,earth4 ,as seen from ,saturn1 ,mercury never goes above #b-a_/b degrees from the ,sun2 ,venus #d-a_/c2 the ,earth #f2 ,mars #i-a_/b2 and ,jupiter #cc-a_/d3 so that ,mercury1 as seen from the ,earth1 has almost as great a ,digression or ,elongation from the ,sun1 as ,jupiter seen from ,saturn4 ,sidenote3 ,a proof of the ,earth's annual motion4 #adh4 ,because the ,earth's ,orbit is included within the ,orbits of ,mars1 ,jupiter1 and ,saturn1 they are seen on all sides of the ,heavens2 and are as often in ,opposition to the ,sun as in ,conjunction with him4 ,if the ,earth stood still1 they would always appear direct in their motions1 never retrograde nor stationary4 ,but they seem to go just as often backward as forward2 which1 if gravity be allowed to exist1 affords a sufficient proof of the ,earth's annual motion4 ,sidenote3 ,fig4 ,,iii4 ,,plate ,,ii4 ,general ,phenomena of a superiour ,planet to an inferiour4 #adi4 ,as ,venus and the ,earth are superiour ,planets to ,mercury1 they shew much the same ,appearances to him that ,mars and ,jupiter do to us4 ,let ,mercury m be at f1 ,venus v at ,f1 and the ,earth at ,e2 in which situation ,venus hides the ,earth from ,mercury2 but1 being in opposition to the ,sun1 she shines on ,mercury with a full illumined ,orb2 though1 with respect to the ,earth1 she is in conjunction with the ,sun and invisible4 ,when ,mercury is at f1 and ,venus at ,g1 her enlightened side not being directly towards him1 she appears a little gibbous2 as ,mars does in a like situation to us3 but1 when ,venus is at ,i1 her enlightened side is so much towards ,mercury at f1 that she appears to him almost of a round figure4 ,at ,k1 ,venus disappears to ,mercury at f1 being then hid by the ,sun2 as all our superiour ,planets are to us1 when in conjunction with the ,sun4 ,when ,venus has1 as it were1 emerged out of the ,sun beams1 as at ,l1 she appears almost full to ,mercury at f2 at ,m and ,n1 a little gibbous2 quite full at ,f1 and largest of all2 being then in opposition to the ,sun1 and consequently nearest to ,mercury at f2 shining strongly on him in the night1 because her distance from him then is somewhat less than a fifth part of her distance from the ,earth1 when she appears roundest to it between ,i and ,k1 or between ,k and ,l1 as seen from the ,earth ,e4 ,consequently1 when ,venus is opposite to the ,sun as seen from ,mercury1 she appears more than #be times as large to him as she does to us when at the fullest4 ,our case is almost similar with respect to ,mars1 when he is opposite to the ,sun2 because he is then so near the ,earth1 and has his whole enlightened side towards it4 ,but1 because the ,orbits of ,jupiter and ,saturn are very large in proportion to the ,earth's1 these two ,planets appear much less magnified at their ,oppositions or diminished at their ,conjunctions than ,mars does1 in proportion to their mean apparent ,diameters4 ,,chap4 ,,vii4 ,the physical ,causes of the ,motions of the ,planets4 ,the ,excentricities of their ,orbits4 ,the ,times in which the ,action of ,gravity would bring them to the ,sun4 ,,archimedes's ideal ,problem for moving the ,earth4 ,the ,world not eternal4 ,sidenote3 ,gravitation and ,projection4 ,fig4 ,,iv4 ,,plate ,,ii4 ,circular ,orbits4 ,fig4 ,,iv4 #aej4 ,from the uniform projectile motion of bodies in straight lines1 and the universal power of attraction1 arises the curvilineal motions of all the ,heavenly bodies4 ,if the body ,a be projected along the right line ,,abx1 in open ,space1 where it meets with no resistance1 and is not drawn aside by any other power1 it will for ever go on with the same velocity1 and in the same direction4 ,for1 the force which moves it from ,a to ,b in any given time1 will carry it from ,b to ,x in as much more time2 and so on1 there being nothing to obstruct or alter it's motion4 ,but if1 when this projectile force has carried it1 suppose to ,b1 the body ,s begins to attract it1 with a power duly adjusted1 and perpendicular to it's motion at ,b1 it will then be drawn from the straight line ,,abx1 and forced to revolve about ,s in the ,circle ,,bytu4 ,when the body ,a comes to ,u1 or any other part of it's ,orbit1 if the small body u1 within the sphere of ,u's attraction1 be projected as in the right line ,z1 with a force perpendicular to the attraction of ,u1 then u will go round ,u in the ,orbit ,w1 and accompany it in it's whole course round the body ,s4 ,here1 ,s may represent the ,sun1 ,u the ,earth1 and u the ,moon4 #aea4 ,if a ,planet at ,b gravitates1 or is attracted1 toward the ,sun1 so as to fall from ,b to y in the time that the projectile force would have carried it from ,b to ,x1 it will describe the curve ,,by by the combined action of these two forces1 in the same time that the projectile force singly would have carried it from ,b to ,x1 or the gravitating power singly have caused it to descend from ,b to y2 and these two forces being duly proportioned1 and perpendicular to one another1 the ,planet obeying them both1 will move in the circle ,,bytu#cj4 ,sidenote3 ,elliptical ,orbits4 ,,plate ,,ii4 #aeb4 ,but if1 whilst the projectile force carries the ,planet from ,b to b1 the ,sun's attraction 7which constitutes the ,planet's gravitation7 should bring it down from ,b to ,i1 the gravitating power would then be too strong for the projectile force2 and would cause the ,planet to describe the curve ,,bc4 ,when the ,planet comes to ,c1 the gravitating power 7which always increases as the square of the distance from the ,sun ,s diminishes7 will be yet stronger for the projectile force2 and by conspiring in some degree therewith1 will accelerate the ,planet's motion all the way from ,c to ,k2 causing it to describe the arcs ,,bc1 ,,cd1 ,,de1 ,,ef1 c4 all in equal times4 ,having it's motion thus accelerated1 it gains so much centrifugal force1 or tendency to fly off at ,k in the line ,kk1 as overcomes the ,sun's attraction3 and the centrifugal force being too great to allow the ,planet to be brought nearer the ,sun1 or even to move round him in the ,circle ,klmn1 c4 it goes off1 and ascends in the curve ,,klmn1 c4 it's motion decreasing as gradually from ,k to ,b as it increased from ,b to ,k1 because the ,sun's attraction acts now against the ,planet's projectile motion just as much as it acted with it before4 ,when the ,planet has got round to ,b1 it's projectile force is as much diminished from it's mean state about ,g or ,n1 as it was augmented at ,k2 and so1 the ,sun's attraction being more than sufficient to keep the ,planet from going off at ,b1 it describes the same ,orbit over again1 by virtue of the same forces or laws4 ,sidenote3 ,fig4 ,,iv4 ,the ,planets describe equal ,areas in equal times4 #aec4 ,a double projectile force will always balance a quadruple power of gravity4 ,let the ,planet at ,b have twice as great an impulse from thence towards ,x1 as it had before3 that is1 in the same length of time that it was projected from ,b to b1 as in the last example1 let it now be projected from ,b to c2 and it will require four times as much gravity to retain it in it's ,orbit3 that is1 it must fall as far as from ,b to #d in the time that the projectile force would carry it from ,b to c2 otherwise it could not describe the curve ,,bd1 as is evident by the ,figure4 ,but1 in as much time as the ,planet moves from ,b to ,c in the higher part of it's ,orbit1 it moves from ,i to ,k or from ,k to ,l in the lower part thereof2 because1 from the joint action of these two forces1 it must always describe equal areas in equal times1 throughout it's annual course4 ,these ,areas are represented by the triangles ,,bsc1 ,,csd1 ,,dse1 ,,esf1 c4 whose contents are equal to one another1 quite round the ,figure4 ,sidenote3 ,a difficulty removed4 #aed4 ,as the ,planets approach nearer the ,sun1 and recede farther from him1 in every ,revolution2 there may be some difficulty in conceiving the reason why the power of gravity1 when it once gets the better of the projectile force1 does not bring the ,planets nearer and nearer the ,sun in every ,revolution1 till they fall upon and unite with him4 ,or why the projectile force1 when it once gets the better of gravity1 does not carry the ,planets farther and farther from the ,sun1 till it removes them quite out of the sphere of his attraction1 and causes them to go on in straight lines for ever afterward4 ,but by considering the effects of these powers as described in the two last ,articles1 this difficulty will be removed4 ,suppose a ,planet at ,b to be carried by the projectile force as far as from ,b to b1 in the time that gravity would have brought it down from ,b to #a3 by these two forces it will describe the curve ,,bc4 ,when the ,planet comes down to ,k1 it will be but half as far from the ,sun ,s as it was at ,b2 and therefore1 by gravitating four times as strongly towards him1 it would fall from ,k to ,v in the same length of time that it would have fallen from ,b to #a in the higher part of it's ,orbit1 that is1 through four times as much space2 but it's projectile force is then so much increased at ,k1 as would carry it from ,k to k in the same time2 being double of what it was at ,b1 and is therefore too strong for the tendency of the gravitating power1 either to draw the ,planet to the ,sun1 or cause it to go round him in the circle ,klmn1 c4 which would require it's falling from ,k to w1 through a greater space than gravity can draw it whilst the projectile force is such as would carry it from ,k to k3 and therefore the ,planet ascends in it's ,orbit ,,klmn1 decreasing in it's velocity for the cause already assigned in #aeb4 ,sidenote3 ,the ,planetary ,orbits elliptical4 ,their ,excentricities4 #aee4 ,the ,orbits of all the ,planets are ,ellipses1 very little different from ,circles3 but the ,orbits of the ,comets are very long ,ellipses2 the lower focus of them all being in the ,sun4 ,if we suppose the mean distance 7or middle between the greatest and least7 of every ,planet and ,comet from the ,sun to be divided into #ajjj equal parts1 the ,excentricities of their ,orbits1 both in such parts and in ,english miles1 will be as follows4 ,mercury's1 #baj parts1 or #f1gbj1jjj miles2 ,venus's1 #g parts1 or #dac1jjj miles2 the ,earth's1 #ag parts1 or #a1cgg1jjj miles2 ,mars's1 #ic parts1 or #aa1dci1jjj miles2 ,jupiter's1 #dh parts1 or #bj1ceb1jjj miles2 ,saturn's1 #ee parts1 or #db1gce1jjj miles4 ,of the nearest of the three forementioned ,comets1 #a1deh1jjj miles2 of the middlemost1 #b1jbe1jjj1jjj miles2 and of the outermost1 #f1fjj1jjj1jjj4 ,sidenote3 ,the above laws sufficient for motions both in circular and elliptic ,orbits4 #aef4 ,by the above-mentioned laws #aej seq4 bodies will move in all kinds of ,ellipses1 whether long or short1 if the spaces they move in be void of resistance4 ,only1 those which move in the longer ,ellipses1 have so much the less projectile force impressed upon them in the higher parts of their ,orbits2 and their velocities1 in coming down towards the ,sun1 are so prodigiously increased by his attraction1 that their centrifugal forces in the lower parts of their ,orbits are so great as to overcome the ,sun's attraction there1 and cause them to ascend again towards the higher parts of their ,orbits2 during which time1 the ,sun's attraction acting so contrary to the motions of those bodies1 causes them to move slower and slower1 until their projectile forces are diminished almost to nothing2 and then they are brought back again by the ,sun's attraction1 as before4 ,sidenote3 ,in what times the ,planets would fall to the ,sun by the power of gravity4 #aeg4 ,if the projectile forces of all the ,planets and ,comets were destroyed at their mean distances from the ,sun1 their gravities would bring them down so1 as that ,mercury would fall to the ,sun in #ae days #ac hours2 ,venus in #ci days #ag hours2 the ,earth or ,moon in #fd days #aj hours2 ,mars in #aba days2 ,jupiter in #bij2 and ,saturn in #gfg4 ,the nearest ,comet in #ac thousand days2 the middlemost in #bc thousand days2 and the outermost in #ff thousand days4 ,the ,moon would fall to the ,earth in #d days #bj hours2 ,jupiter's first ,moon would fall to him in #g hours1 his second in #ae1 his third in #cj1 and his fourth in #ga hours4 ,saturn's first ,moon would fall to him in #h hours2 his second in #ab1 his third in #ai1 his fourth in #fh hours1 and the fifth in #ccf4 ,a stone would fall to the ,earth's center1 if there were an hollow passage1 in #ba minutes #i seconds4 ,mr4 ,,whiston gives the following ,rule for such ,computations4 8#ca;,it is demonstrable1 that half the ,period of any ,planet1 when it is diminished in the sesquialteral proportion of the number #a to the number #b1 or nearly in the proportion of #ajjj to #bhbh1 is the time that it would fall to the ,center of it's ,orbit40 ,this proportion is1 when a quantity or number contains another once and a half as much more4 ,sidenote3 ,the prodigious attraction of the ,sun and ,planets4 #aeh4 ,the quick motions of the ,moons of ,jupiter and ,saturn round their ,primaries1 demonstrate that these two ,planets have stronger attractive powers than the ,earth has4 ,for1 the stronger that one body attracts another1 the greater must be the projectile force1 and consequently the quicker must be the motion of that other body1 to keep it from falling to it's primary or central ,planet4 ,jupiter's second ,moon is #abd thousand miles farther from ,jupiter than our ,moon is from us2 and yet this second ,moon goes almost eight times round ,jupiter whilst our ,moon goes only once round the ,earth4 ,what a prodigious attractive power must the ,sun then have1 to draw all the ,planets and ,satellites of the ,system towards him2 and what an amazing power must it have required to put all these ,planets and ,moons into such rapid motions at first6 ,amazing indeed to us1 because impossible to be effected by the strength of all the living ,creatures in an unlimited number of ,worlds1 but no ways hard for the ,almighty1 whose ,planetarium takes in the whole ,universe6 ,sidenote3 ,,archimedes's ,problem for raising the ,earth4 #aei4 ,the celebrated ,,archimedes affirmed he could move the ,earth if he had a place to stand on to manage his machinery#cb4 ,this assertion is true in ,theory1 but1 upon examination1 will be found absolutely impossible in fact1 even though a proper place and materials of sufficient strength could be had4 ,the simplest and easiest method of moving a heavy body a little way is by a lever or crow1 where a small weight or power applied to the long arm will raise a great weight on the short one4 ,but then1 the small weight must move as much quicker than the great weight as the latter is heavier than the former2 and the length of the long arm of the lever to the length of the short arm must be in the same proportion4 ,now1 suppose a man pulls or presses the end of the long arm with the force of #bjj pound weight1 and that the ,earth contains in round ,numbers #d1jjj1jjj1jjj1jjj1jjj1jjj1jjj or #djjj ,trillions of cubic feet1 each at a mean rate weighing #ajj pound2 and that the prop or center of motion of the lever is #fjjj miles from the ,earth's center3 in this case1 the length of the lever from the ,fulcrum or center of motion to the moving power or weight ought to be #ab1jjj1jjj1jjj1jjj1jjj1jjj1jjj1jjj or #ab ,quadrillions of miles2 and so many miles must the power move1 in order to raise the ,earth but one mile1 whence 'tis easy to compute1 that if ,,archimedes or the power applied could move as swift as a cannon bullet1 it would take #bg1jjj1jjj1jjj1jjj or #bg ,billions of years to raise the ,earth one inch4 ,if any other machine1 such as a combination of wheels and screws1 was proposed to move the ,earth1 the time it would require1 and the space gone through by the hand that turned the machine1 would be the same as before4 ,hence we may learn1 that however boundless our ,imagination and ,theory may be1 the actual operations of man are confined within narrow bounds2 and more suited to our real wants than to our desires4 ,sidenote3 ,hard to determine what ,gravity is4 #afj4 ,the ,sun and ,planets mutually attract each other3 the power by which they do so we call ,gravity4 ,but whether this power be mechanical or no1 is very much disputed4 ,we are certain that the ,planets disturb one another's motions by it1 and that it decreases according to the squares of the distances of the ,sun and ,planets2 as light1 which is known to be material1 likewise does4 ,hence ,gravity should seem to arise from the agency of some subtile matter pressing towards the ,sun and ,planets1 and acting1 like all mechanical causes1 by contact4 ,but on the other hand1 when we consider that the degree or force of ,gravity is exactly in proportion to the quantities of matter in those bodies1 without any regard to their bulks or quantity of surface1 acting as freely on their internal as external parts1 it seems to surpass the power of mechanism2 and to be either the immediate agency of the ,deity1 or effected by a law originally established and imprest on all matter by him4 ,but some affirm that matter1 being altogether inert1 cannot be impressed with any ,law1 even by almighty ,power3 and that the ,deity must therefore be constantly impelling the ,planets toward the ,sun1 and moving them with the same irregularities and disturbances which ,gravity would cause1 if it could be supposed to exist4 ,but1 if a man may venture to publish his own thoughts1 7and why should not one as well as another87 it seems to me no greater absurdity1 to suppose the ,deity capable of superadding a ,law1 or what ,laws he pleases1 to matter1 than to suppose him capable of giving it existence at first4 ,the manner of both is equally inconceivable to us2 but neither of them imply a contradiction in our ideas3 and what implies no contradiction is within the power of ,omnipotence4 ,do we not see that a human creature can prepare a bar of steel so as to make it attract needles and filings of iron2 and that he can put a stop to that power or virtue1 and again call it forth again as often as he pleases8 ,to say that the workman infuses any new power into the bar1 is saying too much2 since the needle and filings1 to which he has done nothing1 re-attract the bar4 ,and from this it appears that the power was originally imprest on the matter of which the bar1 needle1 and filings are composed2 but does not seem to act until the bar be properly prepared by the artificer3 somewhat like a rope coiled up in a ship1 which will never draw a boat or any other thing towards the ship1 unless one end be tied to it1 and the other end to that which is to be hauled up2 and then it is no matter which end of the rope the sailors pull at1 for the rope will be equally stretched throughout1 and the ship and boat will move towards one another4 ,to say that the ,almighty has infused no such virtue or power into the materials which compose the bar1 but that he waits till the operator be pleased to prepare it by due position and friction1 and then1 when the needle or filings are brought pretty near the bar1 the ,deity presses them towards it1 and withdraws his hand whenever the workman either for use1 curiosity or whim1 does what appears to him to destroy the action of the bar1 seems quite ridiculous and trifling2 as it supposes ,god not only to be subservient to our inconstant wills1 but also to do what would be below the dignity of any rational man to be employed about4 #afa4 ,that the projectile force was at first given by the ,deity is evident4 ,for1 since matter can never put itself into motion1 and all bodies may be moved in any direction whatsoever2 and yet all the ,planets both primary and secondary move from west to east1 in planes nearly coincident2 whilst the ,comets move in all directions1 and in planes so different from one another2 these motions can be owing to no mechanical cause of necessity1 but to the free choice and power of an intelligent ,being4 #afb4 ,whatever ,gravity be1 'tis plain that it acts every moment of time3 for should it's action cease1 the projectile force would instantly carry off the ,planets in straight lines from those parts of their ,orbits where ,gravity left them4 ,but1 the ,planets being once put into motion1 there is no occasion for any new projectile force1 unless they meet with some resistance in their ,orbits2 nor for any mending hand1 unless they disturb one another too much by their mutual attractions4 ,sidenote3 ,the ,planets disturb one another's motion4 ,the consequences thereof4 #afc4 ,it is found that there are disturbances among the ,planets in their motions1 arising from their mutual attractions when they are in the same quarter of the ,heavens2 and that our years are not always precisely of the same length#cc4 ,besides1 there is reason to believe that the ,moon is somewhat nearer the ,earth now than she was formerly2 her periodical month being shorter than it was in former ages4 ,for1 our ,astronomical ,tables1 which in the present ,age shew the times of ,solar and ,lunar ,eclipses to great precision1 do not answer so well for very ancient ,eclipses4 ,hence it appears1 that the ,moon does not move in a medium void of all resistance1 #agd2 and therefore her projectile force being a little weakened1 whilst there is nothing to diminish her gravity1 she must be gradually approaching nearer the ,earth1 describing smaller and smaller ,circles round it in every revolution1 and finishing her ,period sooner1 although her absolute motion with regard to space be not so quick now as it was formerly3 and therefore1 she must come to the ,earth at last2 unless that ,being1 which gave her a sufficient projectile force at the beginning1 adds a little more to it in due time4 ,and1 as all the ,planets move in spaces full of ther and light1 which are material substances1 they too must meet with some resistance4 ,and therefore1 if their gravities are not diminished1 nor their projectile forces increased1 they must necessarily approach nearer and nearer the ,sun1 and at length fall upon and unite with him4 ,sidenote3 ,the ,world not eternal4 #afd4 ,here we have a strong philosophical argument against the eternity of the ,world4 ,for1 had it existed from eternity1 and been left by the ,deity to be governed by the combined actions of the above forces or powers1 generally called ,laws1 it had been at an end long ago4 ,and if it be left to them it must come to an end4 ,but we may be certain that it will last as long as was intended by it's ,author1 who ought no more to be found fault with for framing so perishable a work1 than for making man mortal4 ,,chap4 ,,viii4 ,of ,light4 ,it's proportional quantities on the different ,planets4 ,it's ,refractions in ,water and ,air4 ,the ,atmosphere2 it's weight and properties4 ,the ,horizontal ,moon4 ,sidenote3 ,the amazing smallness of the particles of light4 #afe4 ,light consists of exceeding small particles of matter issuing from a luminous body2 as from a lighted candle such particles of matter continually flow in all directions4 ,dr4 ,,niewentyt#cd computes1 that in one second of time there flows #dah1ffj1jjj1jjj1jjj1jjj1jjj1jjj1jjj1jjj 1jjj1jjj1jjj1jjj1jjj particles of light out of a burning candle2 which number contains at least #f1ccg1bdb1jjj1jjj times the number of grains of sand in the whole ,earth2 supposing #ajj grains of sand to be equal in length to an inch1 and consequently1 every cubic inch of the ,earth to contain one million of such grains4 ,sidenote3 ,the dreadful effects that would ensue from their being larger4 #aff4 ,these amazingly small particles1 by striking upon our eyes1 excite in our minds the idea of light3 and1 if they were so large as the smallest particles of matter discernible by our best microscopes1 instead of being serviceable to us1 they would soon deprive us of sight by the force arising from their immense velocity1 which is above #afd thousand miles every second#ce1 or #a1bcj1jjj times swifter than the motion of a cannon bullet4 ,and therefore1 if the particles of light were so large1 that a million of them were equal in bulk to an ordinary grain of land1 we durst no more open our eyes to the light than suffer sand to be shot point blank against them4 ,sidenote3 ,how objects become visible to us4 ,,plate ,,ii4 #afg4 ,when these small particles1 flowing from the ,sun or from a candle1 fall upon bodies1 and are thereby reflected to our eyes1 they excite in us the idea of that body by forming it's picture on the retina#cf4 ,and since bodies are visible on all sides1 light must be reflected from them in all directions4 ,sidenote3 ,the rays of ,light naturally move in straight lines4 ,a proof that they hinder not one another's motions4 #afh4 ,a ray of light is a continued stream of these particles1 flowing from any visible body in straight lines4 ,that they move in straight1 and not in crooked lines1 unless they be refracted1 is evident from bodies not being visible if we endeavour to look at them through the bore of a bended pipe2 and from their ceasing to be seen by the interposition of other bodies1 as the fixed ,stars by the interposition of the ,moon and ,planets1 and the ,sun wholly or in part by the interposition of the ,moon1 ,mercury1 or ,venus4 ,and that these rays do not interfere1 or jostle one another out of their ways1 in flowing from different bodies all around1 is plain from the following ,experiment4 ,make a little hole in a thin plate of metal1 and set the plate upright on a table1 facing a row of lighted candles standing by one another2 then place a sheet of paper or pasteboard at a little distance from the other side of the plate1 and the rays of all the candles1 flowing through the hole1 will form as many specks of light on the paper as there are candles before the plate1 each speck as distinct and large1 as if there were only one candle to cast one speck2 which shews that the rays are no hinderance to each other in their motions1 although they all cross in the hole4 ,sidenote3 ,fig4 ,,xi4 ,in what proportion light and heat decrease at any given distance from the ,sun4 ,,plate ,,ii4 #afi4 ,light1 and therefore heat so far as it depends on the ,sun's rays 7 #he1 towards the end7 decreases in proportion to the squares of the distances of the ,planets from the ,sun4 ,this is easily demonstrated by a ,figure which1 together with it's description1 ,i have taken from ,dr4 ,,smith's ,optics#cg4 ,let the light which flows from a point ,a1 and passes through a square hole ,b1 be received upon a plane ,c1 parallel to the plane of the hole2 or1 if you please1 let the figure ,c be the shadow of the plane ,b2 and when the distance ,c is double of ,b1 the length and breadth of the shadow ,c will be each double of the length and breadth of the plane ,b2 and treble when ,,ad is treble of ,,ab2 and so on3 which may be easily examined by the light of a candle placed at ,a4 ,therefore the surface of the shadow ,c1 at the distance ,,ac double of ,,ab1 is divisible into four squares1 and at a treble distance1 into nine squares1 severally equal to the square ,b1 as represented in the ,figure4 ,the light then which falls upon the plane ,b1 being suffered to pass to double that distance1 will be uniformly spread over four times the space1 and consequently will be four times thinner in every part of that space1 and at a treble distance it will be nine times thinner1 and at a quadruple distance sixteen times thinner1 than it was at first2 and so on1 according to the increase of the square surfaces ,b1 ,c1 ,d1 ,e1 built upon the distances ,,ab1 ,,ac1 ,,ad1 ,,ae4 ,consequently1 the quantities of this rarefied light received upon a surface of any given size and shape whatever1 removed successively to these several distances1 will be but one quarter1 one ninth1 one sixteenth of the whole quantity received by it at the first distance ,,ab4 ,or in general words1 the densities and quantities of light1 received upon any given plane1 are diminished in the same proportion as the squares of the distances of that plane1 from the luminous body1 are increased3 and on the contrary1 are increased in the same proportion as these squares are diminished4 ,sidenote3 ,why the ,planets appear dimmer when viewed thro' telescopes than by the bare eye4 #agj4 ,the more a telescope magnifies the disks of the ,moon and ,planets1 they appear so much dimmer than to the bare eye2 because the telescope cannot magnify the quantity of light1 as it does the surface2 and1 by spreading the same quantity of light over a surface so much larger than the naked eye beheld1 just so much dimmer must it appear when viewed by a telescope than by the bare eye4 ,sidenote3 ,fig4 ,,viii4 ,refraction of the rays of light4 #aga4 ,when a ray of light passes out of one medium#ch into another1 it is refracted1 or turned out of it's first course1 more or less1 as it falls more or less obliquely on the refracting surface which divides the two mediums4 ,this may be proved by several experiments2 of which we shall only give three for example's sake4 #a4 ,in a bason ,,fgh put a piece of money as ,,db1 and then retire from it as to ,a1 till the edge of the bason at ,e just hides the money from your sight3 then1 keeping your head steady1 let another person fill the bason gently with water4 ,as he fills it1 you will see more and more of the piece ,,db2 which will be all in view when the bason is full1 and appear as if lifted up to ,c4 ,for1 the ray ,,aeb1 which was straight whilst the bason was empty1 is now bent at the surface of the water in ,e1 and turned out of it's rectilineal course into the direction ,,ed4 ,or1 in other words1 the ray ,,dek1 that proceeded in a straight line from the edge ,d whilst the bason was empty1 and went above the eye at ,a1 is now bent at ,e2 and instead of going on in the rectilineal direction ,,dek1 goes in the angled direction ,,dea1 and by entering the eye at ,a renders the object ,,db visible4 ,or1 #b;dly1 place the bason where the ,sun shines obliquely1 and observe where the shadow of the rim ,e falls on the bottom1 as at ,b3 then fill it with water1 and the shadow will fall at ,d2 which proves1 that the rays of light1 falling obliquely on the surface of the water1 are refracted1 or bent downwards into it4 #agb4 ,the less obliquely the rays of light fall upon the surface of any medium1 the less they are refracted2 and if they fall perpendicularly thereon1 they are not refracted at all4 ,for1 in the last experiment1 the higher the ,sun rises1 the less will be the difference between the places where the edge of the shadow falls1 in the empty and full bason4 ,and1 #c;dly1 if a stick be laid over the bason1 and the ,sun's rays be reflected perpendicularly into it from a looking-glass1 the shadow of the stick will fall upon the same place of the bottom1 whether the bason be full or empty4 #agc4 ,the denser that any medium is1 the more is light refracted in passing through it4 ,sidenote3 ,the ,atmosphere4 ,the ,air's compression and rarity at different heights4 #agd4 ,the ,earth is surrounded by a thin fluid mass of matter1 called the ,air1 or ,atmosphere1 which gravitates to the ,earth1 revolves with it in it's diurnal motion1 and goes round the ,sun with it every year4 ,this fluid is of an elastic or springy nature1 and it's lowermost parts being pressed by the weight of all the ,air above them1 are squeezed the closer together2 and are therefore densest of all at the ,earth's surface1 and gradually rarer the higher up4 8,it is well known#ci that the ,air near the surface of our ,earth possesses a space about #abjj times greater than water of the same weight4 ,and therefore1 a cylindric column of ,air #abjj foot high is of equal weight with a cylinder of water of the same breadth and but one foot high4 ,but a cylinder of ,air reaching to the top of the ,atmosphere is of equal weight with a cylinder of water about #cc foot high#dj2 and therefore if from the whole cylinder of ,air1 the lower part of #abjj foot high is taken away1 the remaining upper part will be of equal weight with a cylinder of water #cb foot high2 wherefore1 at the height of #abjj feet or two furlongs1 the weight of the incumbent ,air is less1 and consequently the rarity of the compressed ,air is greater than near the ,earth's surface in the ratio of #cc to #cb4 ,and having this ratio we may compute the rarity of the ,air at all heights whatsoever1 supposing the expansion thereof to be reciprocally proportional to its compression2 and this proportion has been proved by the experiments of ,dr4 ,hooke and others4 ,the result of the computation ,i have set down in the annexed ,table1 in the first column of which you have the height of the ,air in miles1 whereof #djjj make a semi-diameter of the ,earth2 in the second the compression of the ,air or the incumbent weight2 in the third it's rarity or expansion1 supposing gravity to decrease in the duplicate ratio of the distances from the ,earth's center4 ,and the small numeral figures are here used to shew what number of cyphers must be joined to the numbers expressed by the larger figures1 as #j4agabbd for #j4jjjjjjjjjjjjjjjjjabbd1 and #bfiefae for #bfiefjjjjjjjjjjjjjjj4 ---------------------------------------- - ,,air's _/ _/ ,height4 ,compression4 ,expansion4 --------------------------------------- #j #cc #a #e #ag4heae #a4hdhf #aj #i4fgag #c4daea #bj #b4heb #aa4ega #dj #j4bebe #acf4hc #djj #j4agabbd #bfiefae #djjj #j4ajeddfe #gcijgajb #djjjj #j4aibafbh #bfbfcahi #djjjjj #j4bajghie #dagihbjg #djjjjjj #j4babihgh #ccdadbji ,infinite4 #j4babfjda #edfbbbji --------------------------------------- ,from this ,table it appears that the ,air in proceeding upwards is rarefied in such manner1 that a sphere of that ,air which is nearest the ,earth but of one inch diameter1 if dilated to an equal rarefaction with that of the ,air at the height of ten semi-diameters of the ,earth1 would fill up more space than is contained in the whole ,heavens on this side the fixed ,stars1 according to the preceding computation of their distance#da40 ,and it likewise appears that the ,moon does not move in a perfectly free and un-resisting medium2 although the air at a height equal to her distance1 is at least #cdjjjaij times thinner than at the ,earth's surface2 and therefore cannot resist her motion so as to be sensible in many ages4 ,sidenote3 ,it's weight how found4 ,,plate ,,ii4 #age4 ,the weight of the ,air1 at the ,earth's surface1 is found by experiments made with the air-pump2 and also by the quantity of mercury that the ,atmosphere balances in the barometer2 in which1 at a mean state2 the mercury stands #bi-a_/b inches high4 ,and if the tube were a square inch wide1 it would at that height contain #bi-a_/b cubic inches of mercury1 which is just #ae pound weight2 and so much weight of air every square inch of the ,earth's surface sustains2 and every square foot #add times as much1 because it contains #add square inches4 ,now as the ,earth's surface contains about #aii1dji1djj square miles1 it must be of no less than #e1eei1bae1jaf1ifj1jjj square feet2 which1 multiplied by #bjaf1 the number of pounds on every foot1 amounts to #aa1bjg1cgg1dgd1aia1cfj1jjj2 or #aa trillion #bjg thousand #cgg billion #dgd thousand #aia million and #cfj thousand pounds1 for the weight of the whole ,atmosphere4 ,at this rate1 a middle sized man1 whose surface may be about #ad square feet1 is pressed by #bh1bbd pound weight of ,air all round2 for fluids press equally up and down and on all sides4 ,but1 because this enormous weight is equal on all sides1 and counterbalanced by the spring of the internal ,air in our blood vessels1 it is not felt4 ,sidenote3 ,a common mistake about the weight of the ,air4 #agf4 ,oftentimes the state of the ,air is such that we feel ourselves languid and dull2 which is commonly thought to be occasioned by the ,air's being foggy and heavy about us4 ,but that the ,air is then too light1 is evident from the mercury's sinking in the barometer1 at which time it is generally found that the ,air has not sufficient strength to bear up the vapours which compose the ,clouds3 for1 when it is otherwise1 the ,clouds mount high1 the ,air is more elastic and weighty about us1 by which means it balances the internal spring of the ,air within us1 braces up our blood-vessels and nerves1 and makes us brisk and lively4 ,sidenote3 ,without an ,atmosphere the ,heavens would always appear dark1 and we should have no twilight4 #agg4 ,according to #db;,dr4 ,,keill1 and other astronomical writers1 it is entirely owing to the ,atmosphere that the ,heavens appear bright in the day-time4 ,for1 without an ,atmosphere1 only that part of the ,heavens would shine in which the ,sun was placed3 and if an observer could live without ,air1 and should turn his back towards the ,sun1 the whole ,heavens would appear as dark as in the night1 and the ,stars would be seen as clear as in the nocturnal sky4 ,in this case1 we should have no twilight2 but a sudden transition from the brightest sunshine to the blackest darkness immediately after sun-set2 and from the blackest darkness to the brightest sun-shine at sun-rising2 which would be extremely inconvenient1 if not blinding1 to all mortals4 ,but1 by means of the ,atmosphere1 we enjoy the ,sun's light1 reflected from the aerial particles1 before he rises and after he sets4 ,for1 when the ,earth by its rotation has withdrawn the ,sun from our sight1 the ,atmosphere being still higher than we1 has his light imparted to it2 which gradually decreases until he has got #ah degrees below the ,horizon2 and then1 all that part of the ,atmosphere which is above us is dark4 ,from the length of twilight1 the ,doctor has calculated the height of the ,atmosphere 7so far as it is dense enough to reflect any light7 to be about #dd miles4 ,but it is seldom dense enough at two miles height to bear up the ,clouds4 ,sidenote3 ,it brings the ,sun in view before he rises1 and keeps him in view after he sets4 #agh4 ,the ,atmosphere refracts the ,sun's rays so1 as to bring him in sight every clear day1 before he rises in the ,horizon2 and to keep him in view for some minutes after he is really set below it4 ,for1 at some times of the year1 we see the ,sun ten minutes longer above the ,horizon than he would be if there were no refractions3 and about six minutes every day at a mean rate4 ,sidenote3 ,fig4 ,,ix4 ,,plate ,,ii4 #agi4 ,to illustrate this1 let ,,iek be a part of the ,earth's surface1 covered with the ,atmosphere ,,hgfc2 and let ,,heo be the#dc sensible ,horizon of an observer at ,e4 ,when the ,sun is at ,a1 really below the ,horizon1 a ray of light ,,ac proceeding from him comes straight to ,c1 where it falls on the surface of the ,atmosphere1 and there entering a denser medium1 it is turned out of its rectilineal course ,a,cd,g1 and bent down to the observer's eye at ,e2 who then sees the ,sun in the direction of the refracted ray ed,e1 which lies above the ,horizon1 and being extended out to the ,heavens1 shews the ,sun at ,b #aga4 ,sidenote3 ,fig4 ,,ix4 #ahj4 ,the higher the ,sun rises1 the less his rays are refracted1 because they fall less obliquely on the surface of the ,atmosphere #agb4 ,thus1 when the ,sun is in the direction of the line ,ef,l continued1 he is so nearly perpendicular to the surface of the ,earth at ,e1 that his rays are but very little bent from a rectilineal course4 ,sidenote3 ,the quantity of refraction4 #aha4 ,the ,sun is about #cb-a_/d min4 of a deg4 in breadth1 when at his mean distance from the ,earth2 and the horizontal refraction of his rays is #cc-c_/d min4 which being more than his whole diameter1 brings all his ,disc in view1 when his uppermost edge rises in the ,horizon4 ,at ten deg4 height the refraction is not quite #e min4 at #bj deg4 only #b min4 #bf sec42 at #cj deg4 but #a min4 #cb sec42 between which and the ,zenith1 it is scarce sensible3 the quantity throughout1 is shewn by the annexed table1 calculated by ,sir ,,isaac ,,newton4 ---------------------------------------- --------- #ahb4 ,a ,,table shewing the ,refractions of the ,sun1 ,moon1 and ,stars2 adapted to their apparent ,altitudes4 ---------------------------------------- -- ,appar4 ,refrac- ,ap4 ,refrac- ,ap4 ,refrac- ,alt4 tion4 ,alt4 tion4 ,alt4 tion4 ---------------------------------------- -- ,d4 ,m4 ,m4 ,s4 ,d4 ,m4 ,s4 ,d4 ,m4 ,s4 ---------------------------------------- -- #j #j #cc #de #ba #b #ah #ef #j #cf #j #ae #cj #bd #bb #b #aa #eg #j #ce #j #cj #bg #ce #bc #b #e #eh #j #cd #j #de #be #aa #bd #a #ei #ei #j #cb #a #j #bc #g #be #a #ed #fj #j #ca ---------------------------------------- -- #a #ae #ba #bj #bf #a #di #fa #j #cj #a #cj #ai #df #bg #a #dd #fb #j #bh #a #de #ah #bb #bh #a #dj #fc #j #bg #b #j #ag #h #bi #a #cf #fd #j #bf #b #cj #ae #b #cj #a #cb #fe #j #be ---------------------------------------- -- #c #j #ac #bj #ca #a #bh #ff #j #bd #c #cj #aa #eg #cb #a #be #fg #j #bc #d #j #aj #dh #cc #a #bb #fh #j #bb #d #cj #i #ej #cd #a #ai #fi #j #ba #e #j #i #b #ce #a #af #gj #j #bj ---------------------------------------- -- #e #cj #h #ba #cf #a #ac #ga #j #ai #f #j #g #de #cg #a #aa #gb #j #ah #f #cj #g #ad #ch #a #h #gc #j #ag #g #j #f #dg #ci #a #f #gd #j #af #g #cj #f #bb #dj #a #d #ge #j #ae ---------------------------------------- -- #h #j #f #j #da #a #b #gf #j #ad #h #cj #e #dj #db #a #j #gg #j #ac #i #j #e #bb #dc #j #eh #gh #j #ab #i #cj #e #f #dd #j #ef #gi #j #aa #aj #j #d #eb #de #j #ed #hj #j #aj ---------------------------------------- -- #aa #j #d #bg #df #j #eb #ha #j #i #ab #j #d #e #dg #j #ej #hb #j #h #ac #j #c #dg #dh #j #dh #hc #j #g #ad #j #c #ca #di #j #dg #hd #j #f #ae #j #c #ag #ej #j #de #he #j #e ---------------------------------------- -- #af #j #c #d #ea #j #dd #hf #j #d #ag #j #b #ec #eb #j #db #hg #j #c #ah #j #b #dc #ec #j #dj #hh #j #b #ai #j #b #cd #ed #j #ci #hi #a #a #bj #j #b #bf #ee #j #ch #ij #j #j ---------------------------------------- -- ,sidenote3 ,,plate ,,ii4 ,the inconstancy of ,refractions4 ,a very remarkable case concerning refraction4 #ahc4 ,in all observations1 to have the true altitude of the ,sun1 ,moon1 or ,stars1 the refraction must be subtracted from the observed altitude4 ,but the quantity of refraction is not always the same at the same altitude2 because heat diminishes the air's refractive power and density1 and cold increases both2 and therefore no one table can serve precisely for the same place at all seasons1 nor even at all times of the same day2 much less for different climates3 it having been observed that the horizontal refractions are near a third part less at the ,equator than at ,paris1 as mentioned by ,dr4 ,,smith in the #cgjth remark on his ,optics1 where the following account is given of an extraordinary refraction of the sun-beams by cold4 8,there is a famous observation of this kind made by some ,hollanders that wintered in ,nova ,zembla in the year #aeif1 who were surprised to find1 that after a continual night of three months1 the ,sun began to rise seventeen days sooner than according to computation1 deduced from the ,altitude of the ,pole observed to be #gf3 which cannot otherwise be accounted for1 than by an extraordinary quantity of refraction of the ,sun's rays1 passing thro' the cold dense air in that climate4 ,,kepler computes that the ,sun was almost five degrees below the ,horizon when he first appeared2 and consequently the refraction of his rays was about nine times greater than it is with us40 #ahd4 ,the ,sun and ,moon appear of an oval figure as ,,fcgd1 just after their rising1 and before their setting3 the reason is1 that the refraction being greater in the ,horizon than at any distance above it1 the lowermost limb ,g appears more elevated than the uppermost4 ,but although the refraction shortens the vertical ,diameter ,,fg1 it has no sensible effect on the horizontal ,diameter ,,cd1 which is all equally elevated4 ,when the refraction is so small as to be imperceptible1 the ,sun and ,moon appear perfectly round1 as ,,aebf4 ,sidenote3 ,our imagination cannot judge rightly of the distance of inaccessible objects4 #ahe4 ,we daily observe1 that the objects which appear most distinct are generally those which are nearest to us2 and consequently1 when we have nothing but our imagination to assist us in estimating of distances1 bright objects seem nearer to us than those which are less bright1 or than the same objects do when they appear less bright and worse defined1 even though their distance in both cases be the same4 ,and as in both cases they are seen under the same angle#dd1 our imagination naturally suggests an idea of a greater distance between us and those objects which appear fainter and worse defined than those which appear brighter under the same ,angles2 especially if they be such objects as we were never near to1 and of whose real ,magnitudes we can be no judges by sight4 ,sidenote3 ,nor always of those which are accessible4 #ahf4 ,but1 it is not only in judging of the different apparent ,magnitudes of the same objects1 which are better or worse defined by their being more or less bright1 that we may be deceived3 for we may make a wrong conclusion even when we view them under equal degrees of brightness1 and under equal ,angles2 although they be objects whose bulks we are generally acquainted with1 such as houses or trees3 for proof of which1 the two following instances may suffice4 ,sidenote3 ,the reason assigned4 ,,plate ,,ii4 ,first1 ,when a house is seen over a very broad river by a person standing on low ground1 who sees nothing of the river1 nor knows of it beforehand2 the breadth of the river being hid from him1 because the banks seem contiguous1 he loses the idea of a distance equal to that breadth2 and the house seems small1 because he refers it to a less distance than it really is at4 ,but1 if he goes to a place from which the river and interjacent ground can be seen1 though no farther from the house1 he then perceives the house to be at a greater distance than he imagined2 and therefore fancies it to be bigger than he did at first2 although in both cases it appears under the same ,angle1 and consequently makes no bigger picture on the retina of his eye in the latter case than it did in the former4 ,many have been deceived1 by taking a red coat of arms1 fixed upon the iron gate in ,clare-,hall walks at ,cambridge1 for a brick house at a much greater distance#de4 ,sidenote3 ,fig4 ,,xii4 ,secondly1 ,in foggy weather1 at first sight1 we generally imagine a small house1 which is just at hand1 to be a great castle at a distance2 because it appears so dull and ill defined when seen through the ,mist1 that we refer it to a much greater distance than it really is at2 and therefore1 under the same ,angle1 we judge it to be much bigger4 ,for1 the near object ,,fe1 seen by the eye ,,abd1 appears under the same ,angle ,,gch1 that the remote object ,,ghi does3 and the rays ,,gfcn and ,,hecm crossing one another at ,c in the pupil of the eye1 limit the size of the picture ,,mn on the retina2 which is the picture of the object ,,fe1 and if ,,fe were taken away1 would be the picture of the object ,,ghi1 only worse defined2 because ,,ghi1 being farther off1 appears duller and fainter than ,,fe did4 ,but if a ,fog1 as ,,kl1 comes between the eye and the object ,,fe1 it appears dull and ill defined like ,,ghi2 which causes our imagination to refer ,,fe to the greater distance ,,ch1 instead of the small distance ,,ce which it really is at4 ,and consequently1 as mis-judging the distance does not in the least diminish the ,angle under which the object appears1 the small hay-rick ,,fe seems to be as big as ,,ghi4 ,sidenote3 ,fig4 ,,ix4 ,why the ,sun and ,moon appear biggest in the ,horizon4 #ahg4 ,the ,sun and ,moon appear bigger in the ,horizon than at any considerable height above it4 ,these ,luminaries1 although at great distances from the ,earth1 appear floating1 as it were1 on the surface of our ,atmosphere ,h,g,ffe,c1 a little way beyond the ,clouds2 of which1 those about ,f1 directly over our heads at ,e1 are nearer us than those about ,h or e in the ,horizon ,h,ee4 ,therefore1 when the ,sun or ,moon appear in the ,horizon at e1 they are not only seen in a part of the ,sky which is really farther from us than if they were at any considerable ,altitude1 as about f2 but they are also seen through a greater quantity of ,air and ,vapours at e than at f4 ,here we have two concurring appearances which deceive our imagination1 and cause us to refer the ,sun and ,moon to a greater distance at their rising or setting about e1 than when they are considerably high as at f3 first1 their seeming to be on a part of the ,atmosphere at e1 which is really farther than f from a spectator at ,e2 and secondly1 their being seen through a grosser medium when at e than when at f2 which1 by rendering them dimmer1 causes us to imagine them to be at a yet greater distance4 ,and as1 in both cases1 they are seen#df much under the same ,angle1 we naturally judge them to be biggest when they seem farthest from us2 like the above-mentioned house #ahf1 seen from a higher ground1 which shewed it to be farther off than it appeared from low ground2 or the hay-rick1 which appeared at a greater distance by means of an interposing ,fog4 ,sidenote3 ,their ,diameters are not less on the ,meridian than in the ,horizon4 #ahh4 ,any one may satisfy himself that the ,moon appears under no greater ,angle in the ,horizon than on the ,meridian1 by taking a large sheet of paper1 and rolling it up in the form of a ,tube1 of such a width1 that observing the ,moon through it when she rises1 she may1 as it were1 just fill the ,tube2 then tie a thread round it to keep it of that size2 and when the ,moon comes to the ,meridian1 and appears much less to the eye1 look at her again through the same ,tube1 and she will fill it just as much1 if not more1 than she did at her rising4 #ahi4 ,when the full ,moon is in perigeo1 or at her least distance from the ,earth1 she is seen under a larger ,angle1 and must therefore appear bigger than when she is ,full at other times3 and if that part of the ,atmosphere where she rises be more replete with vapours than usual1 she appears so much the dimmer2 and therefore we fancy her to be still the bigger1 by referring her to an unusually great distance2 knowing that no objects which are very far distant can appear big unless they be really so4 ,illustration3 ,plate ,,iiii4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 ,,chap4 ,,ix4 ,the ,method of finding the ,distances of the ,sun1 ,moon1 and ,planets4 ,sidenote3 ,,plate ,,iv4 #aij4 ,those who have not learnt how to take the #dg;,altitude of any ,celestial ,phenomenon by a common ,quadrant1 nor know any thing of ,plain ,trigonometry1 may pass over the first ,article of this short ,chapter1 and take the ,astronomer's word for it1 that the distances of the ,sun and ,planets are as stated in the first ,chapter of this ,book4 ,but1 to every one who knows how to take the ,altitude of the ,sun1 the ,moon1 or a ,star1 and can solve a plain right-angled ,triangle1 the following method of finding the distances of the ,sun and ,moon will be easily understood4 ,sidenote3 ,fig ,i4 ,let ,,bag be one half of the ,earth1 ,,ac it's semi-diameter1 ,s the ,sun1 m the ,moon1 and ,,ekol a quarter of the ,circle described by the ,moon in revolving from the ,meridian to the ,meridian again4 ,let ,,crs be the rational ,horizon of an observer at ,a1 extended to the ,sun in the ,heavens1 and ,,hao his sensible ,horizon2 extended to the ,moon's ,orbit4 ,,alc is the ,angle under which the ,earth's semi-diameter ,,ac is seen from the ,moon at ,l1 which is equal to the ,angle ,,oal1 because the right lines ,,ao and ,,cl which include both these ,angles are parallel4 ,,asc is the ,angle under which the ,earth's semi-diameter ,,ac is seen from the ,sun at ,s1 and is equal to the ,angle ,o,af because the lines ,,ao and ,,crs are parallel4 ,now1 it is found by observation1 that the ,angle ,,oal is much greater than the ,angle ,o,af2 but ,,oal is equal to ,,alc1 and ,o,af is equal to ,,asc4 ,now1 as ,,asc is much less than ,,alc1 it proves that the ,earth's semi-diameter ,,ac appears much greater as seen from the ,moon at ,l than from the ,sun at ,s3 and therefore the ,earth is much farther from the ,sun than from the ,moon#dh4 ,the ,quantities of these ,angles are determined by observation in the following manner4 ,sidenote3 ,the ,moon's horizontal ,parallax1 what4 ,the ,moon's distance determined4 ,let a graduated instrument as ,,dae1 7the larger the better7 having a moveable ,index and ,sight-holes1 be fixed in such a manner1 that it's plane surface may be parallel to the ,plan of the ,equator1 and it's edge ,,ad in the ,meridian3 so that when the ,moon is in the ,equinoctial1 and on the ,meridian at ,e1 she may be seen through the sight-holes when the edge of the moveable index cuts the beginning of the divisions at o1 on the graduated limb ,,de2 and when she is so seen1 let the precise time be noted4 ,now1 as the ,moon revolves about the ,earth from the ,meridian to the ,meridian again in #bd hours #dh minutes1 she will go a fourth part round it in a fourth part of that time1 viz4 in #f hours #ab minutes1 as seen from ,c1 that is1 from the ,earth's center or ,pole4 ,but as seen from ,a1 the observer's place on the ,earth's surface1 the ,moon will seem to have gone a quarter round the ,earth when she comes to the sensible ,horizon at ,o2 for the ,index through the sights of which she is then viewed will be at d1 #ij degrees from ,d1 where it was when she was seen at ,e4 ,now1 let the exact moment when the ,moon is seen at ,o 7which will be when she is in or near the sensible ,horizon7 be carefully noted#di1 that it may be known in what time she has gone from ,e to ,o2 which time subtracted from #f hours #ab minutes 7the time of her going from ,e to ,l7 leaves the time of her going from ,o to ,l1 and affords an easy method for finding the ,angle ,,oal 7called the ,moon's horizontal ,parallax1 which is equal to the ,angle ,,alc7 by the following ,analogy3 ,as the time of the ,moon's describing the arc ,,eo is to #ij degrees1 so is #f hours #ab minutes to the degrees of the ,arc ,dd,e1 which measures the ,angle ,,eal2 from which subtract #ij degrees1 and there remains the ,angle ,,oal1 equal to the ,angle ,,alc1 under which the ,earth's ,semi-diameter ,,ac is seen from the ,moon4 ,now1 since all the ,angles of a right-lined ,triangle are equal to #ahj degrees1 or to two right ,angles1 and the sides of a ,triangle are always proportional to the ,sines of the opposite ,angles1 say1 by the ,rule of ,three1 as the ,sine of the ,angle ,,alc at the ,moon ,l is to it's opposite side ,,ac the ,earth's ,semi-diameter1 which is known to be #cihe miles1 so is ,radius1 viz4 the ,sine of #ij degrees1 or of the right ,angle ,,acl to it's opposite side ,,al1 which is the ,moon's distance at ,l from the observer's place at ,a on the ,earth's surface2 or1 so is the ,sine of the ,angle ,,cal to its opposite side ,,cl1 which is the ,moon's distance from the ,earth's centre1 and comes out at a mean rate to be #bdj1jjj miles4 ,the ,angle ,,cal is equal to what ,,oal wants of #ij degrees4 ,sidenote3 ,the ,sun's distance cannot be yet so exactly determined as the ,moon's2 ,how near the truth it may soon be determined4 #aia4 ,the ,sun's distance from the ,earth is found the same way1 but with much greater difficulty2 because his horizontal ,parallax1 or the ,angle ,,oas equal to the ,angle ,,asc1 is so small as1 to be hardly perceptible1 being only #aj seconds of a minute1 or the #cfjth part of a degree4 ,but the ,moon's horizontal ,parallax1 or ,angle ,,oal equal to the ,angle ,,alc1 is very discernible2 being #eg #di1 or #cdfi at it's mean state2 which is more than #cdj times as great as the ,sun's3 and therefore1 the distances of the heavenly bodies being inversely as the ,tangents of their horizontal ,parallaxes1 the ,sun's distance from the ,earth is at least #cdj times as great as the ,moon's2 and is rather understated at #ha millions of miles1 when the ,moon's distance is certainly known to be #bdj thousand4 ,but because1 according to some ,astronomers1 the ,sun's horizontal ,parallax is #aa seconds1 and according to others only #aj1 the former ,parallax making the ,sun's distance to be about #ge1jjj1jjj of miles1 and the latter #hb1jjj1jjj2 we may take it for granted1 that the ,sun's distance is not less than as deduced from the former1 nor more than as shewn by the latter3 and every one who is accustomed to make such observations1 knows how hard it is1 if not impossible1 to avoid an error of a second2 especially on account of the inconstancy of horizontal ,refractions4 ,and here1 the error of one second1 in so small an ,angle1 will make an error of #g millions of miles in so great a distance as that of the ,sun's2 and much more in the distances of the superiour ,planets4 ,but ,dr4 ,,halley has shewn us how the ,sun's distance from the ,earth1 and consequently the distances of all the ,planets from the ,sun1 may be known to within a #ejjth part of the whole1 by a ,transit of ,venus over the ,sun's ,disc1 which will happen on the #fth of ,june1 in the year #agfa2 till which time we must content ourselves with allowing the ,sun's distance to be about #ha millions of miles1 as commonly stated by ,astronomers4 ,sidenote3 ,the ,sun proved to be much bigger than the ,moon4 #aib4 ,the ,sun and ,moon appear much about the same bulk3 ,and every one who understands ,geometry knows how their true bulks may be deduced from the apparent1 when their real distances are known4 ,spheres are to one another as the ,cubes of their ,diameters2 whence1 if the ,sun be #ha millions of miles from the ,earth1 to appear as big as the ,moon1 whose distance does not exceed #bdj thousand miles1 he must1 in solid bulk1 be #db millions #hge thousand times as big as the ,moon4 #aic4 ,the horizontal ,parallaxes are best observed at the ,equator2 #a4 ,because the heat is so nearly equal every day1 that the ,refractions are almost constantly the same4 #b4 ,because the parallactic ,angle is greater there as at ,a 7the distance from thence to the ,earth's ,axis being greater17 than upon any parallel of ,latitude1 as a or b4 ,sidenote3 ,the relative distances of the ,planets from the ,sun are known to great precision1 though their real distances are not well known4 #aid4 ,the ,earth's distance from the ,sun being determined1 the distances of all the other ,planets from him are easily found by the following analogy1 their periods round him being ascertained by observation4 ,as the square of the ,earth's period round the ,sun is to the cube of it's distance from him1 so is the square of the period of any other ,planet to the cube of it's distance1 in such parts or measures as the ,earth's distance was taken2 see #aaa4 ,this proportion gives us the relative mean distances of the ,planets from the ,sun to the greatest degree of exactness2 and they are as follows1 having been deduced from their periodical times1 according to the law just mentioned1 which was discovered by ,,kepler and demonstrated by ,sir ,,isaac ,,newton4 ,periodical ,revolution to the same fixed ,star in days and decimal parts of a day4 ,of ,mercury ,venus ,the ,earth ,mars ,jupiter ,saturn #hg4ifib #bbd4fagf #cfe4befd #fhf4ighe #dccb4ead #ajgei4bge ,relative mean distances from the ,sun4 #chgaj #gbccc #ajjjjj #aebcfi #ebjjif #iedjjf ,from these numbers we deduce1 that if the ,sun's horizontal ,parallax be #aj1 the real mean distances of the ,planets from the ,sun in ,english miles are #ca1gdb1bjj #ei1cac1jfj #hb1jjj1jjj #abd1idb1ehj #dbf1dgh1gbj #ghb1bhd1ibj ,but if the ,sun's ,parallax be #aa their distances are no more than #bi1jcb1ejj #ed1bch1egj #ge1jjj1jjj #aad1bgf1gej #cij1jcd1ejj #gae1ejd1ejj ,errors in distance a rising from the mistake of #a in the ,sun's ,parallax #b1gji1gjj #e1jgd1dij #g1jjj1jjj #aj1ffe1hcj #cf1ddd1bbj #ff1ghj1dbj #aie4 ,these last numbers shew1 that although we have the relative distances of the ,planets from the ,sun to the greatest nicety1 yet the best observers have not hitherto been able to ascertain their true distances to within less than a twelfth part of what they really are4 ,and therefore1 we must wait with patience till the #fth of ,june1 ,a4 ,d4 #agfa2 wishing that the ,sky may then be clear to all places where there are good ,astronomers and accurate instruments for observing the ,transit of ,venus over the ,sun's ,disc at that time3 as it will not happen again1 so as to be visible in ,europe1 in less than #bce years after4 ,sidenote3 ,why the celestial ,poles seem to keep still in the same points of the ,heavens1 notwithstanding the ,earth's motion round the ,sun4 #aif4 ,the ,earth's ,axis produced to the ,stars1 being carried #ejparallel to itself during the ,earth's annual revolution1 describes a circle in the ,sphere of the fixed ,stars equal to the ,orbit of the ,earth4 ,but this ,orbit1 though very large in itself1 if viewed from the ,stars1 would appear no bigger than a point2 and consequently1 the circle described in the ,sphere of the ,stars by the ,axis of the ,earth produced1 if viewed from the ,earth1 must appear but as a point2 that is1 it's diameter appears too little to be measured by observation3 for ,dr4 ,,bradley has assured us1 that if it had amounted to a single second1 or two at most1 he should have perceived it in the great number of observations he has made1 especially upon ,dragonis2 and that it seemed to him very probable that the annual ,parallax of this ,star is not so great as a single second3 and consequently1 that it is above #djj thousand times farther from us than the ,sun4 ,hence the celestial poles seem to continue in the same points of the ,heavens throughout the year2 which by no means disproves the ,earth's annual motion1 but plainly proves the distance of the ,stars to be exceeding great4 ,sidenote3 ,the amazing velocity of light4 ,,plate ,,iv4 #aig4 ,the small apparent motion of the ,stars #aac1 discovered by that great ,astronomer1 he found to be no ways owing to their annual ,parallax 7for it came out contrary thereto7 but to the ,aberration of their light1 which can result from no known cause besides that of the ,earth's annual motion2 and as it agrees so exactly therewith1 it proves beyond dispute that the ,earth has such a motion3 for this ,aberration compleats all it's various ,phenomena every year2 and proves that the velocity of star-light is such as carries it through a space equal to the ,sun's distance from us in #h minutes #ac seconds of time4 ,hence1 the velocity of light is #eaaj thousand #baj times as great as the ,earth's velocity in it's ,orbit2 which velocity 7from what we know already of the ,earth's distance from the ,sun7 may be affected to be at least between #eg and #eh thousand miles every hour3 and supposing it to be #ehjjj1 this number multiplied by the above #ajbaj1 gives #eib million #ahj thousand miles for the hourly motion of light3 which last number divided by #cfjj1 the number of seconds in an hour1 shews that light flies at the rate of more than #afd thousand miles every second of time1 or swing of a common clock pendulum4 ,,chap4 ,x4 ,the ,circles of the ,globe described4 ,the different lengths of days and nights1 and the vicissitudes of seasons1 explained4 ,the explanation of the ,phenomena of ,saturn's ,ring concluded4 7,see #ha and #hb47 ,sidenote3 ,circles of the ,sphere4 ,fig4 ,,ii ,equator1 ,tropics1 ,polar ,circles1 and ,poles4 ,fig4 ,,ii4 ,earth's ,axis4 ,,plate ,,iv4 ,meridians4 #aih4 ,if the reader be hitherto unacquainted with the principal circles of the ,globe1 he should now learn to know them2 which he may do sufficiently for his present purpose in a quarter of an hour1 if he sets the ball of a terrestrial ,globe before him1 or looks at the ,figure of it1 wherein these circles are drawn and named4 ,the ,equator is that great circle which divides the northern half of the ,earth from the southern4 ,the ,tropics are lesser circles parallel to the ,equator1 and each of them is #bc-a_/b degrees from it2 a degree in this sense being the #cfjth part of any great circle which divides the ,earth into two equal parts4 ,the ,tropic of ,cancer lies on the north side of the ,equator1 and the ,tropic of ,capricorn on the south4 ,the ,arctic ,circle has the ,north ,pole for it's center1 and is just as far from the north ,pole as the ,tropics are from the ,equator3 and the ,antarctic ,circle 7hid by the supposed convexity of the ,figure7 is just as far from the ,south ,pole1 every way round it4 ,these ,poles are the very north and south points of the ,globe3 and all other places are denominated northward or southward according to the side of the ,equator they lie on1 and the ,pole to which they are nearest4 ,the ,earth's ,axis is a straight line passing through the center of the ,earth1 perpendicular to the ,equator1 and terminating in the ,poles at it's surface4 ,this1 in the real ,earth and ,planets is only an imaginary line2 but in artificial ,globes or ,planets it is a wire by which they are supported1 and turned round in ,orreries1 or such like machines1 by wheel-work4 ,the circles #ab4 #a4 #b4 #c4 #d1 c4 are ,meridians to all places they pass through2 and we must suppose thousands more to be drawn1 because every place that is ever so little to the east or west of any other place1 has a different ,meridian from that other place4 ,all the ,meridians meet in the ,poles2 and whenever the ,sun's center is passing over any ,meridian1 in his apparent motion round the ,earth1 it is mid-day or noon to all places on that ,meridian4 ,sidenote3 ,zones4 #aii4 ,the broad ,space lying between the ,tropics1 like a girdle surrounding the ,globe1 is called the torrid ,zone1 of which the ,equator is in the middle1 all around4 ,the ,space between the ,tropic of ,cancer and ,arctic ,circle is called the ,north temperate ,zone4 ,that between the ,tropic of ,capricorn and the ,antarctic ,circle1 the ,south temperate ,zone4 ,and the two circular ,spaces bounded by the ,polar ,circles are the two ,frigid ,zones2 denominated north or south1 from that ,pole which is in the center of the one or the other of them4 #bjj4 ,having acquired this easy branch of knowledge1 the learner may proceed to make the following experiment with his terrestrial ball2 which will give him a plain idea of the diurnal and annual motions of the ,earth1 together with the different lengths of days and nights1 and all the beautiful variety of seasons1 depending on those motions4 ,sidenote3 ,fig4 ,,iii4 ,a pleasant experiment shewing the different lengths of days and nights1 and the variety of seasons4 ,summer ,solstice4 ,take about seven feet of strong wire1 and bend it into a circular form1 as abcd1 which being viewed obliquely1 appears elliptical as in the ,figure4 ,place a lighted candle on a table1 and having fixed one end of a silk thread ,k1 to the north pole of a small terrestrial ,globe ,h1 about three inches diameter1 cause another person to hold the wire circle so that it may be parallel to the table1 and as high as the flame of the candle ,i1 which should be in or near the center4 ,then1 having twisted the thread as towards the left hand1 that by untwisting it may turn the ,globe round eastward1 or contrary to the way that the hands of a watch move2 hang the ,globe by the thread within this circle1 almost contiguous to it2 and as the thread untwists1 the ,globe 7which is enlightened half round by the candle as the ,earth is by the ,sun7 will turn round it's ,axis1 and the different places upon it will be carried through the light and dark ,hemispheres1 and have the appearance of a regular succession of days and nights1 as our ,earth has in reality by such a motion4 ,as the ,globe turns1 move your hand slowly so as to carry the ,globe round the candle according to the order of the letters abcd1 keeping it's center even with the wire circle2 and you will perceive1 that the candle being still perpendicular to the ,equator will enlighten the ,globe from pole to pole in it's motion round the circle2 and that every place on the ,globe goes equally through the light and the dark1 as it turns round by the untwisting of the thread1 and therefore has a perpetual ,equinox4 ,the ,globe thus turning round represents the ,earth turning round it's ,axis2 and the motion of the ,globe round the candle represents the ,earth's annual motion round the ,sun1 and shews1 that if the ,earth's ,orbit had no inclination to it's ,axis1 all the days and nights of the year would be equally long1 and there would be no different seasons4 ,but now1 desire the person who holds the wire to hold it obliquely in the position ,,abcd1 raising the side just as much as he depresses the side 1 that the flame may be still in the plane of the circle2 and twisting the thread as before1 that the ,globe may turn round it's ,axis the same way as you carry it round the candle2 that is1 from west to east1 let the ,globe down into the lowermost part of the wire circle at 1 and if the circles be properly inclined1 the candle will shine perpendicularly on the ,tropic of ,cancer1 and the frigid ,zone1 lying within the arctic or north polar ,circle1 will be all in the light1 as in the ,figure2 and will keep in the light let the ,globe turn round it's ,axis ever so often4 ,from the ,equator to the north polar ,circle all the places have longer days and shorter nights2 but from the ,equator to the south polar ,circle just the reverse4 ,the ,sun does not set to any part of the north frigid ,zone1 as shewn by the candle's shining on it so that the motion of the ,globe can carry no place of that ,zone into the dark3 and at the same time the south frigid ,zone is involved in darkness1 and the turning of the ,globe brings none of it's places into the light4 ,if the ,earth were to continue in the like part of it's ,orbit1 the ,sun would never set to the inhabitants of the north frigid ,zone1 nor rise to those of the south4 ,at the ,equator it would be always equal day and night2 and as the places are gradually more and more distant from the ,equator1 towards the arctic ,circle1 they would have longer days and shorter nights1 whilst those on the south side of the ,equator would have their nights longer than their days4 ,in this case there would be continual summer on the north side of the ,equator1 and continual winter on the south side of it4 ,illustration3 ,plate ,v4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sc4 ,sidenote3 ,,plate ,,iv4 ,autumnal ,equinox4 ,but as the ,globe turns round it's ,axis1 move your hand slowly forward so as to carry the ,globe from ,h towards ,e1 and the boundary of light and darkness will approach towards the north ,pole1 and recede towards the south ,pole2 the northern places will go through less and less of the light1 and the southern places through more and more of it2 shewing how the northern days decrease in length1 and the southern days increase1 whilst the ,globe proceeds from ,h to ,f4 ,when the ,globe is at ,e1 it is at a mean state between the lowest and highest parts of it's ,orbit2 the candle is directly over the ,equator1 the boundary of light and darkness just reaches to both the ,poles1 and all places on the ,globe go equally through the light and dark ,hemispheres1 shewing that the days and nights are then equal at all places of the ,earth1 the ,poles only excepted2 for the ,sun is then setting to the north ,pole1 and rising to the south ,pole4 ,sidenote3 ,winter ,solstice4 ,continue moving the ,globe forward1 and as it goes through the quarter ,a1 the north ,pole recedes still farther into the dark ,hemisphere1 and the south ,pole advances more into the light1 as the ,globe comes nearer to 2 and when it comes there at ,f1 the candle is directly over the ,tropic of ,capricorn1 the days are at the shortest1 and nights at the longest1 in the northern ,hemisphere1 all the way from the ,equator to the arctic ,circle2 and the reverse in the southern ,hemisphere from the antarctic ,circle2 within which ,circles it is dark to the north frigid ,zone and light to the south4 ,sidenote3 ,vernal ,equinox4 ,continue both motions1 and as the ,globe moves through the quarter ,b1 the north ,pole advances toward the light1 and the south ,pole recedes as fast from it2 the days lengthen in the northern ,hemisphere1 and shorten in the southern2 and when the ,globe comes to ,g the candle will be again over the ,equator 7as when the ,globe was at ,e7 and the days and nights will again be equal as formerly3 and the north ,pole will be just coming into the light1 the south ,pole going out of it4 ,thus we see the reason why the days lengthen and shorten from the ,equator to the polar ,circles every year2 why there is no day or night for several turnings of the ,earth1 within the polar ,circles2 why there is but one day and one night in the whole year at the ,poles2 and why the days and nights are equally long all the year round at the ,equator1 which is always equally cut by the circle bounding light and darkness4 ,sidenote3 ,remark4 ,fig4 ,,iii4 ,,plate ,v4 #bja4 ,the inclination of an ,axis or ,orbit is merely relative1 because we compare it with some other ,axis or ,orbit which we consider as not inclined at all4 ,thus1 our ,horizon being level to us whatever place of the ,earth we are upon1 we consider it as having no inclination2 and yet1 if we travel #ij degrees from that place1 we shall then have an ,horizon perpendicular to the former2 but it will still be level to us4 ,and1 if this ,book be held so that the #eb;,circle ,,abcd be parallel to the ,horizon1 both the ,circle abcd1 and the ,thread or ,axis ,k will be inclined to it4 ,but if ,book or ,plate be held1 so that the ,thread be perpendicular to the ,horizon1 then the ,orbit ,,abcd will be inclined to the ,thread1 and the ,orbit abcd perpendicular to it1 and parallel to the ,horizon4 ,we generally consider the ,earth's annual ,orbit as having no inclination1 and the ,orbits of all the other ,planets as inclined to it #bj4 #bjb4 ,let us now take a view of the ,earth in it's annual course round the ,sun1 considering it's ,orbit as having no inclination2 and it's ,axis as inclining #bc-a_/b degrees from a line perpendicular to it's ,orbit1 and keeping the same oblique direction in all parts of it's annual course2 or1 as commonly termed1 keeping always parallel to itself #aif4 ,sidenote3 ,fig4 ,i4 ,a concise view of the seasons4 ,let a1 b1 c1 d1 e1 f1 g1 h be the ,earth in eight different parts of it's ,orbit1 equidistant from one another2 ,ns it's ,axis1 ,n the north ,pole1 s the south ,pole1 and ,s the ,sun nearly in the center of the ,earth's ,orbit #ah4 ,as the ,earth goes round the ,sun according to the order of the letters abcd1 c4 it's ,axis ,ns keeps the same obliquity1 and is still parallel to the line ,m,ns4 ,when the ,earth is at a1 it's north ,pole inclines toward the ,sun1 and brings all the northern places more into the light than at any other time of the year4 ,but when the ,earth is at e in the opposite time of the year1 the north ,pole declines from the ,sun1 which occasions the northern places to be more in the dark than in the light2 and the reverse at the southern places1 as is evident by the ,figure1 which ,i have taken from ,dr4 ,,long's ,astronomy4 ,when the ,earth is either at c or g1 it's ,axis inclines not either to or from the ,sun1 but lies sidewise to him2 and then the ,poles are in the boundary of light and darkness2 and the ,sun1 being directly over the ,equator1 makes equal day and night at all places4 ,when the ,earth is at b it is half way between the ,summer ,solstice and ,harvest ,equinox2 when it is at d it is half way from the ,harvest ,equinox to the ,winter ,solstice2 at f half way from the ,winter ,solstice to the ,spring ,equinox3 and at h half way from the ,spring ,equinox to the ,summer ,solstice4 ,sidenote3 ,fig4 ,,ii4 ,,plate ,v4 ,the ,ecliptic4 ,the seasons shewn in another view of the ,earth1 and it's ,orbit4 #bjc4 ,from this oblique view of the ,earth's ,orbit1 let us suppose ourselves to be raised far above it1 and placed just over it's center ,s1 looking down upon it from it's north pole2 and as the ,earth's ,orbit differs but very little from a ,circle1 we shall have it's figure in such a view represented by the ,circle ,,abcdefgh4 ,let us suppose this ,circle to be divided into #ab equal parts called ,signs1 having their names affixed to them2 and each ,sign into #cj equal parts called ,degrees1 numbered #aj1 #bj1 #cj1 as in the outermost ,circle of the ,figure1 which represents the great ,ecliptic in the ,heavens4 ,the ,earth is shewn in eight different positions in this ,circle1 and in each position is the ,equator1 ,t the ,tropic of ,cancer1 the dotted ,circle the parallel of ,london1 ,u the arctic or north polar ,circle1 and ,p the north ,pole where all the ,meridians or hour ,circles meet #aih4 ,as the ,earth goes round the ,sun the north ,pole keeps constantly towards one part of the ,heavens1 as it keeps in the ,figure towards the right hand side of the ,plate4 ,sidenote3 ,vernal ,equinox4 ,when the ,earth is at the beginning of ,libra1 namely on the #bjth of ,march1 in this ,figure 7as at g in ,fig4 ,i47 the ,sun ,s as seen from the ,earth appears at the beginning of ,aries in the opposite part of the ,heavens#ec1 the north ,pole is just coming into the light1 the ,sun is vertical to the ,equator2 which1 together with the ,tropic of ,cancer1 parallel of ,london1 and arctic ,circle1 are all equally cut by the ,circle bounding light and darkness1 coinciding with the six o'clock hour ,circle1 and therefore the days and nights are equally long at all places3 for every part of the ,meridian ,t,la comes into the light at six in the morning1 and revolving with the ,earth according to the order of the hour-letters1 goes into the dark at six in the evening4 ,there are #bd ,meridians or hour-,circles drawn on the ,earth in this ,figure1 to shew the time of ,sun rising and setting at different ,seasons of the ,year4 ,sidenote3 ,fig4 ,,ii4 ,as the ,earth moves in the ,ecliptic according to the order of the letters ,,abcd1 c4 through the ,signs ,libra1 ,scorpio1 and ,sagittarius1 the north ,pole comes more and more into the light2 the days increase as the nights decrease in length1 at all places north of the ,equator 2 which is plain by viewing the ,earth at b on the #eth of ,may1 when it is in the #aeth degree of ,scorpio#ed1 and the ,sun as seen from the ,earth appears in the #aeth degree of ,taurus4 ,for then1 the ,tropic of ,cancer ,t is in the light from a little after five in the morning till almost seven in the evening2 the parallel of ,london from half an hour past four till half an hour past seven2 the polar ,circle ,u from three till nine2 and a large track round the north ,pole ,p has day all the #bd hours1 for many rotations of the ,earth on it's ,axis4 ,sidenote3 ,summer ,solstice4 ,when the ,earth comes to c1 at the beginning of ,capricorn1 and the ,sun as seen from the ,earth appears at the beginning of ,cancer1 on the #bast of ,june1 as in this ,figure1 it is in the position a in ,fig4 ,i2 and it's north ,pole inclines toward the ,sun1 so as to bring all the north frigid ,zone into the light1 and the northern parallels of ,latitude more into the light than the dark from the ,equator to the polar ,circles2 and the more so as they are farther from the ,equator4 ,the ,tropic of ,cancer is in the light from five in the morning till seven at night1 the parallel of ,london from a quarter before four till a quarter after eight2 and the polar ,circle just touches the dark1 so that the ,sun has only the lower half of his ,disc hid from the inhabitants on that ,circle for a few minutes about midnight1 supposing no inequalities in the ,horizon and no ,refractions4 ,sidenote3 ,autumnal ,equinox4 ,winter ,solstice4 ,a bare view of the ,figure is enough to shew1 that as the ,earth advances from ,capricorn toward ,aries1 and the ,sun appears to move from ,cancer toward ,libra1 the north ,pole recedes toward the dark1 which causes the days to decrease1 and the nights to increase in length1 till the ,earth comes to ,aries1 and then they are equal as before2 for the boundary of light and darkness cut the ,equator and all it's parallels equally1 or in halves4 ,the north pole then goes into the dark1 and continues therein until the ,earth goes half way round it's ,orbit2 or1 from the #bc;d of ,september till the #bjth of ,march4 ,in the middle between these times1 viz4 on the #bb;d of ,december1 the north ,pole is as far as it can be in the dark1 which is #bc-a_/b degrees1 equal to the inclination of the ,earth's ,axis from a perpendicular to it's ,orbit3 and then1 the northern parallels are as much in the dark as they were in the light on the #ba of ,june2 the winter nights being as long as the summer days1 and the winter days as short as the summer nights4 ,it is needless to multiply words on this subject1 as we shall have occasion to mention the seasons again in describing the ,orrery1 #dci4 ,only this must be noted1 that all that has been said of the northern ,hemisphere1 the contrary must be understood of the southern2 for on different sides of the ,equator the seasons are contrary1 because1 when the northern ,hemisphere inclines toward the ,sun the southern declines from him4 ,sidenote3 ,the ,phenomena of ,saturn's ,ring4 ,,plate ,v4 #bjd4 ,as ,saturn goes round the ,sun1 his obliquely posited ring1 like our ,earth's ,axis1 keeps parallel to itself1 and is therefore turned edgewise to the ,sun twice in a ,saturnian year1 which is almost as long as #cj of our years #ha4 ,but the ring1 though considerably broad1 is too thin to be seen when it is turned round edgewise to the ,sun1 at which time it is also edgewise to the ,earth2 and therefore it disappears once in every fifteen years to us4 ,as the ,sun shines half a year on the north pole of our earth1 then disappears to it1 and shines as long on the south pole2 so1 during one half of ,saturn's year the ,sun shines on the north side of his ring1 then disappears to it1 and shines as long on it's south side4 ,when the ,earth's ,axis inclines neither to nor from the ,sun1 but sidewise to him1 he instantly ceases to shine on one pole1 and begins to enlighten the other2 and when ,saturn's ,ring inclines neither to nor from the ,sun1 but sidewise to him1 he ceases to shine on the one side of it1 and begins to shine upon the other4 ,sidenote3 ,fig4 ,,iii4 ,let ,s be the ,sun1 ,,abcdefgh ,saturn's ,orbit1 and ,,iklmno the ,earth's ,orbit4 ,both ,saturn and the ,earth move according to the order of the letters1 and when ,saturn is at ,a his ring is turned edgewise to the ,sun ,s1 and he is then seen from the ,earth as if he had lost his ring1 let the ,earth be in any part of it's ,orbit whatever1 except between ,n and ,o2 for whilst it describes that space1 ,saturn is apparently so near the ,sun as to be hid in his beams4 ,as ,saturn goes from ,a to ,c his ring appears more and more open to the ,earth3 at ,c the ring appears most open of all2 and seems to grow narrower and narrower as ,saturn goes from ,c to ,e2 and when he comes to ,e1 the ring is again turned edgewise both to the ,sun and ,earth3 and as neither of it's sides are illuminated1 it is invisible to us1 because it's edge is too thin to be perceptible3 and ,saturn appears again as if he had lost his ring4 ,but as he goes from ,e to ,g1 his ring opens more and more to our view on the under side2 and seems just as open at ,g as it was at ,c2 and may be seen in the night-time from the ,earth in any part of it's ,orbit1 except about ,m1 when the ,sun hides the ,planet from our view4 ,as ,saturn goes from ,g to ,a his ring turns more and more edgewise to us1 and therefore it seems to grow narrower and narrower2 and at ,a it disappears as before4 ,hence1 while ,saturn goes from ,a to ,e the ,sun shines on the upper side of his ring1 and the under side is dark2 but whilst he goes from ,e to ,a the ,sun shines on the under side of his ring1 and the upper side is dark4 ,sidenote3 ,fig4 ,i and ,,iii4 ,it may perhaps be imagined that this ,article might have been placed more properly after #ha than here3 but when the candid reader considers that all the various ,phenomena of ,saturn's ,ring depend upon a cause similar to that of our ,earth's seasons1 he will readily allow that they are best explained together2 and that the two ,figures serve to illustrate each other4 ,sidenote3 ,,plate ,,vi4 ,the ,earth nearer the ,sun in winter than in summer4 ,why the weather is coldest when the ,earth is nearest the ,sun4 #bje4 ,the ,earth's ,orbit being elliptical1 and the ,sun constantly keeping in it's lower ,focus1 which is #a1cgg1jjj miles from the middle point of the longer ,axis1 the ,earth comes twice so much1 or #b1ged1jjj miles nearer the ,sun at one time of the year than at another3 for the ,sun appearing under a larger ,angle in our winter than summer1 proves that the ,earth is nearer the ,sun in winter1 7see the ,note on ,art4 #ahe47 ,but here1 this natural question will arise1 ,why have we not the hottest weather when the ,earth is nearest the ,sun8 ,in answer it must be observed1 that the excentricity of the ,earth's ,orbit1 or #a million #cgg miles bears no greater proportion to the ,earth's mean distance from the ,sun than #ag does to #ajjj2 and therefore1 this small difference of distance cannot occasion any great difference of heat or cold4 ,but the principal cause of this difference is1 that in winter the ,sun's rays fall so obliquely upon us1 that any given number of them is spread over a much greater portion of the ,earth's surface where we live2 and therefore each point must then have fewer rays than in summer4 ,moreover1 there comes a greater degree of cold in the long winter nights1 than there can return of heat in so short days2 and on both these accounts the cold must increase4 ,but in summer the ,sun's rays fall more perpendicularly upon us1 and therefore come with greater force1 and in greater numbers on the same place2 and by their long continuance1 a much greater degree of heat is imparted by day than can fly off by night4 ,sidenote3 ,fig4 ,,ii4 #bjf4 ,that a greater number of rays fall on the same place1 when they come perpendicularly1 than when they come obliquely on it1 will appear by the ,figure4 ,for1 let ,,ab be a certain number of the ,sun's rays falling on ,,cd 7which1 let us suppose to be ,london7 on the #bb;d of ,june3 but1 on the #bb;d of ,december1 the line ,,cd1 or ,london2 has the oblique position ,cd to the same rays2 and therefore scarce a third part of them falls upon it1 or only those between ,a and e2 all the rest e,b being expended on the space d,p1 which is more than double the length of ,,cd or ,cd4 ,besides1 those parts which are once heated1 retain the heat for some time2 which1 with the additional heat daily imparted1 makes it continue to increase1 though the ,sun declines toward the south3 and this is the reason why ,july is hotter than ,june1 although the ,sun has withdrawn from the summer ,tropic2 as we find it is generally hotter at three in the afternoon1 when the ,sun has gone toward the west1 than at noon when he is on the ,meridian4 ,likewise1 those places which are well cooled require time to be heated again2 for the ,sun's rays do not heat even the surface of any body till they have been some time upon it4 ,and therefore we find ,january for the most part colder than ,december1 although the ,sun has withdrawn from the winter ,tropic1 and begins to dart his beams more perpendicularly upon us1 when we have the position ,,cf4 ,an iron bar is not heated immediately upon being put into the fire1 nor grows cold till some time after it has been taken out4 ,,chap4 ,,xi4 ,the ,method of finding the ,longitude by the ,eclipses of ,jupiter's ,satellites3 ,the amazing ,velocity of ,light demonstrated by these ,eclipses4 ,sidenote3 ,first ,meridian1 and ,longitude of places1 what4 #bjg4 ,geographers arbitrarily choose to call the ,meridian of some remarkable place the first ,meridian4 ,there they begin their reckoning2 and just so many degrees and minutes as any other place is to the eastward or westward of that ,meridian1 so much east or west ,longitude they say it has4 ,a degree is the #cfjth part of a ,circle1 be it great or small2 and a minute the #fjth part of a degree4 ,the ,english ,geographers reckon the ,longitude from the ,meridian of the ,royal ,observatory at ,greenwich1 and the ,french from the ,meridian of ,paris4 ,sidenote3 ,,plate ,v4 ,fig4 ,,ii4 ,hour ,circles4 ,an hour of time equal to #ae degrees of motion4 #bjh4 ,if we imagine twelve great ,circles1 one of which is the ,meridian of any given place1 to intersect each other in the two ,poles of the ,earth1 and to cut the ,equator at every #aeth degree1 they will be divided by the ,poles into #bd ,semicircles which divide the ,equator into #bd equal parts2 and as the ,earth turns on it's ,axis1 the planes of these ,semicircles come successively after one another every hour to the ,sun4 ,as in an hour of time there is a revolution of #ae degrees of the ,equator1 in a minute of time there will be a revolution of #ae minutes of the ,equator1 and in a second of time a revolution of #ae seconds4 ,there are two tables annexed to this ,chapter1 for reducing mean solar time into degrees and minutes of the terrestrial ,equator2 and also for converting degrees and parts of the ,equator into mean solar time4 #bji4 ,because the ,sun enlightens only one half of the ,earth at once1 as it turns round it's ,axis he rises to some places at the same moments of absolute ,time that he sets to others2 and when it is mid-day to some places1 it is mid-night to others4 ,the ,,xii on the middle of the ,earth's enlightened side1 next the ,sun1 stands for mid-day2 and the opposite ,,xii on the middle of the dark side1 for mid-night4 ,if we suppose this ,circle of hours to be fixed in the plane of the ,equinoctial1 and the ,earth to turn round within it1 any particular ,meridian will come to the different hours so1 as to shew the true time of the day or night at all places on that ,meridian4 ,therefore1 ,sidenote3 ,and consequently to #ae degrees of ,longitude4 ,lunar ,eclipses useful in finding the ,longitude4 #baj4 ,to every place #ae degrees eastward from any given ,meridian1 it is noon an hour sooner than on that ,meridian2 because their ,meridian comes to the ,sun an hour sooner3 and to all places #ae degrees westward it is noon an hour later #bjh1 because their ,meridian comes an hour later to the ,sun2 and so on3 every #ae degrees of motion causing an hour's difference in time4 ,therefore they who have noon an hour later than we1 have their ,meridian1 that is1 their ,longitude #ae degrees westward from us2 and they who have noon an hour sooner than we1 have their ,meridian #ae degrees eastward from ours3 and so for every hour's difference of time #ae degrees difference of ,longitude4 ,consequently1 if the beginning or ending of a ,lunar ,eclipse be observed1 suppose at ,london1 to be exactly at mid-night1 and in some other place at #aa at night1 that place is #ae degrees westward from the ,meridian of ,london3 if the same ,eclipse be observed at one in the morning at another place1 that place is #ae degrees eastward from the said ,meridian4 ,sidenote3 ,eclipses of ,jupiter's ,satellites much better for that purpose4 #baa4 ,but as it is not easy to determine the exact moment either of the beginning or ending of a ,lunar ,eclipse1 because the ,earth's shadow through which the ,moon passes is faint and ill defined about the edges2 we have recourse to the ,eclipses of ,jupiter's ,satellites1 which disappear so instantaneously as they enter into ,jupiter's shadow1 and emerge so suddenly out of it1 that we may fix the phenomenon to half a second of time4 ,the first or nearest ,satellite to ,jupiter is the most advantageous for this purpose1 because it's motion is quicker than the motion of any of the rest1 and therefore it's immersions and emersions are more frequent4 ,sidenote3 ,how to solve this important problem4 ,,plate ,v4 #bab4 ,the ,english ,astronomers have made ,tables for shewing the times of the ,eclipses of ,jupiter's ,satellites to great precision1 for the ,meridian of ,greenwich4 ,now1 let an observer1 who has these ,tables with a good ,telescope and a well-regulated ,clock at any other place of the ,earth1 observe the beginning or ending of an ,eclipse of one of ,jupiter's ,satellites1 and note the precise moment of time that he saw the ,satellite either immerge into1 or emerge out of the shadow1 and compare that time with the time shewn by the ,tables for ,greenwich2 then1 #ae degrees difference of ,longitude being allowed for every hour's difference of time1 will give the ,longitude of that place from ,greenwich1 as above #baj2 and if there be any odd minutes of time1 for every minute a quarter of a degree1 east or west must be allowed1 as the time of observation is before or after the time shewn by the ,tables4 ,such ,eclipses are very convenient for this purpose at land1 because they happen almost every day2 but are of no use at sea1 because the rolling of the ship hinders all nice telescopical observations4 ,sidenote3 ,fig4 ,,ii4 ,illustrated by an example4 #bac4 ,to explain this by a ,figure1 let ,j be ,jupiter1 ,k1 ,l1 ,m1 ,n his four ,satellites in their respective ,orbits #a1 #b1 #c1 #d2 and let the ,earth be at f 7suppose in ,november1 although that month is no otherways material than to find the ,earth readily in this scheme1 where it is shewn in eight different parts of it's ,orbit47 ,let ,q be a place on the ,meridian of ,greenwich1 and ,r a place on some other ,meridian4 ,let a person at ,r observe the instantaneous vanishing of the first ,satellite ,k into ,jupiter's shadow1 suppose at three o'clock in the morning2 but by the ,tables he finds the immersion of that ,satellite to be at midnight at ,greenwich3 he can then immediately determine1 that as there are three hours difference of time between ,q and ,r1 and that ,r is three hours forwarder in reckoning than ,q1 it must be #de degrees of east ,longitude from the ,meridian of ,q4 ,were this method as practicable at sea as at land1 any sailor might almost as easily1 and with equal certainty1 find the ,longitude as the ,latitude4 ,sidenote3 ,fig4 ,,ii4 ,we seldom see the beginning and end of the same ,eclipse of any of ,jupiter's ,moons4 #bad4 ,whilst the ,earth is going from ,c to ,f in it's ,orbit1 only the immersions of ,jupiter's ,satellites into his shadow are generally seen2 and their emersions out of it while the ,earth goes from ,g to ,b4 ,indeed1 both these appearances may be seen of the second1 third1 and fourth ,satellite when eclipsed1 whilst the ,earth is between ,d and ,e1 or between ,g and ,a2 but never of the first ,satellite1 on account of the smallness of it's ,orbit and the bulk of ,jupiter2 except only when ,jupiter is directly opposite to the ,sun2 that is1 when the ,earth is at g3 and even then1 strictly speaking1 we cannot see either the immersions or emersions of any of his ,satellites1 because his body being directly between us and his conical shadow1 his ,satellites are hid by his body a few moments before they touch his shadow2 and are quite emerged from thence before we can see them1 as it were1 just dropping from him4 ,and when the ,earth is at c1 the ,sun being between it and ,jupiter hides both him and his ,moons from us4 ,in this ,diagram1 the ,orbits of ,jupiter's ,moons are drawn in true proportion to his diameter2 but1 in proportion to the ,earth's ,orbit they are drawn #ha times too large4 ,sidenote3 ,,plate ,,vi4 ,jupiter's conjunctions with the ,sun1 or oppositions to him1 are every year in different parts of the ,heavens4 #bae4 ,in whatever month of the year ,jupiter is in conjunction with the ,sun1 or in opposition to him1 in the next year it will be a month later at least4 ,for whilst the ,earth goes once round the ,sun1 ,jupiter describes a twelfth part of his ,orbit4 ,and therefore1 when the ,earth has finished it's annual period from being in a line with the ,sun and ,jupiter1 it must go as much forwarder as ,jupiter has moved in that time1 to overtake him again3 just like the minute hand of a watch1 which must1 from any conjunction with the hour hand1 go once round the dial-plate and somewhat above a twelfth part more1 to overtake the hour hand again4 ,sidenote3 ,the surprising velocity of light4 #baf4 ,it is found by observation1 that when the ,earth is between the ,sun and ,jupiter1 as at g1 his ,satellites are eclipsed about #h minutes sooner than they should be according to the ,tables3 and when the ,earth is at ,b or ,c1 these ,eclipses happen about #h minutes later than the ,tables predict them4 ,hence it is undeniably certain1 that the motion of light is not instantaneous1 since it takes about #af-a_/b minutes of time to go through a space equal to the diameter of the ,earth's ,orbit1 which is #afb millions of miles in length3 and consequently the particles of light fly about #afd thousand #did miles every second of time1 which is above a million of times swifter than the motion of a cannon bullet4 ,and as light is #af-a_/b minutes in travelling across the ,earth's ,orbit1 it must be #h-a_/d minutes in coming from the ,sun to us3 therefore1 if the ,sun were annihilated we should see him for #h-a_/d minutes after2 and if he were again created he would be #h-a_/d minutes old before we could see him4 ,sidenote3 ,fig4 ,v4 ,illustrated by a ,figure4 #bag4 ,to illustrate this progressive motion of light1 let ,a and ,b be the ,earth in two different parts of it's ,orbit1 whose distance is #ha millions of miles1 equal to the ,earth's distance from the ,sun ,s4 ,it is plain1 that if the motion of light were instantaneous1 the ,satellite #a would appear to enter into ,jupiter's shadow ,,ff at the same moment of time to a spectator in ,a as to another in ,b4 ,but by many years observations it has been found1 that the immersion of the ,satellite into the shadow is seen #h-a_/d minutes sooner when the ,earth is at ,b1 than when it is at ,a4 ,and so1 as ,mr4 ,,romer first discovered1 the motion of light is thereby proved to be progressive1 and not instantaneous1 as was formerly believed4 ,it is easy to compute in what time the ,earth moves from ,a to ,b2 for the chord of #fj degrees of any ,circle is equal to the ,semidiameter of that ,circle2 and as the ,earth goes through all the #cfj degrees of it's ,orbit in a year1 it goes through #fj of those degrees in about #fa days4 ,therefore1 if on any given day1 suppose the first of ,june1 the ,earth is at ,a1 on the first of ,august it will be at ,b3 the chord1 or straight line ,,ab1 being equal to ,,ds the ,radius of the ,earth's ,orbit1 the same with ,,as it's distance from the ,sun4 #bah4 ,as the ,earth moves from ,d to ,c1 through the side ,,ab of it's ,orbit1 it is constantly meeting the light of ,jupiter's ,satellites sooner1 which occasions an apparent acceleration of their ,eclipses3 and as it moves through the other half ,h of it's ,orbit1 from ,c to ,d1 it is receding from their light1 which occasions an apparent retardation of their ,eclipses1 because their light is then longer ere it overtakes the ,earth4 #bai4 ,that these accelerations of the immersions of ,jupiter's ,satellites into his shadow1 as the ,earth approaches towards ,jupiter1 and the retardations of their emersions out of his shadow1 as the ,earth is going from him1 are not occasioned by any inequality arising from the motions of the ,satellites in excentric ,orbits1 is plain1 because it affects them all alike1 in whatever parts of their ,orbits they are eclipsed4 ,besides1 they go often round their ,orbits every year1 and their motions are no way commensurate to the ,earth's4 ,therefore1 a ,phenomenon not to be accounted for from the real motions of the ,satellites1 but so easily deducible from the ,earth's motion1 and so answerable thereto1 must be allowed to result from it4 ,this affords one very good proof of the ,earth's annual motion4 #bbj4 ,,tables for converting mean solar ,,time into ,degrees and ,parts of the terrestrial ,,equator2 and also for converting ,degrees and ,parts of the ,,equator into mean solar ,time4 ---------------------------------------- ----- ,,table ,i4 ,for converting ,time into ,degrees and ,parts of the ,equator4 ---------------------------------------- 99,m4 ,d4 ,m4 99,m4 ,d4 ,m4 ,hours,degrees ,s4 ,m4 ,s4 ,s4 ,m4 ,s4 ,t4 ,s4 ,t4 ,t4 ,s4 ,t4 ---------------------------------------- #a #ae #a #j #ae #ca #g #de #b #cj #b #j #cj #cb #h #j #c #de #c #j #de #cc #h #ae #d #fj #d #a #j #cd #h #cj #e #ge #e #a #ae #ce #h #de ---------------------------------------- #f #ij #f #a #cj #cf #i #j #g #aje #g #a #de #cg #i #ae #h #abj #h #b #j #ch #i #cj #i #ace #i #b #ae #ci #i #de #aj #aej #aj #b #cj #dj #aj #j ---------------------------------------- #aa #afe #aa #b #de #da #aj #ae #ab #ahj #ab #c #j #db #aj #cj #ac #aie #ac #c #ae #dc #aj #de #ad #baj #ad #c #cj #dd #aa #j #ae #bbe #ae #c #de #de #aa #ae ---------------------------------------- #af #bdj #af #d #j #df #aa #cj #ag #bee #ag #d #ae #dg #aa #de #ah #bgj #ah #d #cj #dh #ab #j #ai #bhe #ai #d #de #di #ab #ae #bj #cjj #bj #e #j #ej #ab #cj ---------------------------------------- #ba #cae #ba #e #ae #ea #ab #de #bb #ccj #bb #e #cj #eb #ac #j #bc #cde #bc #e #de #ec #ac #ae #bd #cfj #bd #f #j #ed #ac #cj #be #cge #be #f #ae #ee #ac #de ---------------------------------------- #bf #cij #bf #f #cj #ef #ad #j #bg #dje #bg #f #de #eg #ad #ae #bh #dbj #bh #g #j #eh #ad #cj #bi #dce #bi #g #ae #ei #ad #de #cj #dej #cj #g #cj #fj #ae #j ---------------------------------------- ---------------------------------------- ----------- ,,table ,,ii4 ,for converting ,degrees and ,parts of the ,equator into ,time4 ---------------------------------------- ----- 99,d4 ,h4 ,m4 99,d4 ,h4 ,m4 ,m4 ,m4 ,s4 ,m4 ,m4 ,s4 ,degrees,hours,minutes ,s4 ,s4 ,t4 ,s4 ,s4 ,t4 ---------------------------------------- ----- #a #j #d #ca #b #d #gj #d #dj #b #j #h #cb #b #h #hj #e #bj #c #j #ab #cc #b #ab #ij #f #j #d #j #af #cd #b #af #ajj #f #dj #e #j #bj #ce #b #bj #aaj #g #bj ---------------------------------------- ----- #f #j #bd #cf #b #bd #abj #h #j #g #j #bh #cg #b #bh #acj #h #dj #h #j #cb #ch #b #cb #adj #i #bj #i #j #cf #ci #b #cf #aej #aj #j #aj #j #dj #dj #b #dj #afj #aj #dj ---------------------------------------- ----- #aa #j #dd #da #b #dd #agj #aa #bj #ab #j #dh #db #b #dh #ahj #ab #j #ac #j #eb #dc #b #eb #aij #ab #dj #ad #j #ef #dd #b #ef #bjj #ac #bj #ae #a #j #de #c #j #baj #ad #j ---------------------------------------- ----- #af #a #d #df #c #d #bbj #ad #dj #ag #a #h #dg #c #h #bcj #ae #bj #ah #a #ab #dh #c #ab #bdj #af #j #ai #a #af #di #c #af #bej #af #dj #bj #a #bj #ej #c #bj #bfj #ag #bj ---------------------------------------- ----- #ba #a #bd #ea #c #bd #bgj #ah #j #bb #a #bh #eb #c #bh #bhj #ah #dj #bc #a #cb #ec #c #cb #bij #ai #bj #bd #a #cf #ed #c #cf #cjj #bj #j #be #a #dj #ee #c #dj #caj #bj #dj ---------------------------------------- ----- #bf #a #dd #ef #c #dd #cbj #ba #bj #bg #a #dh #eg #c #dh #ccj #bb #j #bh #a #eb #eh #c #eb #cdj #bb #dj #bi #a #ef #ei #c #ef #cej #bc #bj #cj #b #j #fj #d #j #cfj #bd #j ---------------------------------------- ----- ,these are the ,tables mentioned in the #bjhth ,article1 and are so easy that they scarce require any farther explanation than to inform the reader1 that if1 in ,table ,i4 he reckons the columns marked with ,asterisks to be minutes of time1 the other columns give the equatoreal parts or motion in degrees and minutes2 if he reckons the ,asterisk columns to be seconds1 the others give the motion in minutes and seconds of the ,equator2 if thirds1 in seconds and thirds3 ,and if in ,table ,,ii4 he reckons the ,asterisk columns to be degrees of motion1 the others give the time answering thereto in hours and minutes2 if minutes of motion1 the time is minutes and seconds2 if seconds of motion1 the corresponding time is given in seconds and thirds4 ,an example in each case will make the whole very plain4 ,,example ,i4 ,,example ,,ii4 ,in #aj hours #ae minutes #bd ,in what time will #aec degrees seconds #bj thirds1 ,qu4 ,how #ea minutes #e seconds of the much of the ,equator revolves ,equator revolve through the through the ,meridian8 ,meridian8 ,deg4 ,m4 ,s4 ,h4 ,m4 ,s4 ,t4 ,hours #aj #aej #j #j ,deg4 #aej #aj #j #j #j ,min4 #ae #c #de #j #c #ab #j #j ,sec4 #bd #f #j ,min4 #ea #c #bd #j ,thirds #bj #e ,sec4 #e #bj ------------ ------------ ,answer #aec #ea #e ,answer #aj #ae #bd #bj ,,chap4 ,,xii4 ,of ,solar and ,sidereal ,time4 ,sidenote3 ,sidereal days shorter than solar days1 and why4 #bba4 ,the fixed ,stars appear to go round the ,earth in #bc hours #ef minutes #d seconds1 and the ,sun in #bd hours3 so that the ,stars gain three minutes #ef seconds upon the ,sun every day1 which amounts to one diurnal revolution in a year2 and therefore1 in #cfe days as measured by the returns of the ,sun to the ,meridian1 there are #cff days as measured by the ,stars returning to it3 the former are called ,solar ,days1 and the latter ,sidereal4 ,sidenote3 ,,plate ,,iii4 ,the diameter of the ,earth's ,orbit is but a physical point in proportion to the distance of the ,stars2 for which reason1 and the ,earth's uniform motion on it's ,axis1 any given ,meridian will revolve from any ,star to the same ,star again in every absolute turn of the ,earth on it's ,axis1 without the least perceptible difference of time shewn by a clock which goes exactly true4 ,if the ,earth had only a diurnal motion1 without an annual1 any given ,meridian would revolve from the ,sun to the ,sun again in the same quantity of time as from any ,star to the same ,star again2 because the ,sun would never change his place with respect to the ,stars4 ,but1 as the ,earth advances almost a degree eastward in it's ,orbit in the time that it turns eastward round its ,axis1 whatever ,star passes over the ,meridian on any day with the ,sun1 will pass over the same ,meridian on the next day when the ,sun is almost a degree short of it2 that is1 #c minutes #ef seconds sooner4 ,if the year contained only #cfj days as the ,ecliptic does #cfj degrees1 the ,sun's apparent place1 so far as his motion is equable1 would change a degree every day2 and then the sidereal days would be just four minutes shorter than the solar4 ,sidenote3 ,fig4 ,,ii4 ,let ,,abcdefghiklm be the ,earth's ,orbit1 in which it goes round the ,sun every year1 according to the order of the letters1 that is1 from west to east1 and turns round it's ,axis the same way from the ,sun to the ,sun again every #bd hours4 ,let ,s be the ,sun1 and ,r a fixed ,star at such an immense distance that the diameter of the ,earth's ,orbit bears no sensible proportion to that distance4 ,let ,nm be any particular ,meridian of the ,earth1 and ,n a given point or place upon that ,meridian4 ,when the ,earth is at ,a1 the ,sun ,s hides the ,star ,r1 which would always be hid if the ,earth never removed from ,a2 and consequently1 as the ,earth turns round it's ,axis1 the point ,n would always come round to the ,sun and ,star at the same time4 ,but when the ,earth has advanced1 suppose a twelfth part of it's ,orbit from ,a to ,b1 it's motion round it's ,axis will bring the point ,n a twelfth part of a day or two hours sooner to the ,star than to the ,sun2 for the ,angle ,n,bn is equal to the ,angle ,,asb3 and therefore1 any ,star which comes to the ,meridian at noon with the ,sun when the ,earth is at ,a1 will come to the ,meridian at #aj in the forenoon when the ,earth is at ,b4 ,when the ,earth comes to ,c the point ,n will have the ,star on it's ,meridian at #h in the morning1 or four hours sooner than it comes round to the ,sun2 for it must revolve from ,n to n1 before it has the ,sun in it's ,meridian4 ,when the ,earth comes to ,d1 the point ,n will have the ,star on it's ,meridian at six in the morning1 but that point must revolve six hours more from ,n to n1 before it has mid-day by the ,sun3 for now the ,angle ,,asd is a right ,angle1 and so is ,n,dn2 that is1 the ,earth has advanced #ij degrees in it's ,orbit1 and must turn #ij degrees on its ,axis to carry the point ,n from the ,star to the ,sun3 for the ,star always comes to the ,meridian when ,nm is parallel to ,,rsa2 because ,,ds is but a point in respect of ,,rs4 ,when the ,earth is at ,e1 the ,star comes to the ,meridian at #d in the morning2 at ,f1 at two in the morning2 and at ,g1 the ,earth having gone half round it's ,orbit1 ,n points to the ,star ,r at midnight1 being then directly opposite to the ,sun2 and therefore1 by the ,earth's diurnal motion the ,star comes to the ,meridian #ab hours before the ,sun4 ,when the ,earth is at ,h1 the ,star comes to the ,meridian at #aj in the evening2 at ,i it comes to the ,meridian at #h1 that is1 #af hours before the ,sun2 at ,k #ah hours before him2 at ,l #bj hours2 at ,m #bb2 and at ,a equally with the ,sun again4 ,a ,,table1 shewing how much of the ,celestial ,equator passes over the ,meridian in any part of a mean ,,solar ,,day2 and how much the ,,fixed ,,stars gain upon the mean ,,solar ,,time every ,day1 for a ,month4 ---------------------------------------- ---------- ,time ,motion4 ,time ,motion4 ,time ,motion4 ---------------------------------------- ---------- ,hours ,d4 ,m4 ,s4 99,m4 ,d4 ,m4 ,s4 99,m4 ,d4 ,m4 ,s4 ,s4 ,m4 ,s4 ,t4 ,s4 ,m4 ,s4 ,t4 ,t4 ,s4 ,t4 ,t4 ,s4 ,t4 ---------------------------------------- ---------- #a #ae #b #bh #a #j #ae #b #ca #g #df #af #b #cj #d #ef #b #j #cj #e #cb #h #a #ai #c #de #g #bd #c #j #de #g #cc #h #af #ba #d #fj #i #ea #d #a #j #aj #cd #h #ca #bd #e #ge #ab #ai #e #a #ae #ab #ce #h #df #bf ---------------------------------------- ---------- #f #ij #ad #dg #f #a #cj #ae #cf #i #a #bi #g #aje #ag #ae #g #a #de #ag #cg #i #af #ca #h #abj #ai #dc #h #b #j #bj #ch #i #ca #cd #i #ace #bb #aa #i #b #ae #bb #ci #i #df #cf #aj #aej #bd #ch #aj #b #cj #be #dj #aj #a #ci ---------------------------------------- ---------- #aa #afe #bg #f #aa #b #de #bg #da #aj #af #da #ab #ahj #bi #cd #ab #c #j #cj #db #aj #ca #dc #ac #aie #cb #b #ac #c #ae #cb #dc #aj #df #df #ad #baj #cd #cj #ad #c #cj #cd #dd #aa #a #dh #ae #bbe #cf #eh #ae #c #de #cg #de #aa #af #ea ---------------------------------------- ---------- #af #bdj #ci #bf #af #d #j #ci #df #aa #ca #ec #ag #bee #da #ec #ag #d #ae #da #dg #aa #df #ef #ah #bgj #dd #ba #ah #d #cj #dd #dh #ab #a #eh #ai #bhe #df #di #ai #d #de #dg #di #ab #ag #a #bj #cjj #di #ag #bj #e #j #di #ej #ab #cb #c ---------------------------------------- ---------- #ba #cae #ea #de #ba #e #ae #eb #ea #ab #dg #f #bb #ccj #ed #ac #bb #e #cj #ed #eb #ac #b #h #bc #cde #ef #dj #bc #e #de #eg #ec #ac #ag #aa #bd #cfj #ei #h #bd #f #j #ei #ed #ac #cb #ac #be #cgf #a #cf #be #f #af #b #ee #ac #dg #af ---------------------------------------- ---------- #bf #cia #d #d #bf #f #ca #d #ef #ad #b #ah #bg #djf #f #cb #bg #f #df #g #eg #ad #ag #ba #bh #dba #i #j #bh #g #a #i #eh #ad #cb #bc #bi #dcf #aa #bh #bi #g #af #aa #ei #ad #dg #bf #cj #dea #ac #ef #cj #g #ca #ad #fj #ae #b #bh ---------------------------------------- ---------- ,accelerations of the ,fixed ,stars4 -------------- ,d4 ,h4 ,m4 ,s4 -------------- #a #j #c #ef #b #j #g #eb #c #j #aa #dh #d #j #ae #dd #e #j #ai #ci -------------- #f #j #bc #ce #g #j #bg #ca #h #j #ca #bg #i #j #ce #bc #aj #j #ci #ai -------------- #aa #j #dc #ae #ab #j #dg #aa #ac #j #ea #g #ad #j #ee #c #ae #j #eh #eh -------------- #af #a #b #ed #ag #a #f #ej #ah #a #aj #df #ai #a #ad #db #bj #a #ah #ch -------------- #ba #a #bb #cd #bb #a #bf #cj #bc #a #cj #bf #bd #a #cd #bb #be #a #ch #ag -------------- #bf #a #db #ac #bg #a #df #i #bh #a #ej #e #bi #a #ed #a #cj #a #eg #eg -------------- ,sidenote3 ,,plate ,,iii4 ,an absolute ,turn of the ,earth on it's ,axis never finishes a solar day4 ,fig4 ,,ii4 #bbb4 ,thus it is plain1 that an absolute turn of the ,earth on it's ,axis 7which is always completed when the same ,meridian comes to be parallel to it's situation at any time of the day before7 never brings the same ,meridian round from the ,sun to the ,sun again2 but that the ,earth requires as much more than one turn on it's ,axis to finish a natural day1 as it has gone forward in that time2 which1 at a mean state is a #cfeth part of a ,circle4 ,hence1 in #cfe days the ,earth turns #cff times round it's ,axis2 and therefore1 as a turn of the ,earth on it's ,axis compleats a sidereal day1 there must be one sidereal day more in a year than the number of solar days1 be the number what it will1 on the ,earth1 or any other ,planet4 ,one turn being lost with respect to the number of solar days in a year1 by the ,planet's going round the ,sun2 just as it would be lost to a traveller1 who1 in going round the ,earth1 would lose one day by following the apparent diurnal motion of the ,sun3 and consequently1 would reckon one day less at his return 7let him take what time he would to go round the ,earth7 than those who remained all the while at the place from which he set out4 ,so1 if there were two ,earths revolving equably on their ,axes1 and if one remained at ,a until the other travelled round the ,sun from ,a to ,a again1 that ,earth which kept it's place at ,a would have it's solar and sidereal days always of the same length2 and so1 would have one solar day more than the other at it's return4 ,hence1 if the ,earth turned but once round it's ,axis in a year1 and if that turn was made the same way as the ,earth goes round the ,sun1 there would be continual day on one side of the ,earth1 and continual night on the other4 ,sidenote3 ,to know by the ,stars whether a ,clock goes true or not4 #bbc4 ,the first part of the preceding ,table shews how much of the celestial ,equator passes over the ,meridian in any given part of a mean solar day1 and is to be understood the same way as the ,table in the #bbjth article4 ,the latter part1 intitled1 ,accelerations of the fixed ,stars1 affords us an easy method of knowing whether or no our clocks and watches go true3 ,for if1 through a small hole in a window-shutter1 or in a thin plate of metal fixed to a window1 we observe at what time any ,star disappears behind a chimney1 or corner of a house1 at a little distance2 and if the same ,star disappears the next night #c minutes #ef seconds sooner by the clock or watch2 and on the second night1 #g minutes #eb seconds sooner2 the third night #aa minutes #dh seconds sooner2 and so on1 every night1 as in the ,table1 which shews this difference for #cj natural days1 it is an infallible ,sign that the machine goes true2 otherwise it does not go true2 and must be regulated accordingly3 and as the disappearing of a ,star is instantaneous1 we may depend on this information to half a second4 ,illustration3 ,pl4 ,,vi4 ,j4 ,ferguson inv4 et delin4 ,j4 ,mynde ,sc4 ,,chap4 ,,xiii4 ,of the ,equation of ,time4 ,sidenote3 ,the ,sun and ,clocks equal only on four days of the year4 #bbd4 ,the ,earth's motion on it's ,axis being perfectly uniform1 and equal at all times of the year1 the sidereal days are always precisely of the same length2 and so would the solar or natural days be1 if the ,earth's orbit were a perfect ,circle1 and it's ,axis perpendicular to it's orbit4 ,but the ,earth's diurnal motion on an inclined ,axis1 and it's annual motion in an elliptic orbit1 cause the ,sun's apparent motion in the ,heavens to be unequal3 for sometimes he revolves from the ,meridian to the ,meridian again in somewhat less than #bd hours1 shewn by a well regulated clock2 and at other times in somewhat more3 so that the time shewn by an equal going clock and a true ,sun-dial is never the same but on the #aeth of ,april1 the #afth of ,june1 the #cast of ,august1 and the #bdth of ,december4 ,the clock1 if it goes equally and true all the year round1 will be before the ,sun from the #bdth of ,december till the #aeth of ,april2 from that time till the #afth of ,june the ,sun will be before the clock2 from the #afth of ,june till the #cast of ,august the clock will be again before the ,sun2 and from thence to the #bdth of ,december the ,sun will be faster than the clock4 ,sidenote3 ,use of the ,equation ,table4 #bbe4 ,the ,tables of the ,equation of natural days1 at the end of the next ,chapter1 shew the time that ought to be pointed out by a well regulated clock or watch every day of the year at the precise moment of solar noon2 that is1 when the ,sun's centre is on the ,meridian1 or when a true ,sun-dial shews it to be precisely ,twelve4 ,thus1 on the #eth of ,january in ,leap-year1 when the ,sun is on the ,meridian1 it ought to be #e minutes #ea seconds past twelve by the clock2 and on the #aeth of ,may1 when the ,sun is on the ,meridian1 the time by the clock should be but #ee minutes #eg seconds past eleven2 in the former case1 the clock is #e minutes #ea seconds beforehand with the ,sun2 and in the latter case1 the ,sun is #d minutes #c seconds faster than the clock4 ,the column at the right hand of each month shews the daily difference of this equation1 as it increases or decreases4 ,but without a ,meridian ,line1 or a ,transit-,instrument fixed in the plane of the ,meridian1 we cannot set a ,sun-dial true4 ,sidenote3 ,how to draw a ,meridian ,line4 #bbf4 ,the easiest and most expeditious way of drawing a ,meridian ,line is this3 ,make four or five concentric ,circles1 about a quarter of an inch from one another1 on a flat board about a foot in breadth2 and let the outmost ,circle be but little less than the board will contain4 ,fix a pin perpendicularly in the center1 and of such a length that it's whole shadow may fall within the innermost ,circle for at least four hours in the middle of the day4 ,the pin ought to be about an eighth part of an inch thick1 with a round blunt point4 ,the board being set exactly level in a place where the ,sun shines1 suppose from eight in the morning till four in the afternoon1 about which hours the end of the shadow should fall without all the ,circles2 watch the times in the forenoon1 when the extremity of the shortening shadow just touches the several ,circles1 and there make marks4 ,then1 in the afternoon of the same day1 watch the lengthening shadow1 and where it's end touches the several ,circles in going over them1 make marks also4 ,lastly1 with a pair of compasses1 find exactly the middle point between the two marks on any ,circle1 and draw a straight line from the center to that point2 which ,line will be covered at noon by the shadow of a small upright wire1 which should be put in the place of the pin4 ,the reason for drawing several ,circles is1 that in case one part of the day should prove clear1 and the other part somewhat cloudy1 if you miss the time when the point of the shadow should touch one ,circle1 you may perhaps catch it in touching another4 ,the best time for drawing a ,meridian ,line in this manner is about the middle of summer2 because the ,sun changes his ,declination slowest and his ,altitude fastest in the longest days4 ,if the casement of a window on which the ,sun shines at noon be quite upright1 you may draw a line along the edge of it's shadow on the floor1 when the shadow of the pin is exactly on the ,meridian ,line of the board3 and as the motion of the shadow of the casement will be much more sensible on the ,floor1 than that of the shadow of the pin on the board1 you may know to a few seconds when it touches the ,meridian ,line on the floor1 and so regulate your clock for the day of observation by that line and the ,equation ,tables above-mentioned #bbe4 ,sidenote3 ,equation of natural days explained4 #bbg4 ,as the ,equation of time1 or difference between the time shewn by a well regulated ,clock and a true ,sun-dial1 depends upon two causes1 namely1 the obliquity of the ,ecliptic1 and the unequal motion of the ,earth in it1 we shall first explain the effects of these causes separately considered1 and then the united effects resulting from their combination4 ,sidenote3 ,,plate ,,vi4 ,the first part of the ,equation of time4 #bbh4 ,the ,earth's motion on it's ,axis being perfectly equable1 or always at the same rate1 and the #eeplane of the ,equator being perpendicular to it's ,axis1 'tis evident that in equal times equal portions of the ,equator pass over the ,meridian2 and so would equal portions of the ,ecliptic if it were parallel to or coincident with the ,equator4 ,but1 as the ,ecliptic is oblique to the ,equator1 the equable motion of the ,earth carries unequal portions of the ,ecliptic over the ,meridian in equal times1 the difference being proportionate to the obliquity2 and as some parts of the ,ecliptic are much more oblique than others1 those differences are unequal among themselves4 ,therefore1 if two ,suns should start either from the beginning of ,aries or ,libra1 and continue to move through equal arcs in equal times1 one in the ,equator1 and the other in the ,ecliptic1 the equatoreal ,sun would always return to the ,meridian in #bd hours time1 as measured by a well regulated clock2 but the ,sun in the ,ecliptic would return to the ,meridian sometimes sooner1 and sometimes later than the equatoreal ,sun2 and only at the same moments with him on four days of the year2 namely1 the #bjth of ,march1 when the ,sun enters ,aries2 the #bast of ,june1 when he enters ,cancer2 the #bc;d of ,september1 when he enters ,libra2 and the #bast of ,december1 when he enters ,capricorn4 ,but1 as there is only one ,sun1 and his apparent motion is always in the ,ecliptic1 let us henceforth call him the real ,sun1 and the other which is supposed to move in the ,equator the fictitious2 to which last1 the motion of a well regulated clock always answers4 ,sidenote3 ,fig4 ,,iii4 ,let ,zz be the ,earth1 ,z,f,rz it's ,axis1 abcde c4 the ,equator1 ,,abcde c4 the northern half of the ,ecliptic from to on the side of the ,globe next the eye1 and ,,mnop c4 the southern half on the opposite side from to 4 ,let the points at ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 c4 quite round from to again bound equal portions of the ,ecliptic1 gone through in equal times by the real ,sun2 and those at a1 b1 c1 d1 e1 f1 c4 equal portions of the ,equator described in equal times by the fictitious ,sun2 and let ,zz be the ,meridian4 ,as the real ,sun moves obliquely in the ,ecliptic1 and the fictitious ,sun directly in the ,equator1 with respect to the ,meridian1 a degree1 or any number of degrees1 between and ,f on the ,ecliptic1 must be nearer the ,meridian ,zz1 than a degree1 or any corresponding number of degrees on the ,equator from to f2 and the more so1 as they are the more oblique3 and therefore the true ,sun comes sooner to the ,meridian whilst he is in the quadrant ,f1 than the fictitious ,sun does in the quadrant f2 for which reason1 the solar noon precedes noon by the ,clock1 until the real ,sun comes to ,f1 and the fictitious to f2 which two points1 being equidistant from the ,meridian1 both ,suns will come to it precisely at noon by the ,clock4 ,whilst the real ,sun describes the second quadrant of the ,ecliptic ,,fghikl from to 2 he comes later to the ,meridian every day1 than the fictitious ,sun moving through the second quadrant of the ,equator from f to 2 for the points at ,g1 ,h1 ,i1 ,k1 and ,l being farther from the ,meridian than their corresponding points at g1 h1 i1 k1 and l1 they must be later of coming to it3 and as both ,suns come at the same moment to the point 1 they come to the ,meridian at the moment of noon by the ,clock4 ,in departing from ,libra1 through the third quadrant1 the real ,sun going through ,,mnopq towards at ,r1 and the fictitious ,sun through mnopq towards r1 the former comes to the ,meridian every day sooner than the latter1 until the real ,sun comes to 1 and the fictitious to r1 and then they both come to the ,meridian at the same time4 ,lastly1 as the real ,sun moves equably through ,,stuvw1 from towards 2 and the fictitious ,sun through stuvw1 from r towards 1 the former comes later every day to the ,meridian than the latter1 until they both arrive at the point 1 and then they make noon at the same time with the clock4 ,sidenote3 ,a ,table of the ,equation of ,time depending on the ,sun's place in the ,ecliptic4 ,,plate ,,vi4 #bbi4 ,the annexed ,table shews how much the ,sun is faster or slower than the clock ought to be1 so far as the difference depends upon the obliquity of the ,ecliptic2 of which the ,signs of the first and third quadrants are at the head of the ,table1 and their ,degrees at the left hand2 and in these the ,sun is faster than the ,clock3 the ,signs of the second and fourth quadrants are at the foot of the ,table1 and their degrees at the right hand2 in all which the ,sun is slower than the ,clock3 so that entering the ,table with the given ,sign of the ,sun's place at the head of the ,table1 and the ,degree of his place in that ,sign at the left hand2 or with the given ,sign at the foot of the ,table1 and ,degree at the right hand2 in the ,angle of meeting is the number of minutes and seconds that the ,sun is faster or slower than the clock3 or in other words1 the quantity of time in which the real ,sun1 when in that part of the ,ecliptic1 comes sooner or later to the ,meridian than the fictitious ,sun in the ,equator4 ,thus1 when the ,sun's place is ,taurus #ab degrees1 he is #i minutes #di seconds faster than the clock2 and when his place is ,cancer #ah degrees1 he is #f minutes #b seconds slower4 ---------------------------------------- ----- ,sun faster than the ,clock in ---------------------------------------- - #ast ,q4 #c;d ,q4 -------------------------------- ,degrees ,deg4 ---------------------------------------- - #j #j #j #h #bd #h #df #cj #a #j #bj #h #ce #h #cf #bi #b #j #dj #h #de #h #be #bh #c #a #j #h #ed #h #ad #bg #d #a #ai #i #c #h #a #bf #e #a #ci #i #aa #g #di #be #f #a #ei #i #ah #g #ce #bd #g #b #ah #i #bd #g #ba #bc #h #b #cg #i #ca #g #f #bb #i #b #ef #i #cf #f #ea #ba #aj #c #af #i #da #f #ce #bj #aa #c #cd #i #de #f #ai #ai #ab #c #ec #i #di #f #b #ah #ac #d #aa #i #ea #e #de #ag #ad #d #bi #i #ec #e #bg #af #ae #d #dg #i #ed #e #i #ae #af #e #d #i #ee #d #ej #ad #ag #e #ba #i #ee #d #ca #ac #ah #e #ch #i #ed #d #ab #ab #ai #e #ed #i #eb #c #eb #aa #bj #f #aj #i #ej #c #cb #aj #ba #f #bf #i #dg #c #ab #i #bb #f #da #i #dc #b #ea #h #bc #f #ee #i #ch #b #cj #g #bd #g #i #i #cc #b #i #f #be #g #bc #i #bg #a #dh #e #bf #g #cf #i #bj #a #bg #d #bg #g #di #i #ac #a #e #c #bh #h #a #i #e #j #dc #b #bi #h #ac #h #ef #j #bb #a #cj #h #bd #h #df #j #j #j ---------------------------------------- - #b;d ,q4 ,deg4 #dth ,q4 ---------------------------------------- - ,sun slower than the ,clock in ---------------------------------------- ----- ,sidenote3 ,fig4 ,,iii4 #bcj4 ,this part of the ,equation of time may perhaps be somewhat difficult to understand by a ,figure1 because both halves of the ,ecliptic seem to be on the same side of the ,globe2 but it may be made very easy to any person who has a real ,globe before him1 by putting small patches on every tenth or fifteenth degree both of the ,equator and ,ecliptic2 and then1 turning the ball slowly round westward1 he will see all the patches from ,aries to ,cancer come to the brazen ,meridian sooner than the corresponding patches on the ,equator2 all those from ,cancer to ,libra will come later to the ,meridian than their corresponding patches on the ,equator2 those from ,libra to ,capricorn sooner1 and those from ,capricorn to ,aries later3 and the patches at the beginnings of ,aries1 ,cancer1 ,libra1 and ,capricorn1 being also on the ,equator1 shew that the two ,suns meet there1 and come to the ,meridian together4 ,sidenote3 ,a machine for shewing the sidereal1 the equal1 and the solar ,time4 ,,plate ,,vi4 #bca4 ,let us suppose that there are two little balls moving equably round a celestial ,globe by clock-work1 one always keeping in the ,ecliptic1 and gilt with gold1 to represent the real ,sun2 and the other keeping in the ,equator1 and silvered1 to represent the fictitious ,sun3 and that whilst these balls move once1 round the ,globe according to the order of ,signs1 the ,clock turns the ,globe #cff times round it's ,axis westward4 ,the ,stars will make #cff diurnal revolutions from the brasen ,meridian to it again2 and the two balls representing the real and fictitious ,sun always going farther eastward from any given ,star1 will come later than it to the ,meridian every following day2 and each ball will make #cfe revolutions to the ,meridian2 coming equally to it at the beginnings of ,aries1 ,cancer1 ,libra1 and ,capricorn3 but in every other point of the ,ecliptic1 the gilt ball will come either sooner or later to the ,meridian than the silvered ball1 like the patches above-mentioned4 ,this would be a pretty-enough way of shewing the reason why any given ,star1 which1 on a certain day of the year1 comes to the ,meridian with the ,sun1 passes over it so much sooner every following day1 as on that day twelvemonth to come to the ,meridian with the ,sun again2 and also to shew the reason why the real ,sun comes to the ,meridian sometimes sooner1 sometimes later1 than it is noon by the clock2 and1 on four days of the year1 at the same time2 whilst the fictitious ,sun always comes to the ,meridian when it is twelve at noon by the clock4 ,this would be no difficult task for an artist to perform2 for the gold ball might be carried round the ,ecliptic by a wire from it's north ,pole1 and the silver ball round the ,equator by a wire from it's south ,pole1 with a few wheels to each2 which might be easily added to my improvement of the celestial ,globe1 described in ,no #dhc of the ,philosophical ,transactions2 and of which ,i shall give a description in the latter part of this ,book1 from the #c;d ,figure of the #c;d plate4 ,sidenote3 ,fig4 ,,iii4 #bcb4 ',tis plain that if the ,ecliptic were more obliquely posited to the ,equator1 as the dotted ,circle x1 the equal divisions from to x would come still sooner to the ,meridian ,z#j than those marked ,a1 ,b1 ,c1 ,d1 and ,e do3 for two divisions containing #cj degrees1 from to the second dott1 a little short of the figure #a1 come sooner to the ,meridian than one division containing only #ae degrees from to ,a does1 as the ,ecliptic now stands2 and those of the second quadrant from x to would be so much later4 ,the third quadrant would be as the first1 and the fourth as the second4 ,and it is likewise plain1 that where the ,ecliptic is most oblique1 namely about ,aries and ,libra1 the difference would be greatest3 and least about ,cancer and ,capricorn1 where the obliquity is least4 ,sidenote3 ,the second part of the ,equation of ,time4 ,,plate ,,vi4 #bcd4 ,having explained one cause of the difference of time shewn by a well-regulated ,clock and a true ,sun-dial2 and considered the ,sun1 not the ,earth1 as moving in the ,ecliptic2 we now proceed to explain the other cause of this difference1 namely1 the inequality of the ,sun's apparent motion #bje1 which is slowest in summer1 when the ,sun is farthest from the ,earth1 and swiftest in winter when he is nearest to it4 ,but the ,earth's motion on it's ,axis is equable all the year round1 and is performed from west to east2 which is the way that the ,sun appears to change his place in the ,ecliptic4 #bce4 ,if the ,sun's motion were equable in the ,ecliptic1 the whole difference between the equal time as shewn by a ,clock1 and the unequal time as shewn by the ,sun1 would arise from the obliquity of the ,ecliptic4 ,but the ,sun's motion sometimes exceeds a degree in #bd hours1 though generally it is less3 and when his motion is slowest any particular ,meridian will revolve sooner to him than when his motion is quickest2 for it will overtake him in less time when he advances a less space than when he moves through a larger4 #bcf4 ,now1 if there were two ,suns moving in the plane of the ,ecliptic1 so as to go round it in a year2 the one describing an equal arc every #bd hours1 and the other describing sometimes a less arc in #bd hours1 and at other times a larger2 gaining at one time of the year what it lost at the opposite2 'tis evident that either of these ,suns would come sooner or later to the ,meridian than the other as it happened to be behind or before the other3 and when they were both in conjunction they would come to the ,meridian at the same moment4 ,sidenote3 ,fig4 ,,iv4 #bcg4 ,as the real ,sun moves unequably in the ,ecliptic1 let us suppose a fictitious ,sun to move equably in it4 ,let ,,abcd be the ,ecliptic or ,orbit in which the real ,sun moves1 and the dotted ,circle abcd the imaginary ,orbit of the fictitious ,sun2 each going round in a year according to the order of letters1 or from west to east4 ,let ,,hikl be the ,earth turning round it's ,axis the same way every #bd hours2 and suppose both ,suns to start from ,a and a1 in a right line with the plane of the ,meridian ,,eh1 at the same moment3 the real ,sun at ,a1 being then at his greatest distance from the ,earth1 at which time his motion is slowest2 and the fictitious ,sun at a1 whose motion is always equable because his distance from the ,earth is supposed to be always the same4 ,in the time that the ,meridian revolves from ,h to ,h again1 according to the order of the letters ,,hikl1 the real ,sun has moved from ,a to ,f2 and the fictitious with a quicker motion from a to f1 through a larger arc3 therefore1 the ,meridian ,,eh will revolve sooner from ,h to h under the real ,sun at ,f1 than from ,h to k under the fictitious ,sun at f2 and consequently it will be noon by the ,sun-dial sooner than by the ,clock4 ,sidenote3 ,,plate ,,vi4 ,as the real ,sun moves from ,a towards ,c1 the swiftness of his motion increases all the way to ,c1 where it is at the quickest4 ,but notwithstanding this1 the fictitious ,sun gains so much upon the real1 soon after his departing from ,a1 that the increasing velocity of the real ,sun does not bring him up with the equally moving fictitious ,sun till the former comes to ,c1 and the latter to c1 when each has gone half round it's respective orbit2 and then being in conjunction1 the ,meridian ,,eh revolving to ,,ek comes to both ,suns at the same time1 and therefore it is noon by them both at the same moment4 ,but the increased velocity of the real ,sun1 now being at the quickest1 carries him before the fictitious2 and therefore1 the same ,meridian will come to the fictitious ,sun sooner than to the real3 for whilst the fictitious ,sun moves from c to g1 the real ,sun moves through a greater arc from ,c to ,g3 consequently the point ,k has it's fictitious noon when it comes to k1 but not it's real noon till it comes to l4 ,and although the velocity of the real ,sun diminishes all the way from ,c to ,a1 and the fictitious ,sun by an equable motion is still coming nearer to the real ,sun1 yet they are not in conjunction till the one comes to ,a and the other to a2 and then it is noon by them both at the same moment4 ,and thus it appears1 that the real noon by the ,sun is always later than the fictitious noon by the clock whilst the ,sun goes from ,c to ,a1 sooner whilst he goes from ,a to ,c1 and at these two points the ,sun and ,clock being equal1 it is noon by them both at the same moment4 ,sidenote3 ,apogee1 ,perigee1 and ,apsides1 what4 ,fig4 ,,iv4 #bch4 ,the point ,a is called the ,sun's ,apogee1 because when he is there he is at his greatest distance from the ,earth2 the point ,c his ,perigee1 because when in it he is at his least distance from the ,earth3 and a right line1 as ,,aec1 drawn through the ,earth's center1 from one of these points to the other1 is called the line of the ,apsides4 ,sidenote3 ,mean ,anomaly1 what4 #bci4 ,the distance that the ,sun has gone in any time from his ,apogee 7not the distance he has to go to it though ever so little7 is called his mean ,anomaly1 and is reckoned in ,signs and ,degrees1 allowing #cj ,degrees to a ,sign4 ,thus1 when the ,sun has gone suppose #agd degrees from his ,apogee at ,a1 he is said to be #e ,signs #bd ,degrees from it1 which is his mean ,anomaly3 and when he is gone suppose #cee degrees from his ,apogee1 he is said to be #aa ,signs #be ,degrees from it1 although he be but #e ,degrees short of ,a in coming round to it again4 #bdj4 ,from what was said above it appears1 that when the ,sun's ,anomaly is less than #f ,signs1 that is1 when he is any where between ,a and ,c1 in the half ,,abc of his orbit1 the true noon precedes the fictitious2 but when his ,anomaly is more than #f ,signs1 that is1 when he is any where between ,c and ,a1 in the half ,,cda of his ,orbit1 the fictitious noon precedes the true4 ,when his ,anomaly is #j ,signs #j ,degrees1 that is1 when he is in his ,apogee at ,a2 or #f ,signs #j ,degrees1 which is when he is in his ,perigee at ,c2 he comes to the ,meridian at the moment that the fictitious ,sun does1 and then it is noon by them both at the same instant4 ---------------------------------------- ------------------ ,sun faster than the ,clock if his ,anomaly be ---------------------------------------- ----------- #j ,signs #a #b #c #d #e ,d4 ---------------------------------------- --- ---------------------------------------- ----------- #j #j #j #c #dh #f #ci #g #de #f #dg #c #eg #cj #a #j #h #c #ee #f #dc #g #de #f #dc #c #ej #bi #b #j #af #c #b #f #dg #g #de #f #ci #c #dc #bh #c #j #bd #d #i #f #ea #g #de #f #ce #c #ce #bg #d #j #cb #d #af #f #ed #g #de #f #cj #c #bh #bf #e #j #dj #d #bb #f #eh #g #dd #f #bf #c #bj #be #f #j #dh #d #bi #g #a #g #dd #f #ba #c #ac #bd #g #j #ef #d #ce #g #e #g #dc #f #af #c #e #bc #h #a #c #d #db #g #h #g #db #f #aa #b #eh #bb #i #a #aa #d #dh #g #aa #g #da #f #f #b #ej #ba #aj #a #ai #d #ed #g #ad #g #dj #f #a #b #db #bj #aa #a #bg #e #j #g #ag #g #ch #e #ef #b #ce #ai #ab #a #ce #e #f #g #bj #g #cg #e #ea #b #bg #ah #ac #a #dc #e #ab #g #bb #g #ce #e #de #b #ai #ag #ad #a #ej #e #ah #g #be #g #cd #e #dj #b #aa #af #ae #a #eh #e #bd #g #bg #g #cb #e #cd #b #c #ae #af #b #f #e #cj #g #bi #g #cj #e #bh #a #ee #ad #ag #b #ac #e #ce #g #ca #g #bh #e #bb #a #dg #ac #ah #b #ba #e #da #g #cc #g #be #e #af #a #ci #ab #ai #b #bh #e #df #g #ce #g #bc #e #aj #a #ca #aa #bj #b #cf #e #eb #g #cf #g #bj #e #d #a #bb #aj #ba #b #dc #e #eg #g #ch #g #ah #d #eh #a #ad #i #bb #b #ea #f #b #g #ci #g #ae #d #ea #a #f #h #bc #b #eh #f #g #g #da #g #ab #d #de #j #eh #g #bd #c #f #f #ab #g #db #g #i #d #ch #j #ej #f #be #c #ac #f #af #g #dc #g #e #d #ca #j #da #e #bf #c #bj #f #ba #g #dc #g #b #d #be #j #cc #d #bg #c #bg #f #bf #g #dd #f #eh #d #ah #j #be #c #bh #c #cd #f #cj #g #dd #f #ee #d #aa #j #ag #b #bi #c #da #f #cd #g #de #f #ea #d #d #j #h #a #cj #c #dh #f #ci #g #de #f #dg #c #eg #j #j #j ---------------------------------------- ----------- #aa ,signs #aj #i #h #g #f ,d4 ---------------------------------------- ----------- ,sun slower than the ,clock if his ,anomaly be ---------------------------------------- ------------------ ,sidenote3 ,a ,table of the ,equation of ,time1 depending on the ,sun's ,anomaly4 #bda4 ,the annexed ,table shews the ,variation1 or ,equation of time depending on the ,sun's ,anomaly1 and arising from his unequal motion in the ,ecliptic2 as the former ,table #bbi shews the ,variation depending on the ,sun's place1 and resulting from the obliquity of the ,ecliptic3 this is to be understood the same way as the other1 namely1 that when the ,signs are at the head of the ,table1 the ,degrees are at the left hand2 but when the ,signs are at the foot of the ,table the respective ,degrees are at the right hand2 and in both cases the ,equation is in the ,angle of meeting4 ,when both the above-mentioned ,equations are either faster or slower1 their sum is the absolute ,equation of ,time2 but when the one is faster1 and the other slower1 it is their difference4 ,thus1 suppose the ,equation depending on the ,sun's place1 be #f minutes #da seconds too slow1 and the ,equation depending on the ,sun's ,anomaly1 be #d minutes #bj seconds too slow1 their ,sun is #aa minutes #a second too slow4 ,but if the one had been #f minutes #da seconds too fast1 and the other #d minutes #bj seconds too slow1 their difference had been #b minutes #ba seconds too fast1 because the greater quantity is too fast4 #bdb4 ,the obliquity of the ,ecliptic to the ,equator1 which is the first mentioned cause of the ,equation of ,time1 would make the ,sun and ,clocks agree on four days of the year2 which are1 when the ,sun enters ,aries1 ,cancer1 ,libra1 and ,capricorn3 but the other cause1 now explained1 would make the ,sun and ,clocks equal only twice in a year2 that is1 when the ,sun is in his ,apogee and ,perigee4 ,consequently1 when these two points fall in the beginnings of ,cancer and ,capricorn1 or of ,aries and ,libra1 they concur in making the ,sun and ,clocks equal in these points4 ,but the ,apogee at present is in the #ith degree of ,cancer1 and the ,perigee in the #ith degree of ,capricorn2 and therefore the ,sun and ,clocks cannot be equal about the beginning of these ,signs1 nor at any time of the year1 except when the swiftness or slowness of ,equation resulting from one cause just balances the slowness or swiftness arising from the other4 #bdc4 ,the last ,table but one1 at the end of this ,chapter1 shews the ,sun's place in the ,ecliptic at the noon of every day by the clock1 for the second year after leap-year2 and also the ,sun's ,anomaly to the nearest degree1 neglecting the odd minutes of a degree4 ,their use is only to assist in shewing the method of making a general ,equation ,table from the two fore-mentioned ,tables of ,equation depending on the ,sun's ,place and ,anomaly #bbi1 #bda2 concerning which method we shall give a few examples presently4 ,the following ,tables are such as might be made from these two2 and shew the absolute ,equation of ,time resulting from the combination of both it's causes2 in which the minutes1 as well as degrees1 both of the ,sun's ,place and ,anomaly are considered4 ,the use of these ,tables is already explained1 #bbe2 and they serve for every day in leap-year1 and the first1 second1 and third years after3 ,for on most of the same days of all these years the ,equation differs1 because of the odd six hours more than the #cfe days of which the year consists4 ,sidenote3 ,examples for making ,equation ,tables4 ,,example ,i4 ,on the #aeth of ,april the ,sun is in the #beth degree of ,aries1 and his ,anomaly is #i ,signs #ae ,degrees2 the ,equation resulting from the former is #g minutes #bc seconds of time too fast #bbi2 and from the latter1 #g minutes #bg seconds too slow1 #bda2 the difference is #d seconds that the ,sun is too slow at the noon of that day2 taking it in gross for the degrees of the ,sun's ,place and ,anomaly1 without making proportionable allowance for the odd minutes4 ,hence1 at noon the swiftness of the one ,equation balancing so nearly the slowness of the other1 makes the ,sun and ,clocks equal on some part of that day4 ,,example ,,ii4 ,on the #afth of ,june1 the ,sun is in the #beth degree of ,gemini1 and his ,anomaly is #aa ,signs #af ,degrees2 the ,equation arising from the former is #a minute #dh seconds too fast2 and from the latter #a minute #ej seconds too slow2 which balancing one another at noon to #b seconds1 the ,sun and ,clocks are again equal on that day4 ,,example ,,iii4 ,on the #cast of ,august the ,sun's place is #g degrees #eb minutes of ,virgo 7which we shall call the #hth degree1 as it is so near7 and his ,anomaly is #b ,signs #j ,degrees2 the ,equation arising from the former is #f minutes #da seconds too slow2 and from the latter #f minutes #ci seconds too fast2 the difference being only #b seconds too slow at noon1 and decreasing towards an equality will make the ,sun and ,clocks equal in the afternoon of that day4 ,,example4 ,,iv4 ,on the #bc;d of ,december the ,sun's place is #a degree #da minutes 7call it #b degrees7 of ,capricorn1 and his ,anomaly is #e ,signs #bc ,degrees2 the ,equation for the former is #dc seconds too slow1 and for the latter #eh seconds too fast2 the difference is #ae seconds too fast at noon2 which decreasing will come to an equality1 and so make the ,sun and ,clocks equal in the evening of that day4 ,and thus we find1 that on some part of each of the above-mentioned four days1 the ,sun and ,clocks are equal2 but if we work examples for all other days of the year we shall find them different4 ,and1 ,sidenote3 ,remark4 #bdd4 ,on those days which are equidistant from any ,equinox or ,solstice1 we do not find that the ,equation is as much too fast or too slow1 on the one side1 as it is too slow or too fast on the other4 ,the reason is1 that the line of the ,apsides #bch1 does not1 at present1 fall either into the ,equinoctial or ,solsticial points #bdb4 ,sidenote3 ,the reason why ,equation ,tables are but temporary4 #bde4 ,if the line of the ,apsides1 together with the ,equinoctial and ,solsticial points1 were immoveable1 a general ,equation ,table might be made from the preceding ,equation ,tables1 which would always keep true1 because these ,tables themselves are permanent4 ,but1 with respect to the fixed ,stars1 the line of the ,apsides moves forwards #ab seconds of a degree every year1 and the above points #ej seconds backward4 ,so that if in any given year1 the ,equinoctial points1 and line of the ,apsides were coincident1 in #ajj years afterward they would be separated #a degree #dc minutes #bj seconds2 and consequently in #ebbe4h years they would be separated #ij degrees1 and could not meet again1 so that the same ,equinoctial point should fall again into the ,apogee in less than #bj1ijc years3 and this is the shortest ,period in which the ,equation of ,time can be restored to the same state again1 with respect to the same seasons of the year4 ,,chap4 ,,xiv4 ,of the ,precession of the ,equinoxes4 #bdf4 ,it has been already observed1 #aaf1 that by the ,earth's motion on it's ,axis1 there is more matter accumulated all round the equatoreal parts than any where else on the ,earth4 ,the ,sun and ,moon1 by attracting this redundancy of matter1 bring the ,equator sooner under them in every return towards it than if there was no such accumulation4 ,therefore1 if the ,sun sets out1 as from any ,star1 or other fixed point in the ,heavens1 the moment he is departing from the ,equinoctial or either ,tropic1 he will come to the same again before he compleats his annual course1 so as to arrive at the same fixed ,star or ,point from whence he set out4 ,when the ,sun arrives at the same #ef;,equinoctial or ,solstitial ,point1 he finishes what we call the ,tropical ,year1 which1 by long observation1 is found to contain #cfe days #e hours #dh minutes #eg seconds3 and when he arrives at the same fixed ,star again1 as seen from the ,earth1 he compleats the ,sidereal ,year2 which is found to contain #cfe days #f hours #i minutes #ad-a_/b seconds4 ,the ,sidereal ,year is therefore #bj minutes #ag-a_/b seconds longer than the ,solar or ,tropical year1 and #i minutes #ad-a_/b seconds longer than the ,julian or ,civil year1 which we state at #cfe days #f hours3 so that the ,civil year is almost a mean betwixt the ,sidereal and ,tropical4 ,sidenote3 ,,plate ,,vi4 #bdg4 ,as the ,sun describes the whole ,ecliptic1 or #cfj degrees1 in a ,tropical year1 he moves #ei #h of a degree every day2 and consequently #ej of a degree in #bj minutes #ag-a_/b seconds of time3 therefore1 he will arrive at the same ,equinox or ,solstice when he is #ej of a degree short of the same ,star or fixed point in the ,heavens from which he set out in the year before4 ,so that1 with respect to the fixed ,stars1 the ,sun and ,equinoctial points fall back 7as it were7 #cj degrees in #bafj years2 which will make the ,stars appear to have gone #cj deg4 forward1 with respect to the ,signs of the ,ecliptic in that time3 for the same ,signs always keep in the same points of the ,ecliptic1 without regard to the constellations4 ---------------------------------------- -------------------------- ,a ,,table shewing the ,precession of the ,equinoctial ,points in the ,heavens1 both in ,motion and ,time2 and the ,anticipation of the ,equinoxes on ,earth4 ---------------------------------------- ----------------------- ,precession of the ,equinoctial ,anticipation of ,points in the ,heavens4 the ,equinoxes ,julian ------------------------------------- on the ,earth4 years4 ,motion4 ,time4 ---------------------------------------- -------------- ,s4 ,days ,h4 ,m4 ,s4 ,d4 ,h4 ,m4 ,s4 ---------------------------------------- ---------------------- #a #j #j #j #ej #j #j #bj #ag-a_/b #j #j #aa #c #b #j #j #a #dj #j #j #dj #ce #j #j #bb #f #c #j #j #b #cj #j #a #j #eb-a_/b #j #j #cc #i #d #j #j #c #bj #j #a #ba #aj #j #j #dd #ab #e #j #j #d #aj #j #a #da #bg-a_/b #j #j #ee #ae ---------------------------------------- ---------------------- #f #j #j #e #j #j #b #a #de #j #a #f #ah #g #j #j #e #ej #j #b #bb #b-a_/b #j #a #ag #ba #h #j #j #f #dj #j #b #db #bj #j #a #bh #bd #i #j #j #g #cj #j #c #b #cg-a_/b #j #a #ci #bg #aj #j #j #h #bj #j #c #bb #ee #j #a #ej #cj ---------------------------------------- ---------------------- #bj #j #j #af #dj #j #f #de #ej #j #c #da #j #cj #j #j #be #j #j #aj #h #de #j #e #ca #cj #dj #j #j #cc #bj #j #ac #ca #dj #j #g #bb #j #ej #j #j #da #dj #j #af #ed #ce #j #i #ab #cj #fj #j #j #ej #j #j #bj #ag #cj #j #aa #c #j ---------------------------------------- ---------------------- #gj #j #j #eh #bj #j #bc #dj #be #j #ab #ec #cj #hj #j #a #f #dj #a #c #c #bj #j #ad #dd #j #ij #j #a #ae #j #a #f #bf #ae #j #af #cd #cj #ajj #j #a #bc #bj #a #i #di #aj #j #ah #be #j #bjj #j #b #df #dj #b #ai #ch #bj #a #ab #ej #j ---------------------------------------- ---------------------- #cjj #j #d #aj #j #d #e #bg #cj #b #g #ae #j #djj #j #e #cc #bj #e #ae #af #dj #c #a #dj #j #ejj #j #f #ef #dj #g #a #e #ej #c #bj #e #j #fjj #j #h #bj #j #h #aj #ee #j #d #ad #cj #j #gjj #j #i #dc #bj #i #bj #dd #aj #e #h #ee #j ---------------------------------------- ---------------------- #hjj #j #aa #f #dj #aa #f #cc #bj #f #c #bj #j #ijj #j #ab #bi #j #ab #af #bb #cj #f #ba #de #j #ajjj #j #ac #ec #bj #ad #b #aa #dj #g #af #aj #j #bjjj #j #bg #df #dj #bh #d #bc #bj #ae #h #bj #j #cjjj #a #aa #dj #j #db #f #ce #j #bc #j #cj #j ---------------------------------------- ---------------------- #djjj #a #be #cc #bj #ef #h #df #dj #cj #af #dj #j #ejjj #b #i #bf #dj #gj #aj #eh #bj #ch #h #ej #j #fjjj #b #bc #bj #j #hd #ac #aj #j #df #a #j #j #gjjj #c #g #ac #bj #ih #ae #ba #dj #ec #ag #aj #j #hjjj #c #ba #f #dj #aab #ag #cc #bj #fa #i #bj #j ---------------------------------------- ---------------------- #ijjj #d #e #j #j #abf #ai #de #j #fi #a #cj #j #ajjjj #d #ah #ec #bj #adj #ba #ef #dj #gf #ag #dj #j #bjjjj #i #g #df #dj #bha #ai #ec #bj #aec #aa #bj #j #beibj #ab #j #j #j #cfe #f #j #j #aih #ba #cf #j ---------------------------------------- ---------------------- ,sidenote3 ,fig4 ,,iv4 ,to explain this by a ,figure1 let the ,sun be in conjunction with a fixed ,star at ,s1 suppose in the #cjth degree of 1 on the #bjth day of ,may #agef4 ,then1 making #bafj revolutions through the ,ecliptic ,,vwx1 at the end of so many ,sidereal years1 he will be found again at ,s3 but at the end of so many ,julian years1 he will be found at ,m1 short of ,s3 and at the end of so many ,tropical years1 he will be found short of ,m1 in the #cjth deg4 of ,taurus at ,t1 which has receded back from ,s to ,t in that time1 by the ,precession of the ,equinoctial points ,aries and ,libra4 ,the ,arc ,,st will be equal to the amount of the ,precession of the ,equinox in #bafj years1 at the rate of #ej of a degree1 or #bj min4 #ag-a_/b sec4 of time1 annually3 this1 in so many years1 makes #cj days1 #aj-a_/b hours2 which is the difference between #bafj ,sidereal and ,tropical years3 ,and the ,arc ,,mt will be equal to the space moved through by the ,sun in #bafj times #aa min4 #c sec4 or #af days1 #ac hours #dh minutes1 which is the difference between #bafj ,julian and ,tropical years4 #bdh4 ,from the shifting of the ,equinoctial points1 and with them all the ,signs of the ,ecliptic1 it follows that those ,stars which in the infancy of astronomy were in ,aries are now got into ,taurus2 those of ,taurus into ,gemini1 c4 ,hence likewise it is1 that the ,stars which rose or set at any particular season of the year1 in the time of ,,hesiod1 ,,eudoxus1 ,,virgil1 ,,pliny1 c4 by no means answer at this time to their descriptions4 ,the preceding table shews the quantity of this shifting both in the heavens and on the earth1 for any number of years to #be1ibj2 which compleats the grand celestial period3 within which any number and its quantity is easily found2 as in the following example1 for #egfc years2 which at the ,autumnal ,equinox1 ,a4 ,d4 #agef1 is thought to be the age of the world4 ,so that with regard to the fixed ,stars1 the ,equinoctial points in the heavens1 have receded #bs #bj #b #cj since the creation2 which is as much as the ,sun moves in #ha;d #e;h #jm #ebs4 ,and since that time1 or in #egfc years1 the ,equinoxes with us have fallen back #dd;d #e;h #bam #is2 hence1 reckoning from the time of the ,julian ,equinox1 ,a4 ,d4 #agef1 viz4 ,sept4 #abth1 it appears that the ,autumnal ,equinox at the creation was on the #bfth of ,october4 ---------------------------------------- ------------------- ,precession of the ,equinoctial ,anticipation ,points in the ,heavens4 of the ,julian --------------------------------- ,equinoxes on years4 ,motion4 ,time4 the ,earth4 ---------------------------------------- --------- ,s4 ,d4 ,h4 ,m4 ,s4 ,d4 ,h4 ,m4 ,s4 ---------------------------------------- ------------------ #ejjj #b #i #bf #dj #gj #aj #eh #bj #ch #h #ej #j #gjj #j #i #dc #bj #i #bj #dd #aj #e #h #ee #j #fj #j #j #ej #j #j #bj #ag #cj #j #aa #c #j #c #j #j #b #cj #j #a #j #eb #j #j #cc #i ---------------------------------------- ------------------ #egfc #b #bj #b #cj #ha #e #j #eb #dd #e #ba #i ---------------------------------------- ------------------ ,sidenote3 ,the anticipation of the ,equinoxes and ,seasons4 ,,plate ,,vi4 #bdi4 ,the anticipation of the ,equinoxes1 and consequently of the seasons1 is by no means owing to the ,precession of the ,equinoctial and ,solsticial points in the ,heavens1 7which can only affect the apparent motions1 places and declinations of the fixed ,stars7 but to the difference between the ,civil and ,solar year1 which is #aa minutes #c seconds2 the ,civil year containing #cfe days #f hours1 and the ,solar year #cfe days #e hours #dh minutes #eg seconds4 ,the following table shews the length1 and consequently the difference of any number of ,sidereal1 ,civil1 and ,solar years from #a to #aj1jjj4 ,sidenote3 ,the reason for altering the ,style4 #bej4 ,the above #aa minutes #c seconds1 by which the ,civil or ,julian year exceeds the ,solar1 amounts to #aa days in #adcc years3 and so much our seasons have fallen back with respect to the days of the months1 since the time of the ,nicene ,council in ,a4,d4 #cbe1 and therefore in order to bring back all the ,fasts and ,festivals to the days then settled1 it was requisite to suppress #aa nominal days4 ,and that the same seasons might be kept to the same times of the year for the future1 to leave out the ,bissextile day in ,february at the end of every century of years not divisible by #d2 reckoning them only common years1 as the #agth1 #ahth and #aith centuries1 viz4 the years #agjj1 #ahjj1 #aijj1 c4 because a day intercalated every fourth year was too much1 and retaining the ,bissextile-day at the end of those ,centuries of years which are divisible by #d1 as the #afth1 #bjth and #bdth ,centuries2 viz4 the years #afjj1 #bjjj1 #bdjj1 c4 ,otherwise1 in length of time the seasons would have been quite reversed with regard to the months of the years2 though it would have required near #bc1ghc years to have brought about such a total change4 ,if the ,earth had made exactly #cfe-a_/d diurnal rotations on its axis1 whilst it revolved from any ,equinoctial or ,solstitial point to the same again1 the ,civil and ,solar years would always have kept pace together2 and the style would never have needed any alteration4 ,sidenote3 ,the ,precession of the ,equinoctial ,points4 #bea4 ,having already mentioned the cause of the ,precession of the ,equinoctial points in the heavens1 #bdf1 which occasions a flow deviation of the earth's axis from its parallelism1 and thereby a change of the declination of the ,stars from the ,equator1 together with a slow apparent motion of the ,stars forward with respect to the ,signs of the ,ecliptic2 we shall now describe the ,phenomena by a ,diagram4 ,sidenote3 ,fig4 ,v4 ,let ,,nzsvl be the ,earth1 ,,sona its ,axis produced to the starry ,heavens1 and terminating in ,a1 the present north ,pole of the ,heavens1 which is vertical to ,n the north ,pole of the ,earth4 ,let ,,eoq be the ,equator1 ,t,z the ,tropic of ,cancer1 and ,,vt the ,tropic of ,capricorn3 ,,voz the ,ecliptic1 and ,,bo its ,axis1 both which are immoveable among the ,stars4 ,but1 as #egthe ,equinoctial points recede in the ,ecliptic1 the ,earth's ,axis ,,son is in motion upon the ,earth's center ,o1 in such a manner as to describe the double ,cone ,n,on and ,s,os1 round the ,axis of the ,ecliptic ,,bo1 in the time that the ,equinoctial points move quite round the ,ecliptic1 which is #be1ibj years2 and in that length of time1 the north ,pole of the ,earth's ,axis produced1 describes the ,circle ,,abcda in the starry ,heavens1 round the ,pole of the ,ecliptic1 which keeps immoveable in the center of that ,circle4 ,the ,earth's ,axis being #bc-a_/b degrees inclined to the ,axis of the ,ecliptic1 the ,circle ,,abcda1 described by the north ,pole of the ,earth's ,axis produced to ,a1 is #dg degrees in diameter1 or double the inclination of the ,earth's ,axis4 ,in consequence of this1 the point ,a1 which at present is the ,north ,pole of the ,heavens1 and near to a ,star of the second magnitude in the tail of the constellation called the ,little ,bear1 must be deserted by the ,earth's ,axis2 which moving backwards a degree every #gb years1 will be directed towards the ,star or ,point ,b in #fdhj years hence3 and in double of that time1 or #ab1ifj years1 it will be directed towards the ,star or ,point ,c2 which will then be the ,north ,pole of the ,heavens1 although it is at present #h-a_/b degrees south of the ,zenith of ,london ,l4 ,the present position of the ,equator ,,eoq will then be changed into e,oq1 the ,tropic of ,cancer ,t,z into ,vt1 and the ,tropic of ,capricorn ,,vt into t,z2 as is evident by the ,figure4 ,and the ,sun1 in the same part of the ,heavens where he is now over the earthly ,tropic of ,capricorn1 and makes the shortest days and longest nights in the ,northern ,hemisphere1 will then be over the earthly ,tropic of ,cancer1 and make the days longest1 and nights shortest4 ,so that it will require #ab1ifj years yet more1 or #be1ibj from the present time1 to bring the ,north ,pole ,n quite round1 so as to be directed toward that point of the ,heavens which is vertical to it at present4 ,and then1 and not till then1 the same ,stars which at present describe the ,equator1 ,tropics1 polar ,circles1 and ,poles1 by the ,earth's diurnal motion1 will describe them over again4 ,a ,,table shewing the ,time contained in any number of ,sidereal1 ,julian1 and ,solar ,years1 from #a to #ajjjj4 ---------------------------------------- ---------------------------------- ,sidereal ,years4 ,julian ,years4 ,solar ,years4 ---------------------------------------- ---------------------------- ,years ,days ,h4 ,m4 ,s4 ,days ,h4 ,days ,h4 ,m4 ,s4 ---------------------------------------- -------------------------- ,contain ,contain ,contain #a #cfe #f #i #ad-a_/b #cfe #f #cfe #e #dh #eg #b #gcj #ab #ah #bi #gcj #ab #cgj #aa #cg #ed #c #ajie #ah #bg #dc-a_/b #ajie #ah #ajie #ag #bf #ea #d #adfa #j #cf #eh #adfa #j #adfj #bc #ae #dh #e #ahbf #f #df #ab-a_/b #ahbf #f #ahbf #e #d #de ---------------------------------------- -------------------------- #f #baia #ab #ee #bg #baia #ab #baia #aj #ec #db #g #beef #ai #e #da-a_/b #beef #ah #beef #af #db #ci #h #bibb #a #ac #ef #bibb #j #biba #bb #ca #cf #i #cbhg #g #bc #aj-a_/b #cbhg #f #cbhg #d #bj #cc #aj #cfeb #ac #cb #be #cfeb #ab #cfeb #aj #i #cj ---------------------------------------- -------------------------- #bj #gcje #c #d #ej #gcje #j #gcjd #bj #ai #j #cj #ajieg #af #cg #ae #ajieg #ab #ajieg #f #bh #cj #dj #adfaj #f #i #dj #adfaj #j #adfji #af #ch #j #ej #ahbfb #ai #db #e #ahbfb #ab #ahbfb #b #dg #cj #fj #baiae #i #ad #cj #baiae #j #baiad #ab #eg #j ---------------------------------------- -------------------------- #gj #beefg #bb #df #ee #beefg #ab #beeff #bc #f #cj #hj #bibbj #ab #ai #bj #bebbj #j #bibai #i #af #j #ij #cbhgc #a #ea #de #cbhgb #ab #cbhga #ai #be #cj #ajj #cfebe #ae #bd #aj #cfebe #cfebd #e #ce #bjj #gcjea #f #dh #bj #gcjej #gcjdh #aa #aj ---------------------------------------- -------------------------- #cjj #ajiegf #bb #ab #cj #ajiege #ajiegb #af #de #djj #adfajb #ac #cf #dj #adfajj #adfjif #bb #bj #ejj #ahbfbh #e #j #ej #ahbfbe #ahbfba #c #ee #fjj #baiaec #bj #be #baiaej #baiade #i #cj #gjj #beefgi #aa #di #aj #beefge #beeffi #ae #e ---------------------------------------- -------------------------- #hjj #bibbje #c #ac #bj #bibbjj #bibaic #bj #aj #ijj #cbhgcj #ah #cg #cj #cbhgbe #cbhgah #b #ae #ajjj #cfebef #aj #a #dj #cfebej #cfebdb #g #ej #bjjj #gcjeab #bj #c #bj #gcjejj #gcjdhd #ae #dj #cjjj #ajiegfi #f #e #ajiegej #ajiegbf #bc #cj ---------------------------------------- -------------------------- #djjj #adfajbe #af #f #dj #adfajjj #adfjifi #g #bj #ejjj #ahbfbhb #b #h #bj #ahbfbej #ahbfbaa #ae #aj #fjjj #baiaech #ab #aj #baiaejj #baiadec #ad #dj #gjjj #beefgid #bb #aa #dj #beefgej #beeffif #f #ej #hjjj #bibbjea #h #ac #bj #bibbjjj #bibaich #ad #dj ---------------------------------------- -------------------------- #ijjj #cbhgjcg #ah #ae #cbhgbej #cbhgahj #bb #cj #ajjjj #cfebefd #d #af #dj #cfebejj #cfebdbc #f #bj ---------------------------------------- -------------------------- ---------------------------------------- ---------------------------------------- -------- ,a ,,table shewing the ,sun's true ,place1 and ,distance from his ,apogee1 for the second ,year after ,leap-year4 ---------------------------------------- ---------------------------------------- -- ,january ,february ,march ,april ,may ,june ---------------------------------------- -------------------------------- ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ---------------------------------------- -------------------------------- ,days,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4 ---------------------------------------- ------------------------------------ #a #aa #g #f #bab #ci #g #caj #ec #h #jaa #dj #i #aaj #egaj #jaj #dfaa #a #b #ab #h #f #cac #dj #g #daa #ec #h #aab #ci #i #baa #eeaj #aaa #ddaa #b #c #ac #i #f #dad #da #g #eab #ec #h #bac #ch #i #cab #ecaj #bab #daaa #c #d #ad #aj #f #eae #db #g #fac #ec #h #cad #cg #i #dac #eaaj #cac #chaa #d #e #ae #aa #f #faf #dc #g #gad #ec #h #dae #cf #i #ead #diaj #dad #ceaa #e ---------------------------------------- ------------------------------------ #f #af #ab #f #gag #dc #g #h #e #ec #h #eaf #ce #i #fae #dgaj #eae #ccaa #f #g #ag #ad #f #hah #dd #g #iaf #ec #h #fag #cd #i #gaf #deaj #faf #cjaa #g #h #ah #ae #f #iai #de #g #ajag #ec #h #gah #cc #i #hag #dcaj #gag #bhaa #h #i #ai #af #f #ajbj #df #g #aaah #ec #h #hai #cb #i #iah #daaj #hah #beaa #i #aj #bj #ag #f #aaba #df #g #abai #ec #h #ibj #cj #i #ajai #ciaj #iai #bbaa #aj ---------------------------------------- ------------------------------------ #aa #ba #ah #f #abbb #dg #g #acbj #eb #h #ajba #bi #i #aabj #cgaj #ajbj #bjaa #aa #ab #bb #ai #f #acbc #dg #g #adba #eb #h #aabb #bh #i #abba #cdaj #aaba #agaa #ab #ac #bc #ba #f #adbd #dh #g #aebb #eb #h #abbc #bf #i #acbb #cbaj #abbb #adaa #ac #ad #bd #bb #f #aebe #dh #g #afbc #eb #h #acbd #be #i #adbc #cjaj #acbc #aaaa #ad #ae #be #bc #f #afbf #di #g #agbd #ea #h #adbe #bd #i #aebd #bhaj #adbd #haa #ae ---------------------------------------- ------------------------------------ #af #bf #bd #f #agbg #di #g #ahbe #ea #h #aebf #bb #i #afbe #bfaj #aebe #faa #af #ag #bg #be #f #ahbh #ej #g #aibf #ea #h #afbg #ba #i #agbf #bcaj #afbf #caa #ag #ah #bh #bf #f #aibi #ej #g #bjbg #ej #h #agbh #ai #i #ahbg #baaj #agbg #jaa #ah #ai #bi #bg #f #bj #ea #g #babh #ej #h #ahbi #ah #i #aibh #aiaj #ahbg #ehaa #ah #bj #bh #f #ba #a #ea #g #bbbi #di #h #ai #af #i #bjbi #afaj #aibh #eeaa #ai ---------------------------------------- ------------------------------------ #ba #a #bi #f #bb #b #ea #g #bc #di #h #bj #a #ae #i #ba #aeaj #bjbi #ebaa #bj #bb #b #cj #f #bc #c #eb #g #bd #a #dh #h #ba #b #ac #i #bb #a #aaaj #ba #diaa #ba #bc #c #ca #f #bd #d #eb #g #be #b #dg #h #bb #c #aa #i #bc #b #iaj #bb #a #dfaa #bb #bd #d #cb #f #be #e #eb #g #bf #c #dg #h #bc #d #aj #i #bd #c #faj #bc #b #ddaa #bc #be #e #cc #f #bf #f #eb #g #bg #d #df #h #bd #e #h #i #be #d #daj #bd #c #daaa #bd ---------------------------------------- ------------------------------------ #bf #f #cd #f #bg #g #ec #g #bh #e #de #h #be #f #f #i #bf #e #baj #be #d #chaa #be #bg #g #ce #f #bh #h #ec #g #bi #f #de #h #bf #g #d #i #bg #e #eiaj #bf #e #ceaa #bf #bh #h #cf #f #bi #i #ec #h #j #g #dd #h #bg #h #c #i #bh #f #efaj #bg #f #cbaa #bg #bi #i #cg #g #j #h #dc #h #bh #i #a #i #bi #g #edaj #bh #g #cjaa #bh #cj #aj #ch #g #a #i #db #h #bi #i #ei #i #bi #h #eaaj #bi #h #bgaa #bi ---------------------------------------- ------------------------------------ #ca #aa #ci #g #b #aj #da #i #j #i #dhaa #j ---------------------------------------- ------------------------------------ ---------------------------------------- ---------------------------------------- -------- ,a ,,table shewing the ,sun's true ,place1 and ,distance from his ,apogee1 for the second ,year after ,leap-year4 ---------------------------------------- ---------------------------------------- -- ,july ,august ,september ,october ,november ,december ---------------------------------------- -------------------------------- ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,sun's ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ,place4,anom4 ---------------------------------------- -------------------------------- ,days,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4,d4 ,m4,s4 ,d4 ---------------------------------------- ------------------------------------ #a #i #bd #j #j #h #ei #a #j #h #ea #b #a #h #aj #c #a #i #j #d #b #i #ah #e #a #b #aj #ba #j #a #i #eg #a #a #i #di #b #b #i #i #c #b #aj #j #d #caj #ai #e #b #c #aa #ah #j #baj #ed #a #baj #dg #b #caj #h #c #c #aa #j #d #daa #bj #e #c #d #ab #ae #j #caa #eb #a #caa #de #b #daa #h #c #d #ab #a #d #eab #ba #e #d #e #ac #ac #j #dab #di #a #dab #dc #b #eab #g #c #e #ac #a #d #fac #bb #e #e ---------------------------------------- ------------------------------------ #f #ad #aj #j #eac #dg #a #eac #db #b #fac #f #c #f #ad #a #d #gad #bc #e #f #g #ae #g #j #fad #dd #a #fad #dj #b #gad #f #c #g #ae #b #d #hae #bd #e #g #h #af #d #j #gae #db #a #gae #ci #b #hae #e #c #h #af #b #d #iaf #be #e #h #i #ag #a #j #haf #ci #a #haf #cg #b #iaf #d #c #i #ag #b #d #ajag #bf #e #i #aj #ag #ei #j #hag #cg #a #iag #ce #b #ajag #d #c #aj #ah #c #d #aaah #bg #e #aj ---------------------------------------- ------------------------------------ #aa #ah #ef #j #iah #ce #a #ajah #cd #b #aaah #c #c #aa #ai #c #d #abai #bh #e #aa #ab #ai #ec #j #ajai #cb #a #aaai #cb #b #abai #c #c #ab #bj #d #d #acbj #bi #e #ab #ac #bj #ej #j #aabj #cj #a #abbj #ca #b #acbj #b #c #ac #ba #d #d #adba #cj #e #ac #ad #ba #dg #j #abba #bh #a #acba #bi #b #adba #b #c #ad #bb #e #d #aebb #ca #e #ad #ae #bb #de #j #acbb #be #a #adbb #bh #b #aebb #b #c #ae #bc #e #d #afbc #cb #e #ae ---------------------------------------- ------------------------------------ #af #bc #db #j #adbc #bc #a #aebc #bg #b #afbc #a #c #af #bd #f #d #agbd #cc #e #af #ag #bd #ci #j #aebd #ba #a #afbd #be #b #agbd #a #c #ag #be #g #d #ahbe #cd #e #ag #ah #be #cf #j #afbe #ai #a #agbe #bd #b #ahbe #a #c #ah #bf #g #d #aibf #ce #e #ah #ai #bf #cd #j #agbf #ag #a #ahbf #bc #b #aibf #j #c #ai #bg #h #d #bjbg #cf #e #ai #bj #bg #ca #j #ahbg #ad #a #aibg #ba #b #bjbg #j #c #bj #bh #i #d #babh #ch #e #bj ---------------------------------------- ------------------------------------ #ba #bh #bh #j #aibh #ab #a #bjbh #bj #b #babh #j #c #ba #bi #i #d #bbbi #ci #e #ba #bb #bi #bf #j #bjbi #aj #a #babi #ai #b #bbbi #j #c #bb #aj #d #bc #dj #e #bb #bc #bc #j #ba #h #a #bb #ah #b #bc #j #c #bc #a #aa #d #bd #a #da #e #bc #bd #a #bj #j #bb #a #f #a #bc #a #ag #b #bd #a #j #c #bd #b #ab #d #be #b #db #e #bd #be #b #ah #j #bc #b #d #a #bd #b #af #b #be #b #j #c #be #c #ab #d #bf #c #dd #e #be ---------------------------------------- ------------------------------------ #bf #c #ae #j #bd #c #b #a #be #c #ae #b #bf #c #j #c #bf #d #ac #d #bg #d #de #e #bf #bg #d #ab #j #be #d #j #a #bf #d #ad #b #bg #d #j #c #bg #e #ad #d #bh #e #df #e #bg #bh #e #aj #j #bf #d #eh #a #bg #e #ac #b #bh #e #j #c #bh #f #ae #d #bi #f #dg #e #bh #bi #f #g #j #bg #e #ef #a #bh #f #ab #b #bi #f #j #c #bi #g #af #d #bi #g #dh #e #bi #cj #g #e #j #bh #f #ed #a #bi #g #aa #c #j #g #j #d #j #h #ag #e #j #h #di #f #j ---------------------------------------- ------------------------------------ #ca #h #b #j #bi #g #eb #b #j #h #j #d #a #i #ea #f #a ---------------------------------------- ------------------------------------ ---------------------------------------- ---------------------------------------- -------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- -------- ,the ,bissextile1 or ,leap-year4 ---------------------------------------- ------------------------------------ ,days,january ,dif4,february,dif4 ,march ,dif4 ,april ,dif4 ,may ,dif4 ,june ,dif4 ---------------------------------------- -------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------ ,inc4 ,inc4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #d #j #ab #ad #e #ab #ab #cf #ab #c #dh #aa #ef #dg #aa #eg #bb #bh #g #ac #ah #g #i #b #ab #d #bh #ab #ad #ab #ab #ab #bc #ab #c #cj #aa #ef #dj #aa #eg #ca #bh #g #ac #ai #g #i #c #ab #d #ef #ab #ad #ai #ab #ab #aj #ab #c #aa #aa #ef #cc #aa #eg #dj #bh #f #ad #ah #f #aj #d #ab #e #bd #ab #ad #be #ab #aa #ef #ab #b #ec #aa #ef #bg #aa #eg #ej #bg #e #ad #ah #f #aj #e #ab #e #ea #ab #ad #cj #ab #aa #db #ab #b #ce #aa #ef #ba #aa #eh #j ------------ #bg -------- #d -------- #ad -------- #ah -------- #e -------- #aa #f #ab #f #ah #ab #ad #cd #ab #aa #bh #ab #b #ag #aa #ef #af #aa #eh #aa #bf #c #ae #ag #d #aa #g #ab #f #dd #ab #ad #cg #ab #aa #ac #ab #b #j #aa #ef #ab #aa #eh #bb #bf #c #ae #ag #d #aa #h #ab #g #aj #ab #ad #dj #ab #aj #eh #ab #a #dc #aa #ef #h #aa #eh #cc #be #b #af #ag #d #aa #i #ab #g #ce #ab #ad #db #ab #aj #db #ab #a #bf #aa #ef #d #aa #eh #dd #be #a #af #ag #c #ab #aj #ab #h #j #ab #ad #dc #ab #aj #df #ab #a #i #aa #ef #a #aa #eh #ef ------------ #bd --------,dec4-------- #af -------- #af -------- #b -------- #ab #aa #ab #h #bd #ab #ad #dd #ab #aj #aj #ab #j #ec #aa #ee #ei #aa #ei #h #bc #a #ag #af #a #ab #ab #ab #h #dg #ab #ad #dc #ab #i #ec #ab #j #cg #aa #ee #eh #aa #ei #bj #bc #a #ag #af #a #ab #ac #ab #i #aj #ab #ad #db #ab #i #cf #ab #j #ba #aa #ee #eg #aa #ei #cb #bb #b #ag #ae ,inc4 #ab #ad #ab #i #cb #ab #ad #dj #ab #i #ai #ab #j #f #aa #ee #ef #aa #ei #dd #bb #c #ag #ae #a #ac #ae #ab #i #ed #ab #ad #cg #ab #i #b #aa #ei #ea #aa #ee #eg #aa #ei #eg ------------ #ba -------- #d -------- #ah -------- #ae -------- #a -------- #ac #af #ab #aj #ae #ab #ad #cc #ab #h #dd #aa #ei #cf #aa #ee #eh #ab #j #aj #bj #d #ah #ae #a #ac #ag #ab #aj #ce #ab #ad #bi #ab #h #bf #aa #ei #ba #aa #ee #ei #ab #j #bc #ai #e #ah #ad #b #ab #ah #ab #aj #ed #ab #ad #bd #ab #h #h #aa #ei #g #aa #ef #a #ab #j #ce #ai #e #ah #ac #b #ac #ai #ab #aj #ac #ab #ad #ai #ab #g #ej #aa #eh #ed #aa #ef #c #ab #j #dh #ah #f #ah #ac #c #ac #bj #ab #aj #ca #ab #ad #ac #ab #g #cb #aa #eh #da #aa #ef #f #ab #a #a ------------ #ag -------- #g -------- #ah -------- #ac -------- #c -------- #ac #ba #ab #aa #dh #ab #ad #f #ab #g #ad #aa #eh #bh #aa #ef #i #ab #a #ad #ag #h #ai #ab #d #ac #bb #ab #ab #e #ab #ac #eh #ab #f #ee #aa #eh #af #aa #ef #ac #ab #a #bg #af #h #ai #ab #e #ac #bc #ab #ab #ba #ab #ac #ej #ab #f #cf #aa #eh #d #aa #ef #ah #ab #a #dj #ae #i #ai #ab #e #ac #bd #ab #ab #cf #ab #ac #da #ab #f #ag #aa #eg #eb #aa #ef #bc #ab #a #ec #ad #i #ai #aa #f #ac #be #ab #ab #ej #ab #ac #cb #ab #e #eh #aa #eg #da #aa #ef #bi #ab #b #f ------------ #ac -------- #aj -------- #ah -------- #aj -------- #f -------- #ab #bf #ab #ac #c #ab #ac #bb #ab #e #dj #aa #eg #ca #aa #ef #ce #ab #b #ah #ab #aa #ai #aj #g #ac #bg #ab #ac #ae #ab #ac #aa #ab #e #ba #aa #eg #ba #aa #ef #db #ab #b #ca #ab #aa #ai #i #g #ab #bh #ab #ac #bg #ab #ac #j #ab #e #b #aa #eg #ab #aa #ef #di #ab #b #dc #aa #ab #ah #i #g #ab #bi #ab #ac #ch #ab #ab #dh #ab #d #dd #aa #eg #c #aa #ef #ef #ab #b #ee #aj #ab #ai #h #h #ab #cj #ab #ac #dh #ab #d #be #aa #ef #ee #aa #eg #d #ab #c #g ------------ #i -------------------- #ai -------- #h -------- #i -------- #aa #ca #ab #ac #eg #ab #d #f #aa #eg #ac #h #ah #i ---------------------------------------- ------------------------------------ ,incr4 #i #eg ,incr4 #j #ci ,decr4 #h #cj ,decr4 #f #ec ,decr4 #j #ej ,incr4 #e #de ,decr4 #a #ef ,incr4 #a #ag ---------------------------------------- ---------------------------------------- --------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- --------- ,the ,bissextile1 or ,leap-year4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,august ,dif4,september,dif4 ,october,dif4,november,dif4,december,dif 4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ah #ab #e #df #aa #ei #cc #aa #di #bh #aa #dc #di #aa #di #db #aa #d #ai #ah #a #bd #b #ab #c #bi #ab #e #db #aa #ei #ad #aa #di #aj #aa #dc #dh #aa #ej #f #aa #e #ai #ah ,inc4 #bd #c #ab #c #dj #ab #e #cg #aa #eh #ee #aa #dh #eb #aa #dc #di #aa #ej #cj #aa #e #ai #ah #a #be #d #ab #c #ea #ab #e #cb #aa #eh #cf #aa #dh #cd #aa #dc #ej #aa #ej #ee #aa #f #ai #ah #b #be #e #ab #d #b #ab #e #bf #aa #eh #ag #aa #dh #af #aa #dc #eb #aa #ea #bj ------------ #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #ab #ab #e #bj #aa #eg #eg #aa #dg #ei #aa #dc #ee #aa #ea #df #aj #g #bj #ag #d #bf #g #ab #d #bb #ab #e #ac #aa #eg #cg #aa #dg #db #aa #dc #ei #aa #eb #ab #i #h #bj #af #e #bf #h #ab #d #ca #ab #e #e #aa #eg #ag #aa #dg #bf #aa #dd #d #aa #eb #ch #i #h #bj #ae #f #bh #i #ab #d #dj #ab #d #eg #aa #ef #eg #aa #dg #aa #aa #dd #aj #aa #ec #f #h #i #ba #ae #f #bg #aj #ab #d #dh #ab #d #dh #aa #ef #cf #aa #df #ef #aa #dd #af #aa #ec #cc ------------ #h -------- #i --------- #ba -------- #ae -------- #g -------- #bh #aa #ab #d #ef #ab #d #ci #aa #ef #ae #aa #df #da #aa #dd #bc #aa #ed #a #h #aj #ba #ae #h #bi #ab #ab #e #d #ab #d #bi #aa #ee #ed #aa #df #bf #aa #dd #ca #aa #ed #cj #g #aj #ba #ad #i #bi #ac #ab #e #aa #ab #d #ai #aa #ee #cc #aa #df #ab #aa #dd #dj #aa #ed #ei #g #aa #ba #ac #aj #bi #ad #ab #e #ah #ab #d #h #aa #ee #ab #aa #de #ei #aa #dd #ej #aa #ee #bh #f #ab #ba #ac #aa #bi #ae #ab #e #bd #ab #c #ef #aa #ed #ea #aa #de #df #aa #de #a #aa #ee #eg ------------ #f -------- #ab --------- #ba -------- #ab -------- #ab -------- #bi #af #ab #e #cj #ab #c #dd #aa #ed #cj #aa #de #cd #aa #de #ac #aa #ef #bf #e #ab #bj #aa #ac #cj #ag #ab #e #ce #ab #c #cb #aa #ed #aj #aa #de #bc #aa #de #bf #aa #ef #ef #e #ac #ba #aa #ac #cj #ah #ab #e #dj #ab #c #ai #aa #ec #di #aa #de #ab #aa #de #ci #aa #eg #bf #d #ac #ba #aa #ad #cj #ai #ab #e #dd #ab #c #f #aa #ec #bh #aa #de #a #aa #de #ec #aa #eg #ef #d #ad #ba #aj #ae #cj #bj #ab #e #dh #ab #b #eb #aa #ec #g #aa #dd #ea #aa #df #h #aa #eh #bf ------------ #c -------- #ad --------- #ba -------- #i -------- #af -------- #cj #ba #ab #e #ea #ab #b #ch #aa #eb #df #aa #dd #db #aa #df #bd #aa #eh #ef #b #ae #ba #i #af #cj #bb #ab #e #ec #ab #b #bc #aa #eb #be #aa #dd #cc #aa #df #dj #aa #ei #bf #b #ae #bj #h #ag #cj #bc #ab #e #ee #ab #b #h #aa #eb #e #aa #dd #be #aa #df #eg #aa #ei #ef #b #af #bj #g #ah #cj #bd #ab #e #eg #ab #a #eb #aa #ea #de #aa #dd #ah #aa #dg #ae #ab #j #bf #a #af #bj #g #ai #cj #be #ab #e #eh #ab #a #cf #aa #ea #be #aa #dd #aa #aa #dg #cd #ab #j #ef ------------ #a -------- #ag --------- #bj -------- #f -------- #bj -------- #cj #bf #ab #e #ei #ab #a #ai #aa #ea #e #aa #dd #e #aa #dg #ed #ab #a #bf ,dec4 #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #b #aa #ej #de #aa #dd #j #aa #dh #ad #ab #a #ef #a #ag #bj #d #ba #bi #bh #ab #e #eg #ab #j #de #aa #ej #be #aa #dc #ef #aa #dh #ce #ab #b #be #b #ag #ai #c #bb #bi #bi #ab #e #ee #ab #j #bh #aa #ej #f #aa #dc #ec #aa #dh #eg #ab #b #ed #b #ah #ai #b #bb #bi #cj #ab #e #ec #ab #j #aj #aa #di #dg #aa #dc #ea #aa #di #ai #ab #c #bc ------------ #c -------- #ah --------- #ai -------- #a -------- #bc -------- #bi #ca #ab #e #ej #aa #ei #eb #aa #dc #ej #ab #c #eb #d #ai #a ---------------------------------------- ------------------------------------- ,incr4 #b #da ,decr4 #e #ed ,decr4 #i #df ,decr4 #e #ch ,decr4 #j #a ,incr4 #ad #aj ,decr4 #j #h ,incr4 #e #cj ---------------------------------------- ---------------------------------------- --------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- --------- ,the ,bissextile1 or ,leap-year4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,august ,dif4,september,dif4 ,october,dif4,november,dif4,december,dif 4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ah #ab #e #df #aa #ei #cc #aa #di #bh #aa #dc #di #aa #di #db #aa #d #ai #ah #a #bd #b #ab #c #bi #ab #e #db #aa #ei #ad #aa #di #aj #aa #dc #dh #aa #ej #f #aa #e #ai #ah ,inc4 #bd #c #ab #c #dj #ab #e #cg #aa #eh #ee #aa #dh #eb #aa #dc #di #aa #ej #cj #aa #e #ai #ah #a #be #d #ab #c #ea #ab #e #cb #aa #eh #cf #aa #dh #cd #aa #dc #ej #aa #ej #ee #aa #f #ai #ah #b #be #e #ab #d #b #ab #e #bf #aa #eh #ag #aa #dh #af #aa #dc #eb #aa #ea #bj ------------ #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #ab #ab #e #bj #aa #eg #eg #aa #dg #ei #aa #dc #ee #aa #ea #df #aj #g #bj #ag #d #bf #g #ab #d #bb #ab #e #ac #aa #eg #cg #aa #dg #db #aa #dc #ei #aa #eb #ab #i #h #bj #af #e #bf #h #ab #d #ca #ab #e #e #aa #eg #ag #aa #dg #bf #aa #dd #d #aa #eb #ch #i #h #bj #ae #f #bh #i #ab #d #dj #ab #d #eg #aa #ef #eg #aa #dg #aa #aa #dd #aj #aa #ec #f #h #i #ba #ae #f #bg #aj #ab #d #dh #ab #d #dh #aa #ef #cf #aa #df #ef #aa #dd #af #aa #ec #cc ------------ #h -------- #i --------- #ba -------- #ae -------- #g -------- #bh #aa #ab #d #ef #ab #d #ci #aa #ef #ae #aa #df #da #aa #dd #bc #aa #ed #a #h #aj #ba #ae #h #bi #ab #ab #e #d #ab #d #bi #aa #ee #ed #aa #df #bf #aa #dd #ca #aa #ed #cj #g #aj #ba #ad #i #bi #ac #ab #e #aa #ab #d #ai #aa #ee #cc #aa #df #ab #aa #dd #dj #aa #ed #ei #g #aa #ba #ac #aj #bi #ad #ab #e #ah #ab #d #h #aa #ee #ab #aa #de #ei #aa #dd #ej #aa #ee #bh #f #ab #ba #ac #aa #bi #ae #ab #e #bd #ab #c #ef #aa #ed #ea #aa #de #df #aa #de #a #aa #ee #eg ------------ #f -------- #ab --------- #ba -------- #ab -------- #ab -------- #bi #af #ab #e #cj #ab #c #dd #aa #ed #cj #aa #de #cd #aa #de #ac #aa #ef #bf #e #ab #bj #aa #ac #cj #ag #ab #e #ce #ab #c #cb #aa #ed #aj #aa #de #bc #aa #de #bf #aa #ef #ef #e #ac #ba #aa #ac #cj #ah #ab #e #dj #ab #c #ai #aa #ec #di #aa #de #ab #aa #de #ci #aa #eg #bf #d #ac #ba #aa #ad #cj #ai #ab #e #dd #ab #c #f #aa #ec #bh #aa #de #a #aa #de #ec #aa #eg #ef #d #ad #ba #aj #ae #cj #bj #ab #e #dh #ab #b #eb #aa #ec #g #aa #dd #ea #aa #df #h #aa #eh #bf ------------ #c -------- #ad --------- #ba -------- #i -------- #af -------- #cj #ba #ab #e #ea #ab #b #ch #aa #eb #df #aa #dd #db #aa #df #bd #aa #eh #ef #b #ae #ba #i #af #cj #bb #ab #e #ec #ab #b #bc #aa #eb #be #aa #dd #cc #aa #df #dj #aa #ei #bf #b #ae #bj #h #ag #cj #bc #ab #e #ee #ab #b #h #aa #eb #e #aa #dd #be #aa #df #eg #aa #ei #ef #b #af #bj #g #ah #cj #bd #ab #e #eg #ab #a #eb #aa #ea #de #aa #dd #ah #aa #dg #ae #ab #j #bf #a #af #bj #g #ai #cj #be #ab #e #eh #ab #a #cf #aa #ea #be #aa #dd #aa #aa #dg #cd #ab #j #ef ------------ #a -------- #ag --------- #bj -------- #f -------- #bj -------- #cj #bf #ab #e #ei #ab #a #ai #aa #ea #e #aa #dd #e #aa #dg #ed #ab #a #bf ,dec4 #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #b #aa #ej #de #aa #dd #j #aa #dh #ad #ab #a #ef #a #ag #bj #d #ba #bi #bh #ab #e #eg #ab #j #de #aa #ej #be #aa #dc #ef #aa #dh #ce #ab #b #be #b #ag #ai #c #bb #bi #bi #ab #e #ee #ab #j #bh #aa #ej #f #aa #dc #ec #aa #dh #eg #ab #b #ed #b #ah #ai #b #bb #bi #cj #ab #e #ec #ab #j #aj #aa #di #dg #aa #dc #ea #aa #di #ai #ab #c #bc ------------ #c -------- #ah --------- #ai -------- #a -------- #bc -------- #bi #ca #ab #e #ej #aa #ei #eb #aa #dc #ej #ab #c #eb #d #ai #a ---------------------------------------- ------------------------------------- ,incr4 #b #da ,decr4 #e #ed ,decr4 #i #df ,decr4 #e #ch ,decr4 #j #a ,incr4 #ad #aj ,decr4 #j #h ,incr4 #e #cj ---------------------------------------- ---------------------------------------- --------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- --------- ,the first after ,leap-year4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,august ,dif4,september,dif4 ,october,dif4,november,dif4,december,dif 4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ae #ab #e #dh #aa #ei #ch #aa #di #cc #aa #dc #di #aa #di #cf #ab #d #ai #ai #j #bd #b #ab #c #bg #ab #e #dd #aa #ei #ai #aa #di #ad #aa #dc #di #aa #ej #j #aa #e #ai #ai ,inc4 #bd #c #ab #c #ch #ab #e #ci #aa #ei #j #aa #dh #ee #aa #dc #di #aa #ej #bd #aa #e #ai #ah #a #be #d #ab #c #di #ab #e #cd #aa #eh #da #aa #dh #cg #aa #dc #ej #aa #ej #di #aj #f #bj #ag #b #be #e #ab #c #ei #ab #e #bh #aa #eh #ba #aa #dh #bj #aa #dc #eb #aa #ea #ad ------------ #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #i #ab #e #bb #aa #eh #a #aa #dh #c #aa #dc #ee #aa #ea #dj #aj #g #bj #ag #c #bf #g #ab #d #ai #ab #e #ae #aa #eg #da #aa #dg #df #aa #dc #eh #aa #eb #f #aj #g #bj #ag #d #bg #h #ab #d #bi #ab #e #h #aa #eg #ba #aa #dg #bi #aa #dd #b #aa #eb #cc #i #h #bj #af #e #bg #i #ab #d #ch #ab #e #j #aa #eg #a #aa #dg #ac #aa #dd #g #aa #ec #j #h #i #bj #ae #f #bg #aj #ab #d #df #ab #d #ea #aa #ef #da #aa #df #eh #aa #dd #ac #aa #ec #bg ------------ #h -------- #i --------- #bj -------- #ae -------- #g -------- #bh #aa #ab #d #ed #ab #d #db #aa #ef #ba #aa #df #dc #aa #dd #bj #aa #ec #ce #h #aj #ba #ad #h #bh #ab #ab #e #b #ab #d #cb #aa #ef #j #aa #df #bi #aa #dd #bh #aa #ed #bc #h #aj #ba #ac #i #bi #ac #ab #e #aj #ab #d #bb #aa #ee #ci #aa #df #af #aa #dd #cg #aa #ed #eb #g #aa #ba #ac #aj #bi #ad #ab #e #ag #ab #d #aa #aa #ee #ah #aa #df #c #aa #dd #dg #aa #ee #ba #f #aa #ba #ac #aa #bi #ae #ab #e #bc #ab #d #j #aa #ed #eg #aa #de #ej #aa #dd #eh #aa #ee #ej ------------ #f -------- #ab --------- #ba -------- #ac -------- #ab -------- #cj #af #ab #e #bi #ab #c #dh #aa #ed #cf #aa #de #cg #aa #de #aj #aa #ef #ai #e #ab #ba #ab #ac #cj #ag #ab #e #cd #ab #c #cf #aa #ed #ae #aa #de #be #aa #de #bc #aa #ef #di #e #ac #ba #aa #ac #cj #ah #ab #e #ci #ab #c #bc #aa #ec #ed #aa #de #ad #aa #de #cf #aa #eg #ai #d #ac #ba #aa #ad #cj #ai #ab #e #dc #ab #c #aj #aa #ec #cc #aa #de #c #cc #de #ej #aa #eg #di #d #ad #ba #aj #ad #cj #bj #ab #e #dg #ab #b #ef #aa #ec #ab #aa #dd #ec #aa #df #d #aa #eh #ai ------------ #d -------- #ad --------- #ba -------- #aj -------- #ae -------- #cj #ba #ab #e #ea #ab #b #db #aa #eb #ea #aa #dd #dc #aa #df #ai #aa #eh #di #c #ae #bj #i #af #cj #bb #ab #e #ed #ab #b #ag #aa #eb #ca #aa #dd #cd #aa #df #ce #aa #ei #ai #b #ae #bj #h #ag #cj #bc #ab #e #ef #ab #b #ab #aa #eb #aa #aa #dd #bf #aa #df #eb #aa #ei #di #a #af #ba #g #ah #cj #bd #ab #e #eg #ab #a #ef #aa #ea #ej #aa #dd #ai #aa #dg #aj #ab #j #ai #a #af #ba #f #ai #cj #be #ab #e #eh #ab #a #dj #aa #ea #bi #aa #dd #ac #aa #dg #bi #ab #j #di ------------,dec4-------- #af --------- #bj -------- #f -------- #ai -------- #cj #bf #ab #e #ei #ab #a #bd #aa #ea #i #aa #dd #g #aa #dg #dh #ab #a #ai #a #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #g #aa #ej #dj #aa #dd #b #aa #dh #h #ab #a #di #a #ag #ai #d #ba #bi #bh #ab #e #eg #ab #a #ej #aa #ej #cj #aa #dc #eh #aa #dh #bi #ab #b #ah #b #ah #ai #c #bb #bi #bi #ab #e #ee #ab #a #cb #aa #ej #aa #aa #dc #ee #aa #dh #ea #ab #b #dg #b #ah #ai #c #bb #bi #cj #ab #e #ec #ab #j #ad #aa #di #eb #aa #dc #eb #aa #di #ac #ab #c #af ------------ #b -------- #ah --------- #ai -------- #b -------- #bc -------- #bi #ca #ab #e #ea #aa #ei #ef #aa #dc #ej #ab #c #de #c #ah #a #bi ---------------------------------------- ------------------------------------- ,incr4 #b #dc ,decr4 #e #eb ,decr4 #i #df ,decr4 #e #dc ,decr4 #j #j ,incr4 #ad #i ,decr4 #j #h ,incr4 #e #bd ---------------------------------------- ---------------------------------------- -------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- -------- ,the second after ,leap-year4 ---------------------------------------- ------------------------------------ ,days ,january,dif4,february,dif4 ,march ,dif4 ,april ,dif4 ,may ,dif4 ,june ,dif4 ---------------------------------------- -------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------ ,inc4 ,dec4 ,inc4 ,dec4 ,dec4 ,inc4 #a #ab #d #ad #ab #ad #i #ab #ab #db #ab #c #ef #aa #ef #ej #aa #eg #af #bh #g #ac #ah #h #i #b #ab #d #db #ab #ad #af #ab #ab #bj #ab #c #ch #aa #ef #db #aa #eg #be #bh #f #ac #ah #g #aj #c #ab #e #aj #ab #ad #bb #ab #ab #af #ab #c #bj #aa #ef #ce #aa #eg #ce #bg #e #ac #ah #f #aj #d #ab #e #cg #ab #ad #bg #ab #ab #c #ab #c #b #aa #ef #bi #aa #eg #de #bg #e #ad #ah #f #aj #e #ab #f #d #ab #ad #cb #ab #aa #di #ab #b #dd #aa #ef #bc #aa #eg #ee ------------ #bg -------- #d -------- #ad -------- #ah -------- #e -------- #aj #f #ab #f #cj #ab #ad #cf #ab #aa #ce #ab #b #bf #aa #ef #ah #aa #eh #e #bf #c #ae #ag #e #aa #g #ab #f #ef #ab #ad #ci #ab #aa #bj #ab #b #i #aa #ef #bc #aa #eh #af #bf #b #ae #ag #d #aa #h #ab #g #bb #ab #ad #da #ab #aa #e #ab #a #eb #aa #ef #i #aa #eh #bg #be #b #ae #ag #c #aa #i #ab #g #dg #ab #ad #dc #ab #aj #ej #ab #a #ce #aa #ef #f #aa #eh #ch #bd #a #af #ag #c #ab #aj #ab #h #aa #ab #ad #dd #ab #aj #cd #ab #a #ah #aa #ef #c #aa #eh #ej ------------ #bd --------,dec4-------- #af -------- #ag -------- #b -------- #ab #aa #ab #h #ce #ab #ad #dd #ab #aj #ah #ab #a #a #aa #ef #a #aa #ei #b #bc #a #ag #af #b #ab #ab #ab #h #eh #ab #ad #dc #ab #aj #a #ab #j #de #aa #ee #ei #aa #ei #ad #bb #b #ag #af #b #ab #ac #ab #i #bj #ab #ad #da #ab #i #dd #ab #j #bi #aa #ee #eg #aa #ei #bf #bb #c #ag #af #a #ab #ad #ab #i #db #ab #ad #ch #ab #i #bg #ab #j #ac #aa #ee #ef #aa #ei #ch #ba #c #ag #ae ,inc4 #ab #ae #ab #aj #c #ab #ad #ce #ab #i #aj #aa #ei #eh #aa #ee #ef #aa #ei #ej ------------ #ba -------- #d -------- #ah -------- #ae -------- #a -------- #ac #af #ab #aj #bd #ab #ad #ca #ab #h #eb #aa #ei #dc #aa #ee #eg #ab #j #c #bj #d #ah #ad #a #ac #ag #ab #aj #dd #ab #ad #bg #ab #h #cd #aa #ei #bi #aa #ee #eh #ab #j #af #ai #e #ah #ad #b #ac #ah #ab #aa #c #ab #ad #bb #ab #h #af #aa #ei #ae #aa #ef #j #ab #j #bi #ah #f #ah #ad #b #ac #ai #ab #aa #ba #ab #ad #af #ab #g #eh #aa #ei #a #aa #ef #b #ab #j #db #ah #g #ah #ad #c #ac #bj #ab #aa #ci #ab #ad #i #ab #g #dj #aa #eh #dg #aa #ef #e #ab #j #ee ------------ #ag -------- #g -------- #ah -------- #ac -------- #c -------- #ac #ba #ab #aa #ef #ab #ad #b #ab #g #bb #aa #eh #cd #aa #ef #h #ab #a #h #af #h #ah #ab #c #ac #bb #ab #ab #ab #ab #ac #ed #ab #g #d #aa #eh #bb #aa #ef #aa #ab #a #ba #ae #i #ai #ab #d #ac #bc #ab #ab #bg #ab #ac #de #ab #f #de #aa #eh #aj #aa #ef #ae #ab #a #cd #ae #i #ai #ab #e #ac #bd #ab #ab #db #ab #ac #cf #ab #f #bf #aa #eg #eh #aa #ef #bj #ab #a #dg #ad #aj #ai #aa #f #ab #be #ab #ab #ef #ab #ac #bf #ab #f #g #aa #eg #dg #aa #ef #bf #ab #a #ei ------------ #ac -------- #aj -------- #ai -------- #aa -------- #f -------- #ac #bf #ab #ac #i #ab #ac #af #ab #e #dh #aa #eg #cf #aa #ef #cb #ab #b #ab #ab #aa #ai #aj #f #ac #bg #ab #ac #ba #ab #ac #e #ab #e #bi #aa #eg #bf #aa #ef #ch #ab #b #be #aa #aa #ai #aj #g #ab #bh #ab #ac #cb #ab #ab #ed #ab #e #aj #aa #eg #af #aa #ef #de #ab #b #cg #aj #ab #ai #i #g #ab #bi #ab #ac #db #ab #d #ea #aa #eg #g #aa #ef #eb #ab #b #di #aj #ah #i #h #ab #cj #ab #ac #eb #ab #d #cc #aa #ef #eh #aa #eg #j #ab #c #a ------------ #i -------------------- #ah -------- #h -------- #h -------- #aa #ca #ab #ad #a #ab #d #ae #aa #eg #h #h #ah #h ---------------------------------------- ------------------------------------ ,incr4 #i #dg ,incr4 #j #ce ,decr4 #h #bg ,decr4 #f #eh ,decr4 #j #ed ,incr4 #e #de ,decr4 #a #ej ,incr4 #a #ab ---------------------------------------- ---------------------------------------- --------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- --------- ,the second after ,leap-year4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,august ,dif4,september,dif4 ,october,dif4,november,dif4,december,dif 4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #ab #ab #e #dh #aa #ei #dc #aa #di #cg #aa #dc #di #aa #di #cj #ab #d #ai #ai #a #bc #b #ab #c #bd #ab #e #dd #aa #ei #bd #aa #di #ah #aa #dc #dh #aa #di #ec #aa #d #ai #ah ,inc4 #bd #c #ab #c #ce #ab #e #dj #aa #ei #e #aa #di #j #aa #dc #di #aa #ej #ag #aa #e #ai #ah #a #be #d #ab #c #df #ab #e #ce #aa #eh #df #aa #dh #db #aa #dc #ej #aa #ej #db #aa #e #bj #ah #b #be #e #ab #c #eg #ab #e #cj #aa #eh #bf #aa #dh #bd #aa #dc #eb #aa #ea #g ------------- #aj -------- #f --------- #bj -------- #ag -------- #c -------- #bf #f #ab #d #g #ab #e #bd #aa #eh #f #aa #dh #g #aa #dc #ee #aa #ea #cc #aj #g #bj #ag #c #bf #g #ab #d #ag #ab #e #ag #aa #eg #df #aa #dg #ej #aa #dc #eh #aa #ea #ei #i #g #bj #ag #d #bf #h #ab #d #bf #ab #e #aj #aa #eg #bf #aa #dg #cc #aa #dd #b #aa #eb #be #i #h #ba #af #e #bg #i #ab #d #ce #ab #e #b #aa #eg #e #aa #dg #ag #aa #dd #g #aa #eb #eb #i #i #bj #af #f #bh #aj #ab #d #dd #ab #d #ec #aa #ef #de #aa #dg #a #aa #dd #ac #aa #ec #bj ------------ #h -------- #i --------- #ba -------- #ae -------- #g -------- #bh #aa #ab #d #eb #ab #d #dd #aa #ef #bd #aa #df #df #aa #dd #bj #aa #ec #dh #h #i #ba #ad #h #bh #ab #ab #e #j #ab #d #ce #aa #ef #c #aa #df #cb #aa #dd #bh #aa #ed #af #h #aj #ba #ad #i #bh #ac #ab #e #h #ab #d #be #aa #ee #db #aa #df #ah #aa #dd #cg #aa #ed #dd #g #aa #bj #ac #i #bi #ad #ab #e #ae #ab #d #ac #aa #ee #bb #aa #df #e #aa #dd #df #aa #ed #ac #f #aa #bj #ac #aj #bi #ae #ab #e #ba #ab #d #c #aa #ee #b #aa #de #eb #aa #dd #ef #aa #ee #db ------------ #f -------- #ab --------- #ba -------- #ac -------- #aa -------- #bi #af #ab #e #bg #ab #c #ea #aa #ed #da #aa #de #ci #aa #de #g #aa #ef #aa #f #ab #ba #ab #ab #cj #ag #ab #e #cc #ab #c #ci #aa #ed #bj #aa #de #bg #aa #de #ai #aa #ef #da #e #ab #ba #aa #ac #cj #ah #ab #e #ch #ab #c #bg #aa #ec #ei #aa #de #af #aa #de #cb #aa #eg #aa #d #ac #bj #aj #ad #cj #ai #ab #e #db #ab #c #ad #aa #ec #ci #aa #de #f #aa #de #df #aa #eg #da #d #ad #ba #aj #ae #cj #bj #ab #e #df #ab #c #j #aa #ec #ah #aa #dd #ef #aa #df #a #aa #eh #aa ------------ #c -------- #ad --------- #ba -------- #aj -------- #ae -------- #cj #ba #ab #e #di #ab #b #df #aa #eb #eg #aa #dd #df #aa #df #af #aa #eh #da #c #ae #bj #i #af #cj #bb #ab #e #eb #ab #b #ca #aa #eb #cg #aa #dd #cg #aa #df #cb #aa #ei #aa #b #ae #ba #h #ag #cj #bc #ab #e #ed #ab #b #af #aa #eb #af #aa #dd #bi #aa #df #di #aa #ei #da #b #ae #ba #g #ah #cj #bd #ab #e #ef #ab #b #a #aa #ea #ee #aa #dd #bb #aa #dg #g #ab #j #aa #b #af #ba #g #ah #cj #be #ab #e #eh #ab #a #de #aa #ea #cd #aa #dd #ae #aa #dg #be #ab #j #da ------------ #a -------- #af --------- #bj -------- #f -------- #ai -------- #cj #bf #ab #e #ei #ab #a #bi #aa #ea #ad #aa #dd #i #aa #dg #dd #ab #a #aa ,dec4 #ag #bj #e #bj #cj #bg #ab #e #eh #ab #a #ab #aa #ej #ed #aa #dd #d #aa #dh #d #ab #a #da #a #ag #bj #e #ba #cj #bh #ab #e #eg #ab #j #ee #aa #ej #cd #aa #dc #ei #aa #dh #be #ab #b #aa #a #ah #ai #d #ba #bi #bi #ab #e #ef #ab #j #cg #aa #ej #ae #aa #dc #ee #aa #dh #df #ab #b #dj #b #ah #ai #c #bb #bi #cj #ab #e #ed #ab #j #ai #aa #di #ef #aa #dc #eb #aa #di #h #ab #c #i ------------ #c -------- #ah --------- #ai -------- #b -------- #bb -------- #bi #ca #ab #e #ea #ab #j #a #aa #dc #ej #ab #c #ch #c #ah #a #bi ---------------------------------------- ------------------------------------- ,incr4 #b #df ,decr4 #e #dg ,decr4 #i #dg ,decr4 #e #dg ,decr4 #j #a ,incr4 #ad #h ,decr4 #j #h ,incr4 #e #ai ---------------------------------------- ---------------------------------------- -------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- -------- ,the third after ,leap-year4 ---------------------------------------- ------------------------------------ ,days ,january,dif4,february,dif4 ,march ,dif4 ,april ,dif4 ,may ,dif4 ,june ,dif4 ---------------------------------------- -------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------ ,inc4 ,inc4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #d #g #ab #ad #f #ab #ab #dd #ab #d #a #aa #ef #eb #aa #eg #ae #bh #g #ab #ah #h #i #b #ab #d #ce #ab #ad #ac #ab #ab #cb #ab #c #dc #aa #ef #dd #aa #eg #bd #bh #g #ac #ah #g #i #c #ab #e #c #ab #ad #bj #ab #ab #ai #ab #c #be #aa #ef #cg #aa #eg #cc #bg #f #ac #ah #g #i #d #ab #e #cj #ab #ad #bf #ab #ab #f #ab #c #g #aa #ef #cj #aa #eg #db #bg #e #ad #ah #f #aj #e #ab #e #eg #ab #ad #ca #ab #aa #eb #ab #b #di #aa #ef #bd #aa #eg #eb ------------ #bg -------- #d -------- #ad -------- #ah -------- #e -------- #aj #f #ab #f #bd #ab #ad #ce #ab #aa #ch #ab #b #ca #aa #ef #ai #aa #eh #b #bf #c #ad #ah #e #aa #g #ab #f #ej #ab #ad #ch #ab #aa #bd #ab #b #ac #aa #ef #ad #aa #eh #ac #be #b #ae #ah #d #aa #h #ab #g #ae #ab #ad #da #ab #aa #i #ab #a #ee #aa #ef #aj #aa #eh #bd #be #a #af #ag #d #aa #i #ab #g #dj #ab #ad #dc #ab #aj #ec #ab #a #ch #aa #ef #f #aa #eh #ce #be #a #af #ag #c #aa #aj #ab #h #e #ab #ad #dd #ab #aj #cg #ab #a #ba #aa #ef #c #aa #eh #df ------------ #bd --------,dec4-------- #af -------- #af -------- #b -------- #ab #aa #ab #h #bi #ab #ad #dd #ab #aj #ba #ab #a #e #aa #ef #a #aa #eh #eh #bc #a #af #af #b #ab #ab #ab #h #eb #ab #ad #dc #ab #aj #e #ab #j #di #aa #ee #ei #aa #ei #aj #bc #b #ag #af #b #ab #ac #ab #i #ae #ab #ad #da #ab #aj #dh #ab #j #cc #aa #ee #eg #aa #ei #bb #bb #b #ag #af #a #ab #ad #ab #i #cg #ab #ad #ci #ab #i #ca #ab #j #ag #aa #ee #ef #aa #ei #cd #ba #c #ag #ae ,inc4 #ac #ae #ab #i #eh #ab #ad #cf #ab #i #ad #ab #j #b #aa #ee #ef #aa #ei #dg ------------ #ba -------- #d -------- #ag -------- #ae -------- #a -------- #ac #af #ab #aj #ai #ab #ad #cb #ab #h #eg #aa #ei #dg #aa #ee #eg #ab #j #j #bj #d #ah #ae #a #ac #ag #ab #aj #ci #ab #ad #bh #ab #h #ci #aa #ei #cb #aa #ee #eh #ab #j #ac #ai #e #ah #ad #a #ac #ah #ab #aj #eh #ab #ad #bc #ab #h #ba #aa #ei #ah #aa #ee #ei #ab #j #bf #ah #f #ah #ad #b #ac #ai #ab #aa #af #ab #ad #ag #ab #h #c #aa #ei #d #aa #ef #a #ab #j #ci #ah #g #ah #ad #b #ac #bj #ab #aa #cd #ab #ad #aj #ab #g #de #aa #eh #ej #aa #ef #c #ab #j #eb ------------ #ag -------- #g -------- #ah -------- #ac -------- #c -------- #ac #ba #ab #aa #ea #ab #ad #c #ab #g #bg #aa #eh #cg #aa #ef #f #ab #a #e #af #h #ai #ac #d #ab #bb #ab #ab #g #ab #ac #ee #ab #g #h #aa #eh #bd #aa #ef #aj #ab #a #ag #af #h #ai #ab #d #ac #bc #ab #ab #bc #ab #ac #dg #ab #f #di #aa #eh #ab #aa #ef #ad #ab #a #cj #ae #i #ai #ab #e #ac #bd #ab #ab #ch #ab #ac #ch #ab #f #cj #aa #eh #j #aa #ef #ai #ab #a #dc #ad #i #ai #aa #e #ac #be #ab #ab #eb #ab #ac #bi #ab #f #aa #aa #eg #di #aa #ef #bd #ab #a #ef ------------ #ac -------- #aj -------- #ah -------- #aa -------- #f -------- #ac #bf #ab #ac #e #ab #ac #ai #ab #e #ec #aa #eg #ch #aa #ef #cj #ab #b #i #ab #aa #ai #aj #f #ac #bg #ab #ac #ag #ab #ac #h #ab #e #cd #aa #eg #bh #aa #ef #cf #ab #b #bb #aa #ab #ai #aj #g #ab #bh #ab #ac #bh #ab #ab #ef #ab #e #ae #aa #eg #ah #aa #ef #dc #ab #b #cd #aa #ab #ah #i #g #ab #bi #ab #ac #ci #ab #d #eg #aa #eg #i #aa #ef #ej #ab #b #df #aj #ai #i #h #ab #cj #ab #ac #di #ab #d #ch #aa #eg #j #aa #ef #eh #ab #b #eh ------------ #i -------------------- #ai -------- #h -------- #h -------- #ab #ca #ab #ac #eh #ab #d #ai #aa #eg #f #h #ah #i ---------------------------------------- ------------------------------------ ,incr4 #i #ea ,incr4 #j #ch ,decr4 #h #be ,decr4 #g #a ,decr4 #j #ef ,incr4 #e #dc ,decr4 #a #dh ,incr4 #a #aj ---------------------------------------- ---------------------------------------- --------- ,a ,,table of the ,equation of natural ,days1 shewing what ,time it ought to be by the ,clock when the ,sun is on the ,meridian4 ---------------------------------------- ---------------------------------------- --------- ,the third after ,leap-year4 ---------------------------------------- ------------------------------------- ,days ,july ,dif4 ,august ,dif4,september,dif4 ,october,dif4,november,dif4,december,dif 4 ---------------------------------------- --------------------------------- ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ,h4 ,m4 ,s4 ,s4 ---------------------------------------- ------------------------------------- ,inc4 ,dec4 ,dec4 ,dec4 ,dec4 ,inc4 #a #ab #c #aj #ab #e #di #aa #ei #dg #aa #di #db #aa #dc #di #aa #di #be #aa #d #ai #ah #a #bc #b #ab #c #ba #ab #e #de #aa #ei #bh #aa #di #bd #aa #dc #dh #aa #di #dh #aa #d #ai #ah ,inc4 #bd #c #ab #c #cb #ab #e #da #aa #ei #i #aa #di #f #aa #dc #dh #aa #ej #ab #aa #e #ai #ah #a #bd #d #ab #c #dc #ab #e #cf #aa #eh #ej #aa #dh #dh #aa #dc #di #aa #ej #cf #aa #e #ai #ah #b #be #e #ab #c #ed #ab #e #ca #aa #eh #ca #aa #dh #cj #aa #dc #ea #aa #ea #a ------------ #aj -------- #f --------- #bj -------- #ah -------- #b -------- #be #f #ab #d #d #ab #e #be #aa #eh #aa #aa #dh #ab #aa #dc #ec #aa #ea #bf #aj #g #bj #ag #c #bf #g #ab #d #ad #ab #e #ah #aa #eg #ea #aa #dg #ee #aa #dc #ef #aa #eb #eb #aj #g #bj #af #d #bg #h #ab #d #bd #ab #e #aa #aa #eg #ca #aa #dg #ci #aa #dd #j #aa #eb #ai #i #g #bj #af #e #bg #i #ab #d #cc #ab #e #d #aa #eg #aa #aa #dg #bc #aa #dd #e #aa #eb #df #i #h #bj #af #f #bg #aj #ab #d #db #ab #d #ef #aa #ef #ea #aa #dg #g #aa #dd #aa #aa #ec #ac ------------ #h -------- #h --------- #bj -------- #ae -------- #g -------- #bh #aa #ab #d #ej #ab #d #dh #aa #ef #ca #aa #df #eb #aa #dd #ah #aa #ec #da #h #i #ba #ae #h #bh #ab #ab #d #eh #ab #d #cg #aa #ef #aj #aa #df #cg #aa #dd #bf #aa #ed #i #h #aj #ba #ad #h #bh #ac #ab #e #f #ab #d #bg #aa #ee #di #aa #df #bc #aa #dd #cd #aa #ed #cg #g #aj #ba #ad #i #bi #ad #ab #e #ac #ab #d #ag #aa #ee #bh #aa #df #i #aa #dd #dc #aa #ee #f #f #aa #ba #ac #aj #cj #ae #ab #e #ai #ab #d #f #aa #ee #g #aa #de #ef #aa #dd #ec #aa #ee #cf ------------ #f -------- #ab --------- #bj -------- #ab -------- #aa -------- #bi #af #ab #e #be #ab #c #ed #aa #ed #dg #aa #de #dd #aa #de #d #aa #ef #f #f #ab #ba #ab #ab #cj #ag #ab #e #ca #ab #c #db #aa #ed #bf #aa #de #cb #aa #de #af #aa #ef #cf #e #ac #ba #ab #ac #cj #ah #ab #e #cf #ab #c #bi #aa #ed #e #aa #de #bj #aa #de #bi #aa #eg #f #e #ac #ba #aa #ad #bi #ai #ab #e #da #ab #c #af #aa #ec #dd #aa #de #i #aa #de #dc #aa #eg #ce #d #ac #ba #aj #ad #cj #bj #ab #e #de #ab #c #c #aa #ec #bc #aa #dd #ei #aa #de #eg #aa #eh #e ------------ #d -------- #ad --------- #bj -------- #i -------- #ae -------- #cj #ba #ab #e #di #ab #b #di #aa #ec #c #aa #dd #ej #aa #df #ab #aa #eh #cd #c #ae #ba #i #af #cj #bb #ab #e #eb #ac #b #cd #aa #eb #db #aa #dd #da #aa #df #bh #aa #ei #d #c #ae #ba #i #ag #cj #bc #ab #e #ee #ab #b #ai #aa #eb #ba #aa #dd #cb #aa #df #de #aa #ei #cd #b #ae #bj #h #ag #cj #bd #ab #e #eg #ab #b #d #aa #eb #a #aa #dd #bd #aa #dg #b #ab #j #d #a #af #ba #g #ah #cj #be #ab #e #eh #ab #a #dh #aa #ea #dj #aa #dd #ag #aa #dg #bj #ab #j #cd ------------ #a -------- #af --------- #bj -------- #f -------- #ai -------- #cj #bf #ab #e #ei #ab #a #cb #aa #ea #bj #aa #dd #aa #aa #dg #ci #ab #a #d ,dec4 #af #bj #e #bj #cj #bg #ab #e #eh #ab #a #af #aa #ea #j #aa #dd #f #aa #dg #ei #ab #a #cd #a #ag #bj #e #bj #cj #bh #ab #e #eg #ab #j #ei #aa #ej #dj #aa #dd #a #aa #dh #ai #ab #b #d #a #ag #bj #d #ba #bi #bi #ab #e #ef #ab #j #db #aa #ej #bj #aa #dc #eg #aa #dh #dj #ab #b #cc #b #ah #ai #c #bb #bi #cj #ab #e #ed #ab #j #bd #aa #ej #a #aa #dc #ed #aa #di #b #ab #c #b ------------ #b -------- #ah --------- #ai -------- #c -------- #bc -------- #bi #ca #ab #e #eb #ab #j #f #aa #dc #ea #ab #c #ca #c #ai #b #bi ---------------------------------------- ------------------------------------- ,incr4 #b #dh ,decr4 #e #dc ,decr4 #i #df ,decr4 #e #ea ,decr4 #j #a ,incr4 #ad #f ,decr4 #j #g ,incr4 #e #ad ,,chap4 ,,xv4 ,the ,moon's surface mountainous3 ,her ,phases described3 ,her path1 and the paths of ,jupiter's ,moons delineated3 ,the proportions of the ,diameters of their ,orbits1 and those of ,saturn's ,moons1 to each other2 and to the ,diameter of the ,sun4 ,sidenote3 ,,pl4 ,,vii4 ,the ,moon's surface mountainous4 #beb4 ,by looking at the ,moon with an ordinary telescope we perceive that her surface is diversified with long tracts of prodigious high mountains and deep cavities4 ,some of her mountains1 by comparing their height with her diameter 7which is #bahj miles7 are found to be three times higher than the highest hills on our ,earth4 ,this ruggedness of the ,moon's surface is of great use to us1 by reflecting the ,sun's light to all sides3 for if the ,moon were smooth and polished like a looking-glass1 or covered with water1 she could never distribute the ,sun's light all round2 only in some positions she would shew us his image1 no bigger than a point1 but with such a lustre as would be hurtful to our eyes4 ,sidenote3 ,why no hills appear on her edge4 #bec4 ,the ,moon's surface being so uneven1 many have wondered why her edge appears not jagged1 as well as the curve bounding the light and dark places4 ,but if we consider1 that what we call the edge of the ,moon's ,disc is not a single line set round with mountains1 in which case it would appear irregularly indented1 but a large ,zone having many mountains lying behind one another from the observer's eye1 we shall find that the mountains in some rows will be opposite to the vales in others2 and so fill up the inequalities as to make her appear quite round3 just as when one looks at an orange1 although it's roughness be very discernible on the side next the eye1 especially if the ,sun or a ,candle shines obliquely on that side1 yet the line terminating the visible part still appears smooth and even4 ,illustration3 ,plate ,,vii4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 ,sidenote3 ,the ,moon has no twilight4 ,fig4 ,i4 #bed4 ,as the ,sun can only enlighten that half of the ,earth which is at any moment turned towards him1 and being withdrawn from the opposite half leaves it in darkness2 so he likewise doth to the ,moon3 only with this difference1 that the ,earth being surrounded by an ,atmosphere1 and the ,moon having none1 we have twilight after the ,sun sets2 but the ,lunar ,inhabitants have an immediate transition from the brightest ,sun-shine to the blackest darkness #agg4 ,for1 let tkrsw be the ,earth1 and ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 ,h the ,moon in eight different parts of her ,orbit4 ,as the ,earth turns round its ,axis1 from west to east1 when any place comes to t the twilight begins there1 and when it revolves from thence to r the ,sun ,s rises2 when the place comes to s the ,sun sets1 and when it comes to w the twilight ends4 ,but as the ,moon turns round her ,axis1 which is only once a month1 the moment that any point of her surface comes to r 7see the ,moon at ,g7 the ,sun rises there without any previous warning by twilight2 and when the same point comes to s the ,sun sets1 and that point goes into darkness as black as at midnight4 ,sidenote3 ,the ,moon's ,phases4 #bee4 ,the ,moon being an opaque spherical body1 7for her hills take off no more from her roundness than the inequalities on the surface of an orange takes off from its roundness7 we can only see that part of the enlightened half of her which is towards the ,earth4 ,and therefore1 when the ,moon is at ,a1 in conjunction with the ,sun ,s1 her dark half is towards the ,earth1 and she disappears as at a1 there being no light on that half to render it visible4 ,when she comes to her first ,octant at ,b1 or has gone an eighth part of her orbit from her ,conjunction1 a quarter of her enlightened side is towards the ,earth1 and she appears horned as at b4 ,when she has gone a quarter of her orbit from between the ,earth and ,sun to ,c1 she shews us one half of her enlightened side as at c1 and we say1 she is a quarter old4 ,at ,d she is in her second ,octant1 and by shewing us more of her enlightened side she appears gibbous as at d4 ,at ,e her whole enlightened side is towards the ,earth1 and therefore she appears round as at e1 when we say1 it is ,full ,moon4 ,in her third ,octant at ,f1 part of her dark side being towards the ,earth1 she again appears gibbous1 and is on the decrease1 as at f4 ,at ,g we see just one half of her enlightened side1 and she appears half decreased1 or in her third ,quarter1 as at g4 ,at ,h we only see a quarter of her enlightened side1 being in her fourth ,octant1 where she appears horned as at h4 ,and at ,a1 having compleated her course from the ,sun to the ,sun again1 she disappears2 and we say1 it is ,new ,moon4 ,thus in going from ,a to ,e the ,moon seems continually to increase2 and in going from ,e to ,a1 to decrease in the same proportion2 having like ,phases at equal distances from ,a or ,e1 but as seen from the ,sun ,s1 she is always ,full4 ,sidenote3 ,the ,moon's ,disc not always quite round when full4 #bef4 ,the ,moon appears not perfectly round when she is ,full in the highest or lowest part of her ,orbit1 because we have not a direct view of her enlightened side at that time4 ,when ,full in the highest part of her orbit1 a small deficiency appears on her lower edge2 and the contrary when ,full in the lowest part of her ,orbit4 ,sidenote3 ,the ,phases of the ,earth and ,moon contrary4 #beg4 ',tis plain by the ,figure1 that when the ,moon changes to the ,earth1 the ,earth appears ,full to the ,moon2 and vice vers4 ,for when the ,moon is at ,a1 ,new to the ,earth1 the whole enlightened side of the ,earth is towards the ,moon3 and when the ,moon is at ,e1 ,full to the ,earth1 it's dark side is towards her4 ,hence a ,new ,moon answers to a ,full ,earth1 and a ,full ,moon to a ,new ,earth4 ,the ,quarters are also reversed to each other4 ,sidenote3 ,an agreeable ,phenomenon4 #beh4 ,between the third ,quarter and ,change1 the ,moon is frequently visible in the forenoon1 even when the ,sun shines2 and then she affords us an opportunity of seeing a very agreeable appearance1 wherever we find a globular stone above the level of the eye1 as suppose on the top of a gate4 ,for1 if the ,sun shines on the stone1 and we place ourselves so as the upper part of the stone may just seem to touch the point of the ,moon's lowermost horn1 we shall then see the enlightened part of the stone exactly of the same shape with the ,moon2 horned as she is1 and inclining the same way to the ,horizon4 ,the reason is plain2 for the ,sun enlightens the stone the same way as he does the ,moon3 and both being ,globes1 when we put ourselves into the above situation1 the ,moon and stone have the same position to our eyes2 and therefore we must see as much of the illuminated part of the one as of the other4 ,sidenote3 ,the nonagesimal ,degree1 what4 #bei4 ,the position of the ,moon's ,cusps1 or a right line touching the points of her horns1 is very differently inclined to the ,horizon at different hours of the same days of her age4 ,sometimes she stands1 as it were1 upright on her lower horn1 and then such a line is perpendicular to the ,horizon3 when this1 happens1 she is in what the ,astronomers call the ,nonagesimal ,degree2 which is the highest point of the ,ecliptic above the ,horizon at that time1 and is #ij degrees from both sides of the ,horizon where it is then cut by the ,ecliptic4 ,but this never happens when the ,moon is on the ,meridian1 except when she is at the very beginning of ,cancer or ,capricorn4 ,sidenote3 ,how the inclination of the ,ecliptic may be found by the position of the ,moon horns4 ,,pl4 ,,vii4 #bfj4 ,the inclination of that part of the ,ecliptic to the ,horizon in which the ,moon is at any time when horned1 may be known by the position of her horns2 for a right line touching their points is perpendicular to the ,ecliptic4 ,and as the ,angle that the ,moon's orbit makes with the ,ecliptic can never raise her above1 nor depress her below the ,ecliptic1 more than two minutes of a degree1 as seen from the ,sun2 it can have no sensible effect upon the position of her horns4 ,therefore1 if a ,quadrant be held up1 so as one of it's edges may seem to touch the ,moon's horns1 the graduated side being kept towards the eye1 and as far from the eye as it can be conveniently held1 the arc between the ,plumb-line and that edge of the ,quadrant which seems to touch the ,moon's horns will shew the inclination of that part of the ,ecliptic to the ,horizon4 ,and the arc between the other edge of the ,quadrant and ,plumb-line will shew the inclination of the ,moon's horns to the ,horizon at that time also4 ,sidenote3 ,fig4 ,i4 ,why the ,moon appears as big as the ,sun4 #bfa4 ,the ,moon generally appears as large as the ,sun2 for the ,angle vk,a1 under which the ,moon is seen from the ,earth1 is the same with the ,angle ,lk,m1 under which the ,sun is seen from it4 ,and therefore the ,moon may hide the ,sun's whole ,disc from us1 as she sometimes does in solar ,eclipses4 ,the reason why she does not eclipse the ,sun at every ,change shall be explained afterwards4 ,if the ,moon were farther from the ,earth as at a1 she could never hide the whole of the ,sun from us2 for then she would appear under the ,angle ,nk,o1 eclipsing only that part of the ,sun which lies between ,n and ,o3 were she still further from the ,earth1 as at ,x1 she would appear under the small ,angle ,tk,w1 like a spot on the ,sun1 hiding only the part ,,tw from our sight4 ,sidenote3 ,a proof of the ,moon's turning round her ,axis4 #bfb4 ,the ,moon turns round her ,axis in the time that she goes round her orbit2 which is evident from hence1 that a spectator at rest1 without the periphery of the ,moon's orbit1 would see all her sides turned regularly towards him in that time4 ,she turns round her ,axis from any ,star to the same ,star again in #bg days #h hours2 from the ,sun to the ,sun again in #bi-a_/b days3 the former is the length of her sidereal day1 and the latter the length of her solar day4 ,a body moving round the ,sun would have a solar day in every revolution1 without turning on it's ,axis2 the same as if it had kept all the while at rest1 and the ,sun moved round it3 but without turning round it's ,axis it could never have one sidereal day1 because it would always keep the same side towards any given ,star4 ,sidenote3 ,her periodical and synodical ,revolution4 #bfc4 ,if the ,earth had no annual motion1 the ,moon would go round it so as to compleat a ,lunation1 a sidereal1 and a solar day1 all in the same time4 ,but1 because the ,earth goes forward in it's orbit while the ,moon goes round the ,earth in her orbit1 the ,moon must go as much more than round her orbit from ,change to ,change in compleating a solar day as the ,earth has gone forward in it's orbit during that time1 i4 e4 almost a twelfth part of a ,circle4 ,sidenote3 ,familiarly represented4 ,a ,table shewing the times that the hour and minute hands of a watch are in conjunction4 ,a machine for shewing the motions of the ,sun and ,moon4 ,,pl4 ,,vii4 #bfd4 ,the ,moon's periodical and synodical revolution may be familiarly represented by the motions of the hour and minute hands of a watch round it's dial-plate1 which is divided into #ab equal parts or hours1 as the ,ecliptic is divided into #ab ,signs1 and the year into #ab months4 ,let us suppose these #ab hours to be #ab months1 the hour hand the ,sun1 and the minute hand the ,moon2 then will the former go round once in a year1 and the latter once in a month2 but the ,moon1 or minute hand must go more than round from any point of the ,circle where it was last conjoined with the ,sun1 or hour hand1 to overtake it again3 for the hour hand being in motion1 can never be overtaken by the minute hand at that point from which they started at their last conjunction4 ,the first column of the annexed ,table shews the number of conjunctions which the hour and minute hand make whilst the hour hand goes once round the dial-plate2 and the other columns shew the times when the two hands meet at every conjunction4 ,thus1 suppose the two hands to be in conjunction at ,,xii1 as they always are2 then1 at the first following conjunction it is #e minutes #bg seconds #af thirds #ba fourths #di-a_/aa fifths past ,i where they meet2 at the second conjunction it is #aj minutes #ed seconds #cb thirds #dc fourths #ch-a_/b fifths past ,,ii2 and so on4 ,this1 though an easy illustration of the motions of the ,sun and ,moon1 is not precise as to the times of their conjunctions2 because1 while the ,sun goes round the ,ecliptic1 the ,moon makes #ab-a_/c conjunctions with him2 but the minute hand of a watch or clock makes only #aa conjunctions with the hour hand in one period round the dial-plate4 ,but if1 instead of the common wheel-work at the back of the dial-plate1 the ,axis of the minute hand had a pinion of #f leaves turning a wheel of #dj1 and this last turning the hour hand1 in every revolution it makes round the dial-plate the minute hand would make #ab-a_/c conjunctions with it2 and so would be a pretty device for shewing the motions of the ,sun and ,moon2 especially1 as the slowest moving hand might have a little ,sun fixed on it's point1 and the quickest a little ,moon4 ,besides1 the plate1 instead of hours and quarters1 might have a ,circle of months1 with the #ab ,signs and their ,degrees2 and if a plate of #bi-a_/b equal parts for the days of the ,moon's age were fixed to the ,axis of the ,sun-hand1 and below it1 so as the ,sun always kept at the #a_/b day of that plate1 the ,moon-hand would shew the ,moon's age upon that plate for every day pointed out by the ,sun-hand in the ,circle of months2 and both ,sun and ,moon would shew their places in the ,ecliptic3 for the ,sun would go round the ,ecliptic in #cfe ,days and the ,moon in #bg-a_/c days1 which is her periodical revolution2 but from the ,sun to the ,sun again1 or from ,change to ,change1 in #bi-a_/b days1 which is her synodical revolution4 ------------------------------------ ,conj4 ,h4 ,m4 ,s4 v pts4 ------------------------------------ #a ,i #e #bg #af #ba #di-a_/aa #b ,,ii #aj #ed #cb #dc #ch-b_/aa #c ,,iii #af #ba #di #e #bg-c_/aa #d ,,iiii #ba #di #e #bg #af-d_/aa #e ,v #bg #af #ba #di #e-e_/aa #f ,,vi #cb #dc #ch #aj #ed-f_/aa #g ,,vii #ch #aj #ed #cb #dc-g_/aa #h ,,viii #dc #ch #aj #ed #cb-h_/aa #i ,,ix #di #e #bg #af #ba-i_/aa #aj ,x #ed #cb #dc #ch #aj-aj_/aa #aa ,,xii #j #j #j #j #j ------------------------------------ ,sidenote3 ,the ,moon's motion thro' open space described4 #bfe4 ,if the ,earth had no annual motion1 the ,moon's motion round the ,earth1 and her track in absolute space1 would be always the same#eh4 ,but as the ,earth and ,moon move round the ,sun1 the ,moon's real path in the ,heavens is very different from her path round the ,earth3 the latter being in a progressive ,circle1 and the former in a curve of different degrees of concavity1 which would always be the same in the same parts of the ,heavens1 if the ,moon performed a compleat number of ,lunations in a year4 ,sidenote3 ,an idea of the ,earth's path and the ,moon's4 #bff4 ,let a nail in the end of the axle of a chariot-wheel represent the ,earth1 and a pin in the nave the ,moon2 if the body of the chariot be propped up so as to keep that wheel from touching the ground1 and the wheel be then turned round by hand1 the pin will describe a ,circle both round the nail and in the space it moves through4 ,but if the props be taken away1 the horses put to1 and the chariot driven over a piece of ground which is circularly convex2 the nail in the axle will describe a circular curve1 and the pin in the nave will still describe a circle round the progressive nail in the axle1 but not in the space through which it moves4 ,in this case1 the curve described by the nail will resemble in miniature as much of the ,earth's annual path round the ,sun1 as it describes whilst the ,moon goes as often round the ,earth as the pin does round the nail3 and the curve described by the nail will have some resemblance of the ,moon's path during so many ,lunations4 ,sidenote3 ,fig4 ,,ii4 ,,pl4 ,,vii4 ,let us now suppose that the ,radius of the circular curve described by the nail in the axle is to the ,radius of the ,circle which the pin in the nave describes round the axle as #ccg-a_/b to #a2 which is the proportion of the ,radius or ,semidiameter of the ,earth's ,orbit to that of the ,moon's2 or of the circular curve ,a #a #b #c #d #e #f #g ,b c4 to the little ,circle a2 and then1 whilst the progressive nail describes the said curve from ,a to ,e1 the pin will go once round the nail with regard to the center of it's path1 and in doing so1 will describe the curve abcde4 ,the former will be a true representation of the ,earth's path for one ,lunation1 and the latter of the ,moon's for that time4 ,here we may set aside the inequalities of the ,moon's ,moon1 and also the ,earth's moving round it's common center of gravity and the ,moon's3 all which1 if they were truly copied in this experiment1 would not sensibly alter the figure of the paths described by the nail and pin1 even though they should rub against a plain upright surface all the way1 and leave their tracks visible4 ,and if the chariot should be driven forward on such a convex piece of ground1 so as to turn the wheel several times round1 the track of the pin in the nave would still be concave toward the center of the circular curve described by the pin in the ,axle2 as the ,moon's path is always concave to the ,sun in the center of the ,earth's annual ,orbit4 ,sidenote3 ,proportion of the ,moon's ,orbit to the ,earth's4 ,in this ,diagram1 the thickest curve line ,,abcd1 with the numeral figures set to it1 represents as much of the ,earth's annual ,orbit as it describes in #cb days from west to east2 the little ,circles at a1 b1 c1 d1 e shew the ,moon's ,orbit in due proportion to the ,earth's2 and the smallest curve abcdef represents the line of the ,moon's path in the ,heavens for #cb days1 accounted from any particular ,new ,moon at a4 ,the machine1 ,fig4 #eth is for delineating the ,moon's path1 and will be described1 with the rest of my ,astronomical machinery1 in the last ,chapter4 ,the ,sun is supposed to be in the center of the curve ,a #a #b #c #d #e #f #g ,b c4 and the small dotted ,circles upon it represent the ,moon's ,orbit1 of which the ,radius is in the same proportion to the ,earth's path in this scheme1 that the ,radius of the ,moon's ,orbit in the ,heavens bears to the ,radius of the ,earth's annual path round the ,sun2 that is1 as #bdj1jjj to #ha1jjj1jjj1 or as #a to #ccg-a_/b4 ,sidenote3 ,fig4 ,,ii4 ,when the ,earth is at ,a the ,new ,moon is at a2 and in the seven days that the ,earth describes the curve #a #b #c #d #e #f #g1 the ,moon in accompanying the ,earth describes the curve ab2 and is in her first ,quarter at b when the ,earth is at ,b4 ,as the ,earth describes the curve ,b #h #i #aj #aa #ab #ac #ad the ,moon describes the curve bc2 and is opposite to the ,sun at c1 when the ,earth is at ,c4 ,whilst the ,earth describes the curve ,c #ae #af #ag #ah #ai #bj #ba #bb the ,moon describes the curve cd2 and is in her third ,quarter at d when the ,earth is at ,d4 ,once more1 whilst the ,earth describes the curve ,d #bc #bd #be #bf #bg #bh #bi the ,moon describes the curve de2 and is again in conjunction at e with the ,sun when the ,earth is at ,e1 between the #bith and #cjth day of the ,moon's age1 accounted by the numeral ,figures from the ,new ,moon at ,a4 ,in describing the curve abcde1 the ,moon goes round the progressive ,earth as really as if she had kept in the dotted ,circle ,a1 and the ,earth continued immoveable in the center of that ,circle4 ,sidenote3 ,the ,moon's motion always concave towards the ,sun4 ,and thus we see1 that although the ,moon goes round the ,earth in a ,circle1 with respect to the ,earth's center1 her real path in the ,heavens is not very different in appearance from the ,earth's path4 ,to shew that the ,moon's path is concave to the ,sun1 even at the time of ,change1 it is carried on a little farther into a second ,lunation1 as to f4 ,sidenote3 ,how her motion is alternately retarded and accelerated4 #bfg4 ,the ,moon's absolute motion from her ,change to her first ,quarter1 or from a to b1 is so much slower than the ,earth's1 that she falls #bdj thousand miles 7equal to the ,semidiameter of her ,orbit7 behind the ,earth at her first ,quarter in b1 when the ,earth is in ,b2 that is1 she falls back a space equal to her distance from the ,earth4 ,from that time her motion is gradually accelerated to her ,opposition or ,full at c1 and then she is come up as far as the ,earth1 having regained what she lost in her first ,quarter from a to b4 ,from the ,full to the last ,quarter at d her motion continues accelerated1 so as to be just as far before the ,earth at ,d1 as she was behind it at her first ,quarter in b4 ,but1 from d to e her motion is retarded so1 that she loses as much with respect to the ,earth as is equal to her distance from it1 or to the ,semidiameter of her ,orbit2 and by that means she comes to e1 and is then in conjunction with the ,sun as seen from the ,earth at ,e4 ,hence we find1 that the ,moon's absolute motion is slower than the ,earth's from her third ,quarter to her first2 and swifter than the ,earth's from her first ,quarter to her third3 her path being less curved than the ,earth's in the former case1 and more in the latter4 ,yet it is still bent the same way towards the ,sun2 for if we imagine the concavity of the ,earth's ,orbit to be measured by the length of a perpendicular line ,cg1 let down from the ,earth's place upon the straight line bgd at the ,full of the ,moon1 and connecting the places of the ,earth at the end of the ,moon's first and third ,quarters1 that length will be about #fdj thousand miles2 and the ,moon when ,new only approaching nearer to the ,sun by #bdj thousand miles than the ,earth is1 the length of the perpendicular let down from her place at that time upon the same straight line1 and which shews the concavity of that part of her path1 will be about #djj thousand miles4 ,sidenote3 ,a difficulty removed4 ,,pl4 ,,vii4 #bfh4 ,the ,moon's path being concave to the ,sun throughout1 demonstrates that her gravity towards the ,sun1 at her conjunction1 exceeds her gravity towards the ,earth4 ,and if we consider that the quantity of matter in the ,sun is almost #bcj thousand times as great as the quantity of matter in the ,earth1 and that the attraction of each body diminishes as the square of the distance from it increases1 we shall soon find1 that the point of equal attraction where these two powers would be equally strong1 is about #gj thousand miles nearer the ,earth than the ,moon is at her ,change4 ,it may now appear surprising that the ,moon does not abandon the ,earth when she is between it and the ,sun1 because she is considerably more attracted by the ,sun than by the ,earth at that time4 ,but this difficulty vanishes when we consider1 that the ,moon is so near the ,earth in proportion to the ,earth's distance from the ,sun1 that she is but very little more attracted by the ,sun at that time than the ,earth is2 and whilst the ,earth's attraction is greater upon the ,moon than the difference of the ,sun's attraction upon the ,earth and her 7and that it is always much greater is demonstrable7 there is no danger of the ,moon's leaving the ,earth2 for if she should fall towards the ,sun1 the ,earth would follow her almost with equal speed4 ,the absolute attraction of the ,earth upon a drop of falling rain is much greater than the absolute attraction of the particles of that drop upon each other1 or of it's center upon all parts of it's circumference2 but then the side of the drop next the ,earth is attracted with so very little more force than it's center1 or even it's opposite side2 that the attraction of the center of the drop upon it's side next the ,earth is much greater than the difference of force by which the ,earth attracts it's nearer surface and center3 on which account the drop preserves it's round figure1 and might be projected about the ,earth by a strong circulating wind so as to be kept from falling to the ,earth4 ,it is much the same with the ,earth and ,moon in respect to the ,sun2 for if we should suppose the ,moon's ,orbit to be filled with a fluid ,globe1 of which all the parts would be attracted towards the ,earth in it's center1 but the whole of it much more attracted by the ,sun2 one part of it could not fall to the ,sun without the other1 and a sufficient projectile force would carry the whole fluid ,globe round the ,sun4 ,a ship1 at the distance of the ,moon1 sailing round the ,earth on the surface of the fluid ,globe1 could no more be taken away by the ,sun when it is on the side next him1 than the ,earth could be taken away from it when it is on the opposite side2 which could never happen unless the ,earth's projectile motion were stopt2 and if it were stopt1 the ,ship with the whole fluid ,globe1 ,earth and all together1 would as naturally fall to the ,sun as a drop of rain in calm air falls to the ,earth4 ,hence we may see1 that the ,earth is in no more danger of being left by the ,moon at the ,change1 than the ,moon is of being left by the ,earth at the ,full3 the diameter of the ,moon's ,orbit being so small in comparison of the ,sun's distance1 that the ,moon is but little more or less attracted than the ,earth at any time4 ,and as the ,moon's projectile force keeps her from falling to the ,earth1 so the ,earth's projectile force keeps it from falling to the ,sun4 ,sidenote3 ,fig4 ,,iii4 #bfi4 ,all the curves which ,jupiter's ,satellites describe1 are different from the path described by our ,moon1 although these ,satellites go round ,jupiter1 as the ,moon goes round the ,earth4 ,let ,,abcde c4 be as much of ,jupiter's ,orbit as he describes in #ah days from ,a to ,t2 and the curves a1 b1 c1 d will be the paths of his four ,moons going round him in his progressive motion4 ,sidenote3 ,the absolute ,path of ,jupiter and his ,satellites delineated4 ,fig4 ,,iii4 ,now let us suppose all these ,moons to set out from a conjunction with the ,sun1 as seen from ,jupiter4 ,when ,jupiter is at ,a his first or nearest ,moon will be at a1 his second at b1 his third at c1 and his fourth at d4 ,at the end of #bd terrestrial hours after this conjunction1 ,jupiter has moved to ,b1 his first ,moon or ,satellite has described the curve a#a1 his second the curve b#a1 his third c#a1 and his fourth d#a4 ,the next day when ,jupiter is at ,c1 his first ,satellite has described the curve a#b from its conjunction1 his second the curve b#b1 his third the curve c#b1 and his fourth the curve d#b1 and so on4 ,the numeral ,figures under the capital letters shew ,jupiter's place in his path every day for #ah days1 accounted from ,a to ,t2 and the like ,figures set to the paths of his ,satellites1 shew where they are at the like times4 ,the first ,satellite1 almost under ,c1 is stationary at as seen from the ,sun2 and retrograde from to #b3 at #b it appears stationary again1 and thence it moves forward until it has past #c1 being twice stationary1 and once retrograde between #c and #d4 ,the path of this ,satellite intersects itself every #db-a_/b hours of our time1 making such loops as in the ,diagram at #b4 #c4 #e4 #g4 #i4 #aj4 #ab4 #ad4 #af4 #ah1 a little after every ,conjunction4 ,the second ,satellite b1 moving slower1 barely crosses it's path every #c days #ac hours2 as at #d4 #g4 #aa4 #ad4 #ah1 making only five loops and as many conjunctions in the time that the first makes ten4 ,the third ,satellite c moving still slower1 and having described the curve c #a4 #b4 #c4 #d4 #e4 #f4 #g1 comes to an ,angle at #g in conjunction with the ,sun at the end of #g days #d hours2 and so goes on to describe such another curve #g4 #h4 #i4 #aj4 #aa4 #ab4 #ac4 #ad1 and is at #ad in it's next conjunction4 ,the fourth ,satellite d is always progressive1 making neither loops nor angles in the ,heavens2 but comes to it's next conjunction at e between the numeral figures #af and #ag1 or in #af days #ah hours4 ,in order to have a tolerably good figure of the paths of these ,satellites1 ,i took the following method4 ,sidenote3 ,fig4 ,,iv4 ,,pl4 ,,vii4 ,how to delineate the paths of ,jupiter's ,moons4 ,and ,saturn's4 ,having drawn their ,orbits on a ,card1 in proportion to their relative distances from ,jupiter1 ,i measured the radius of the ,orbit of the fourth ,satellite1 which was an inch and a tenth part2 then multiplied this by #dbd for the radius of ,jupiter's ,orbit1 because ,jupiter is #dbd times as far from the ,sun's center as his fourth ,satellite is from his center2 and the product thence arising was #dff-d_/aj inches4 ,then taking a small cord of this length1 and fixing one end of it to the floor of a long room by a nail1 with a black lead pencil at the other end ,i drew the curve ,,abcd c4 and set off a degree and an half thereon1 from ,a to ,t2 because ,jupiter moves only so much1 whilst his outermost ,satellite goes once round him1 and somewhat more2 so that this small portion of so large a circle differs but very little from a straight line4 ,this done1 ,i divided the space ,,at into #ah equal parts1 as ,,ab1 ,,bc1 c4 for the daily progress of ,jupiter2 and each part into #bd for his hourly progress4 ,the ,orbit of each ,satellite was also divided into as many equal parts as the ,satellite is hours in finishing it's synodical period round ,jupiter4 ,then drawing a right line through the center of the ,card1 as a diameter to all the #d ,orbits upon it1 ,i put the card upon the line of ,jupiter's motion1 and transferred it to every horary division thereon1 keeping always the said diameter-line on the line of ,jupiter's path2 and running a pin through each horary division in the ,orbit of each ,satellite as the card was gradually transferred along the ,line ,,abcd etc4 of ,jupiter's motion1 ,i marked points for every hour through the ,card for the ,curves described by the ,satellites as the primary planet in the center of the ,card was carried forward on the line3 and so finished the ,figure1 by drawing the lines of each ,satellite's motion1 through those 7almost innumerable7 points3 by which means1 this is perhaps as true a ,figure of the paths of these ,satellites as can be desired4 ,and in the same manner might those for ,saturn's ,satellites be delineated4 ,sidenote3 ,the grand ,period of ,jupiter's ,moons4 #bgj4 ,it appears by the scheme1 that the three first ,satellites come almost into the same line or position every seventh day2 the first being only a little behind with the second1 and the second behind with the third4 ,but the period of the fourth ,satellite is so incommensurate to the periods of the other three1 that it cannot be guessed at by the diagram when it would fall again into a line of conjunction with them1 between ,jupiter and the ,sun4 ,and no wonder2 for supposing them all to have been once in conjunction1 it will require #c1jhg1jdc1dic1bfj years to bring them in a conjunction again3 ,see #gc4 ,sidenote3 ,fig4 ,,iv4 ,the proportions of the ,orbits of the ,planets and ,satellites4 #bga4 ,in ,fig4 #dth we have the proportions of the ,orbits of ,saturn's five ,satellites1 and of ,jupiter's four1 to one another1 to our ,moon's ,orbit1 and to the ,disc of the ,sun4 ,s is the ,sun2 ,m m the ,moon's ,orbit 7the ,earth supposed to be at ,e27 ,j ,jupiter2 #a4 #b4 #c4 #d the ,orbits of his four ,moons or ,satellites2 ,sat ,saturn2 and #a4 #b4 #c4 #d4 #e the ,orbits of his five ,moons4 ,hence it appears1 that the ,sun would much more than fill the whole ,orbit of the ,moon2 for the ,sun's diameter is #gfc1jjj miles1 and the diameter of the ,moon's ,orbit only #dhj1jjj4 ,in proportion to all these ,orbits of the ,satellites1 the ,radius of ,saturn's annual ,orbit would be #ba-a_/d yards1 of ,jupiter's orbit #aa-b_/c1 and of the ,earth's #b-a_/d1 taking them in round numbers4 #bgb4 ,the annexed table shews at once what proportion the ,orbits1 ,revolutions1 and ,velocities1 of all the ,satellites bear to those of their primary ,planets1 and what sort of curves the several ,satellites describe4 ,for1 those ,satellites whose velocities round their primaries are greater than the velocities of their primaries in open space1 make loops at their conjunctions #bfi2 appearing retrograde as seen from the ,sun whilst they describe the inferior parts of their ,orbits1 and direct whilst they describe the superior4 ,this is the case with ,jupiter's first and second ,satellites1 and with ,saturn's first4 ,but those ,satellites whose velocities are less than the velocities of their primary planets move direct in their whole circumvolutions2 which is the case of the third and fourth ,satellites of ,jupiter1 and of the second1 third1 fourth1 and fifth ,satellites of ,saturn1 as well as of our ,satellite the ,moon3 ,but the ,moon is the only ,satellite whose motion is always concave to the ,sun4 ,there is a table of this sort in ,de la ,caile's ,astronomy1 but it is very different from the above1 which ,i have computed from our ,english accounts of the periods and distances of these ,planets and ,satellites4 ---------------------------------------- --------------------------- ,proportion of ,proportion of ,proportion of the ,radius of the ,time of the ,velocity of ,the the ,planet's the ,planet's each ,satellite ,satellites ,orbit to the ,revolution to to the ,velocity ,radius of the the ,revolution of its primary ,orbit of each of each ,planet4 ,satellite4 ,satellite4 ---------------------------------------- --------------------------- of ,saturn #a ,as #ecbb to #a ,as #egch to #a ,as #egch to #ecbb #b #daee #a #ciab #a #ciab #daee #c #bied #a #bcdg #a #bcdg #bied #d #abie #a #fgd #a #fgd #abie #e #dcb #a #acd #a #acd #dcb ---------------------------------------- --------------------------- of ,jupiter #a ,as #ahea to #a ,as #bdde to #a ,as #bdde to #ahea #b #aafe #a #abai #a #abai #aafe #c #gca #a #fjd #a #fjd #gca #d #dbd #a #beh #a #beh #dbd ---------------------------------------- --------------------------- ,the ,moon ,as #ccg-a_/b to #a ,as #ab-a_/c to #a ,as #ab-a_/c to #ccg-a_/b ---------------------------------------- --------------------------- ,,chap4 ,,xvi4 ,the ,phenomena of the ,harvest-,moon explained by a common ,globe3 ,the years in which the ,harvest-,moons are least and most beneficial from #agea1 to #ahfa4 ,the long duration of ,moon-light at the ,poles in winter4 ,sidenote3 ,no ,harvest-,moon at the ,equator4 #bgc4 ,it is generally believed that the ,moon rises about #dh minutes later every day than on the preceding2 but this is true only with regard to places on the ,equator4 ,in places of considerable ,latitude there is a remarkable difference1 especially in the harvest time2 with which ,farmers were better acquainted than ,astronomers till of late2 and gratefully ascribed the early rising of the ,full ,moon at that time of the year to the goodness of ,god1 not doubting that he had ordered it so on purpose to give them an immediate supply of moon-light after sun-set for their greater conveniency in reaping the fruits of the earth4 ,sidenote3 ,but remarkable according to the distance of places from it4 ,in this instance of the harvest-moon1 as in many others discoverable by ,astronomy1 the wisdom and beneficence of the ,deity is conspicuous1 who really ordered the course of the ,moon so1 as to bestow more or less light on all parts of the earth as their several circumstances and seasons render it more or less serviceable4 ,about the ,equator1 where there is no variety of seasons1 and the weather changes seldom1 and at stated times1 ,moon-light is not necessary for gathering in the produce of the ground2 and there the moon rises about #dh minutes later every day or night than on the former4 ,at considerable distances from the ,equator1 where the weather and seasons are more uncertain1 the autumnal ,full ,moons rise very soon after sun-set for several evenings together4 ,at the polar circles1 where the mild season is of very short duration1 the autumnal ,full ,moon rises at ,sun-set from the first to the third quarter4 ,and at the ,poles1 where the ,sun is for half a year absent1 the winter ,full moons shine constantly without setting from the first to the third quarter4 ,sidenote3 ,the reason of this4 ,it is soon said that all these ,phenomena are owing to the different ,angles made by the ,horizon and different parts of the ,moon's orbit2 and that the ,moon can be full but once or twice in a year in those parts of her orbit which rise with the least angles4 ,but to explain this subject intelligibly we must dwell much longer upon it4 ,sidenote3 ,,plate ,,iii4 #bgd4 ,the #eiplane of the ,equinoctial is perpendicular to the ,earth's ,axis3 and therefore1 as the ,earth turns round its ,axis1 all parts of the ,equinoctial make equal ,angles with the ,horizon both at rising and setting2 so that equal portions of it always rise or set in equal times4 ,consequently1 if the ,moon's motion were equable1 and in the ,equinoctial1 at the rate of #ab degrees from the ,sun every day1 as it is in her orbit1 she would rise and set #dh minutes later every day than on the preceding3 for #ab degrees of the ,equinoctial rise or set in #dh minutes of time in all ,latitudes4 ,sidenote3 ,fig4 ,,iii4 #bge4 ,but the ,moon's motion is so nearly in the ,ecliptic that we may consider her at present as moving in it4 ,now the different parts of the ,ecliptic1 on account of its obliquity to the ,earth's ,axis1 make very different ,angles with the ,horizon as they rise or set4 ,those parts or ,signs which rise with the smallest ,angles set with the greatest1 and vice vers4 ,in equal times1 whenever this ,angle is least1 a greater portion of the ,ecliptic rises than when the ,angle is larger2 as may be seen by elevating the pole of a ,globe to any considerable ,latitude1 and then turning it round its ,axis in the ,horizon4 ,consequently1 when the ,moon is in those ,signs which rise or set with the smallest ,angles1 she rises or sets with the least difference of time2 and with the greatest difference in those ,signs which rise or set with the greatest ,angles4 ,sidenote3 ,fig4 ,,iii4 ,the different ,angles made by the ,ecliptic and ,horizon4 ,but1 because all who read this ,treatise may not be provided with ,globes1 though in this case it is requisite to know how to use them1 we shall substitute the ,figure of a ,globe2 in which ,,fup is the ,axis1 ,,tr the ,tropic of ,cancer1 ,,lt the ,tropic of ,capricorn1 ,,eu the ,ecliptic touching both the ,tropics which are #dg degrees from each other1 and ,,ab the ,horizon4 ,the ,equator1 being in the middle between the ,tropics1 is cut by the ,ecliptic in two opposite points1 which are the beginnings of ,aries and ,libra4 ,k is the ,hour circle with its ,index1 ,f the ,north pole of the ,globe elevated to the ,latitude of ,london#fj1 namely #ea-a_/b degrees above the ,horizon2 and ,p the ,south ,pole depressed as much below it4 ,because of the oblique position of the ,sphere in this ,latitude1 the ,ecliptic has the high elevation ,n above the ,horizon1 making the ,angle ,,nu of #fb degrees with it when ,cancer is on the ,meridian1 at which time ,libra rises in the ,east4 ,but let the ,globe be turned half round its ,axis1 till ,capricorn comes to the ,meridian and ,aries rises in the ,east1 and then the ,ecliptic will have the low elevation ,,nl above the ,horizon making only an ,angle ,,nul of #ae degrees1 with it2 which is #dg degrees less than the former ,angle1 equal to the distance between the ,tropics4 ,sidenote3 ,least and greatest1 when4 #bgf4 ,the smallest ,angle made by the ,ecliptic and ,horizon is when ,aries rises1 at which time ,libra sets3 the greatest when ,libra rises1 at which time ,aries sets4 ,from the rising of ,aries to the rising of ,libra 7which is twelve #fa,sidereal hours7 the angle increases2 and from the rising of ,libra to the rising of ,aries it decreases in the same proportion4 ,by this article and the preceding1 it appears that the ,ecliptic rises fastest about ,aries and slowest about ,libra4 ---------------------------------- ,signs ,rising ,setting ,diff4 ,diff4 ,days ----------------- ,degrees ,h4 ,m4 ,h4 ,m4 ---------------------------------- #a #ac #a #e #j #ej #b #bf #a #aj #j #dc #c #aj #a #ad #j #cg #d #bc #a #ag #j #cb #e #f #a #af #j #bh #f #ai #a #ae #j #bd #g #b #a #ae #j #bj #h #ae #a #ae #j #ah #i #bh #a #ae #j #ag #aj #ab #a #ae #j #bb #aa #be #a #ad #j #cj #ab #h #a #ac #j #ci #ac #ba #a #aj #j #dg #ad #d #a #d #j #ef #ae #ag #j #df #a #e #af #a #j #dj #a #h #ag #ad #j #ce #a #ab #ah #bg #j #cj #a #ae #ai #aj #j #be #a #af #bj #bc #j #bj #a #ag #ba #g #j #ag #a #af #bb #bj #j #ag #a #ae #bc #c #j #bj #a #ae #bd #af #j #bd #a #ae #be #bi #j #cj #a #ad #bf #ac #j #dj #a #ac #bg #bf #j #ej #a #g #bh #i #a #j #a #eh ---------------------------------- ,sidenote3 ,quantity of this ,angle at ,london4 #bgg4 ,on the ,parallel of ,london1 as much of the ,ecliptic rises about ,pisces and ,aries in two hours as the ,moon goes through in six days3 and therefore whilst the ,moon is in these ,signs1 she differs but two hours in rising for six days together2 that is1 #bj minutes later every day or night than on the preceding4 ,but in fourteen days afterwards1 the ,moon comes to ,virgo and ,libra2 which are the opposite ,signs to ,pisces and ,aries2 and then she differs almost four times as much in rising2 namely1 one hour and about fifteen minutes later every day or night than the former1 whilst she is in these ,signs2 for by #bge their rising ,angle is at least four times as great as that of ,pisces and ,aries4 ,the annexed ,table shews the daily mean difference of the ,moon's rising and setting on the ,parallel of ,london1 for #bh days2 in which time the ,moon finishes her period round the ,ecliptic1 and gets #i degrees into the same ,sign from the beginning of which she set out4 ,so it appears by the ,table1 that while the ,moon is in and she rises an hour and a quarter later every day than the former2 and differs only #bd1 #bj1 #ah or #ag minutes in setting4 ,but1 when she comes to and 1 she is only #bj or #ag minutes later of rising2 and an hour and a quarter later in setting4 #bgh4 ,all these things will be made plain by putting small patches on the ,ecliptic of a ,globe1 as far from one another as the ,moon moves from any ,point of the celestial ,ecliptic in #bd hours1 which at a mean rate is #fbac-a_/f degrees2 and then in turning the globe round1 observe the rising and setting of the patches in the ,horizon1 as the ,index points out the different times in the hour circle4 ,a few of these patches are represented by dots at #j #a #b #c c4 on the ,ecliptic1 which has the position ,,lui when ,aries rises in the ,east2 and by the dots #j #a #b #c1 c4 when ,libra rises in the ,east1 at which time the ,ecliptic has the position ,,eu3 making an angle of #fb degrees with the ,horizon in the latter case1 and an angle of no more than #ae degrees with it in the former2 supposing the ,globe rectified to the ,latitude of ,london4 #bgi4 ,having rectified the ,globe1 turn it until the patch at #j1 about the beginning of ,pisces on the half ,,lui of the ,ecliptic1 comes to the ,eastern side of the ,horizon2 and then keeping the ball steady1 set the hour ,index to ,,xii1 because that hour may perhaps be more easily remembred than any other4 ,then1 turn the ,globe round westward1 and in that time1 suppose the patch #j to have moved thence to #a1 #ac-a_/f degrees1 whilst the ,earth turns once round its ,axis1 and you will see that #a rises only about #bj minutes later than #j did on the day before4 ,turn the ,globe round again1 and in that time suppose the same patch to have moved from #a to #b2 and it will rise only #bj minutes later by the hour-index than it did at #a on the day or turn before4 ,at the end of the next turn1 suppose the patch to have gone from #b to #c at ,u1 and it will rise #bj minutes later than it did at #b4 ,and so on for six turns1 in which time there will scarce be two hours difference3 ,nor would there have been so much if the #f degrees of the ,sun's motion in that time had been allowed for4 ,at the first ,turn the patch rises south of the ,east1 at the middle ,turn due ,east1 and at the last ,turn north of the ,east4 ,but these patches will be #i hours of setting on the western side of the ,horizon1 which shews that the ,moon will be so much later of setting in that week in which she moves through these two ,signs4 ,the cause of this difference is evident2 for ,pisces and ,aries make only an ,angle of #ae degrees with the ,horizon when they rise2 but they make an ,angle of #fb degrees with it when they set #bge4 ,as the ,signs ,taurus1 ,gemini1 ,cancer1 ,leo1 ,virgo1 and ,libra rise successively1 the ,angle increases gradually which they make with the ,horizon2 and decreases in the same proportion as they set4 ,and for that reason1 the ,moon differs gradually more in the time of her rising every day whilst she is in these ,signs1 and less in her setting3 ,after which1 through the other six ,signs1 viz4 ,scorpio1 ,sagittary1 ,capricorn1 ,aquarius1 ,pisces1 and ,aries1 the rising difference becomes less every day1 until it be at the least of all1 namely1 in ,pisces and ,aries4 #bhj4 ,the ,moon goes round the ,ecliptic in #bg days #h hours2 but not from ,change to ,change in less than #bi days #ab hours3 so that she is in ,pisces and ,aries at least once in every ,lunation1 and in some ,lunations twice4 ,sidenote3 ,why the ,moon is always ,full in different ,signs4 ,her periodical and synodical ,revolution exemplified4 #bha4 ,if the ,earth had no annual motion1 the ,sun would never appear to shift his place in the ,ecliptic4 ,and then every ,new ,moon would fall in the same ,sign and degree of the ,ecliptic1 and every ,full ,moon in the opposite3 for the ,moon would go precisely round the ,ecliptic from ,change to ,change4 ,so that if the ,moon was once ,full in ,pisces1 or ,aries1 she would always be ,full when she came round to the same ,sign and ,degree again4 ,and as the ,full ,moon rises at ,sun-set 7because when any point of the ,ecliptic sets the opposite point rises7 she would constantly rise within two hours of ,sun-set during the week in which she were ,full4 ,but in the time that the ,moon goes round the ,ecliptic from any conjunction or opposition1 the ,earth goes almost a ,sign forward2 and therefore the ,sun will seem to go as far forward in that time1 namely #bg-a_/b degrees3 so that the ,moon must go #bg-a_/b degrees more than round2 and as much farther as the ,sun advances in that interval1 which is #b-a_/ae degrees1 before she can be in conjunction with1 or opposite to the ,sun again4 ,hence it is evident1 that there can be but one conjunction or opposition of the ,sun and ,moon in a year in any particular part of the ,ecliptic4 ,this may be familiarly exemplified by the hour and minute hands of a watch1 which are never in conjunction or opposition in that part of the dial-plate where they were so last before4 ,and indeed if we compare the twelve hours on the dial-plate to the twelve ,signs of the ,ecliptic1 the hour-hand to the ,sun and the minute-hand to the ,moon1 we shall have a tolerably near resemblance in miniature to the motions of our great celestial ,luminaries4 ,the only difference is1 that whilst the ,sun goes once round the ,ecliptic the ,moon makes #ab-a_/c conjunctions with him3 but whilst the hour-hand goes round the dial-plate the minute-hand makes only #aa conjunctions with it2 because the minute hand moves slower in respect of the hour-hand than the ,moon does with regard to the ,sun4 ,sidenote3 ,the ,harvest and ,hunter's ,moon4 #bhb4 ,as the ,moon can never be full but when she is opposite to the ,sun1 and the ,sun is never in ,virgo and ,libra but in our autumnal months1 'tis plain that the ,moon is never full in the opposite ,signs1 ,pisces and ,aries1 but in these two months4 ,and therefore we can have only two ,full ,moons in the year1 which rise so near the time of ,sun-set for a week together as above-mentioned4 ,the former of these is called the ,harvest ,moon1 and the latter the ,hunter's ,moon4 ,sidenote3 ,why the ,moon's regular rising is never perceived but in ,harvest4 #bhc4 ,here it will probably be asked1 why we never observe this remarkable rising of the ,moon but in harvest1 since she is in ,pisces and ,aries at least twelve times in the year besides2 and must then rise with as little difference of time as in harvest8 ,the answer is plain3 for in winter these ,signs rise at noon2 and being then only a ,quarter of a ,circle distant from the ,sun1 the ,moon in them is in her first ,quarter3 but when the ,sun is above the ,horizon the ,moon's rising is neither regarded nor perceived4 ,in spring these ,signs rise with the ,sun because he is then in them2 and as the ,moon changeth in them at that time of the year1 she is quite invisible4 ,in summer they rise about mid-night1 and the ,sun being then three ,signs1 or a ,quarter of a ,circle before them1 the ,moon is in them about her third ,quarter2 when rising so late1 and giving but very little light1 her rising passes unobserved4 ,and in autumn1 these ,signs being opposite to the ,sun1 rise when he sets1 with the ,moon in opposition1 or at the ,full1 which makes her rising very conspicuous4 #bhd4 ,at the ,equator1 the ,north and ,south ,poles lie in the ,horizon2 and therefore the ,ecliptic makes the same ,angle southward with the ,horizon when ,aries rises as it does northward when ,libra rises4 ,consequently1 as the ,moon at all the fore-mentioned patches rises and sets nearly at equal ,angles with the ,horizon all the year round2 and about #dh minutes later every day or night than on the preceding1 there can be no particular ,harvest ,moon at the ,equator4 #bhe4 ,the farther that any place is from the ,equator1 if it be not beyond the ,polar ,circle1 the ,angle gradually diminishes which the ,ecliptic and ,horizon make when ,pisces and ,aries rise2 and therefore when the ,moon is in these ,signs she rises with a nearly proportionable difference later every day than on the former2 and is for that reason the more remarkable about the ,full1 until we come to the ,polar ,circles1 or #ff degrees from the ,equator2 in which ,latitude the ,ecliptic and ,horizon become coincident1 every day for a moment1 at the same sidereal hour 7or #c minutes #ef seconds sooner every day than the former7 and the very next moment one half of the ,ecliptic containing ,capricorn1 ,aquarius1 ,pisces1 ,aries1 ,taurus1 and ,gemini rises1 and the opposite half sets4 ,therefore1 whilst the ,moon is going from the beginning of ,capricorn to the beginning of ,cancer1 which is almost #ad days1 she rises at the same sidereal hour2 and in autumn just at ,sun-set1 because all that half of the ,ecliptic in which the ,sun is at that time sets at the same sidereal hour1 and the opposite half rises3 that is1 #c minutes #ef seconds1 of mean solar time1 sooner every day than on the day before4 ,so whilst the ,moon is going from ,capricorn to ,cancer she rises earlier every day than on the preceding2 contrary to what she does at all places between the polar ,circles4 ,but during the above fourteen days1 the ,moon is #bd sidereal hours later in setting2 for the six ,signs which rise all at once on the eastern side of the ,horizon are #bd hours in setting on the western side of it3 as any one may see by making chalk-marks at the beginning of ,capricorn and of ,cancer1 and then1 having elevated the ,pole #ff-a_/b degrees1 turn the ,globe slowly round it's ,axis1 and observe the rising and setting of the ,ecliptic4 ,as the beginning of ,aries is equally distant from the beginning of ,cancer and of ,capricorn1 it is in the middle of that half of the ,ecliptic which rises all at once4 ,and when the ,sun is at the beginning of ,libra1 he is in the middle of the other half4 ,therefore1 when the ,sun is in ,libra and the ,moon in ,capricorn1 the ,moon is a ,quarter of a ,circle before the ,sun2 opposite to him1 and consequently full in ,aries1 and a ,quarter of a ,circle behind him when in ,cancer4 ,but when ,libra rises ,aries sets1 and all that half of the ,ecliptic of which ,aries is the middle4 ,and therefore1 at that time of the year the ,moon rises at ,sun-set from her first to her third ,quarter4 ,sidenote3 ,the ,harvest ,moons regular on both sides of the ,equator4 #bhf4 ,in northern ,latitudes1 the autumnal ,full ,moons are in ,pisces and ,aries2 and the vernal ,full ,moons in ,virgo and ,libra3 in southern ,latitudes just the reverse because the seasons are contrary4 ,but ,virgo and ,libra rise at as small ,angles with the ,horizon in southern ,latitudes as ,pisces and ,aries do in the northern2 and therefore the ,harvest ,moons are just as regular on one side of the ,equator as on the other4 #bhg4 ,as these ,signs which rise with the least ,angles set with the greatest1 the vernal ,full ,moons differ as much in their times of rising every night as the autumnal ,full ,moons differ in their times of setting2 and set with as little difference as the autumnal ,full ,moons rise3 the one being in all cases the reverse of the other4 ,sidenote3 ,the ,moon's ,nodes4 #bhh4 ,hitherto1 for the sake of plainness1 we have supposed the ,moon to move in the ,ecliptic1 from which the ,sun never deviates4 ,but the orbit in which the ,moon really moves is different from the ,ecliptic3 one half being elevated #e-a_/c degrees above it1 and the other half as much depressed below it4 ,the ,moon's orbit therefore intersects the ,ecliptic in two points diametrically opposite to each other3 and these intersections are called the ,moon's ,nodes4 ,so the ,moon can never be in the ,ecliptic but when she is in either of her ,nodes1 which is at least twice in every course from ,change to ,change1 and sometimes thrice4 ,for1 as the ,moon goes almost a whole ,sign more than round her ,orbit from ,change to ,change2 if she passes by either ,node about the time of ,change1 she will pass by the other in about fourteen days after1 and come round to the former ,node two days again before the next ,change4 ,that ,node from which the ,moon begins to ascend northward1 or above the ,ecliptic1 in northern ,latitudes1 is called the ,ascending ,node2 and the other the ,descending ,node1 because the ,moon1 when she passes by it1 descends below the ,ecliptic southward4 #bhi4 ,the ,moon's oblique motion with regard to the ,ecliptic causes some difference in the times of her rising and setting from what is already mentioned4 ,for whilst she is northward of the ,ecliptic1 she rises sooner and sets later than if she moved in the ,ecliptic3 and when she is southward of the ,ecliptic she rises later and sets sooner4 ,this difference is variable even in the same ,signs1 because the ,nodes shift backward about #ai-b_/c degrees in the ,ecliptic every year2 and so go round it contrary to the order of ,signs in #ah years #bbe days4 #bij4 ,when the ,ascending ,node is in ,aries1 the southern half of the ,moon's ,orbit makes an ,angle of #e-a_/c degrees less with the ,horizon than the ,ecliptic does1 when ,aries rises in northern ,latitudes3 for which reason the ,moon rises with less difference of time whilst she is in ,pisces and ,aries than there would be if she kept in the ,ecliptic4 ,but in #i years and #aab days afterward1 the ,descending ,node comes to ,aries2 and then the ,moon's ,orbit makes an ,angle #e-a_/c degrees greater with the ,horizon when ,aries rises1 than the ,ecliptic does at that time2 which causes the ,moon to rise with greater difference of time in ,pisces and ,aries than if she moved in the ,ecliptic4 #bia4 ,to be a little more particular1 when the ,ascending ,node is in ,aries1 the ,angle is only #i-b_/c degrees on the parallel of ,london when ,aries rises4 ,but when the ,descending ,node comes to ,aries1 the ,angle is #bj-a_/c degrees2 this occasions as great a difference of the ,moon's rising in the same ,signs every #i years1 on the parallel of ,london1 as there would be on two parallels #aj-b_/c degrees from one another1 if the ,moon's course were in the ,ecliptic4 ,the following ,table shews how much the obliquity of the ,moon's ,orbit affects her rising and setting on the parallel of ,london from the #abth to the #ahth day of her age2 supposing her to be ,full at the autumnal ,equinox2 and then1 either in the ,ascending ,node1 highest part of her ,orbit1 ,descending ,node1 or lowest part of her ,orbit4 ,m signifies morning1 ,a afternoon2 and the line at the foot of the ,table shews a week's difference in rising and setting4 ---------------------------------------- ---------------------------- ,full in her ,in the ,full in her ,in the lowest ,ascending highest part ,descending part of her node4 of her ,orbit4 node4 ,orbit4 ,moon's ---------------------------------------- ----------------- ,age ,rises ,sets ,rises ,sets ,rises ,sets ,rises ,sets at at at at at at at at ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ---------------------------------------- ------------------------ ,a ,m ,a ,m ,a ,m ,a ,m #ab #e #ae #c #bj #d #cj #c #ae #d #cb #c #dj #e #af #c #j #ac #e #cb #d #be #d #ej #d #de #e #ae #d #bj #f #j #d #ae #ad #e #dh #e #cj #e #ae #f #j #e #de #e #dj #f #bj #e #bh #ae #f #e #g #j #e #db #g #bj #f #ae #f #ef #f #de #f #cb #af #f #bj #h #ae #f #b #h #ce #f #df #h #j #g #h #g #de #ag #f #cf #i #ab #f #bf #i #de #g #ah #i #ae #g #cj #i #ae #ah #f #ed #aj #cj #g #j #aj #dj #h #j #aj #bj #g #eb #aj #j ---------------------------------------- ------------------------ ,dif4 #a #ci #g #aj #b #cj #g #be #c #bh #f #dj #b #cf #g #j ---------------------------------------- ------------------------ ,this ,table was not computed1 but only estimated as near as could be done from a common ,globe1 on which the ,moon's ,orbit was delineated with a black lead pencil4 ,it may at first sight appear erroneous2 since as we have supposed the ,moon to be full in either ,node at the autumnal ,equinox1 she ought by the ,table to rise just at six o'clock1 or at ,sun-set1 on the #aeth day of her age2 being in the ,ecliptic at that time4 ,but it must be considered1 that the ,moon is only #ad-a_/d days old when she is ,full2 and therefore in both cases she is a little past the ,node on the #aeth day1 being above it at one time1 and below it at the other4 ,sidenote3 ,the period of the ,harvest ,moons4 #bib4 ,as there is a compleat revolution of the ,nodes in #ah-b_/c years1 there must be a regular period of all the ,varieties which can happen in the rising and setting of the ,moon during that time4 ,but this shifting of the ,nodes never affects the ,moon's rising so much1 even in her quickest descending ,latitude1 as not to allow us still the benefit of her rising nearer the time of ,sun-set for a few days together about the ,full in ,harvest1 than when she is ,full at any other time of the year4 ,the following ,table shews in what years the ,harvest-,moons are least beneficial as to the times of their rising1 and in what years most1 from #agea to #ahfa4 ,the column of years under the letter ,l are those in which the ,harvest-,moons are least of all beneficial1 because they fall about the ,descending ,node3 and those under ,m are the most of all beneficial1 because they fall about the ,ascending ,node4 ,in all the columns from ,n to ,s the ,harvest-,moons descend gradually in the ,lunar ,orbit1 and rise to less heights above the ,horizon4 ,from ,s to ,n they ascend in the same proportion1 and rise to greater heights above the ,horizon4 ,in both the columns under ,s the ,harvest-,moons are in the lowest part of the ,moon's ,orbit1 that is1 farthest ,south of the ,ecliptic2 and therefore stay shortest of all above the ,horizon3 in the columns under ,n just the reverse4 ,and in both cases1 their rising1 though not at the same times1 are nearly the same with regard to difference of time1 as if the ,moon's ,orbit were coincident with the ,ecliptic4 ---------------------------------------- -------------------- ,years in which the ,harvest-,moons are least beneficial4 ,n ,l ,s #agea #ageb #agec #aged #agee #agef #ageg #ageh #agei #aggj #agga #aggb #aggc #aggd #agge #aggf #aggg #aggh #aghh #aghi #agij #agia #agib #agic #agid #agie #agif #agig #ahjg #ahjh #ahji #ahaj #ahaa #ahab #ahac #ahad #ahae #ahbf #ahbg #ahbh #ahbi #ahcj #ahca #ahcb #ahcc #ahcd #ahdd #ahde #ahdf #ahdg #ahdh #ahdi #ahej #ahea #aheb ,years in which they are most beneficial4 ,s ,m ,n #agfj #agfa #agfb #agfc #agfd #agfe #agff #agfg #agfh #agfi #aggi #aghj #agha #aghb #aghc #aghd #aghe #aghf #aghg #agih #agii #ahjj #ahja #ahjb #ahjc #ahjd #ahje #ahjf #ahaf #ahag #ahah #ahai #ahbj #ahba #ahbb #ahbc #ahbd #ahbe #ahce #ahcf #ahcg #ahch #ahci #ahdj #ahda #ahdb #ahdc #ahec #ahed #ahee #ahef #aheg #aheh #ahei #ahfj #ahfa ---------------------------------------- -------------------- ,sidenote3 ,,pl4 ,,viii4 #bic4 ,at the ,polar ,circles1 when the ,sun touches the ,summer ,tropic1 he continues #bd hours above the ,horizon2 and #bd hours below it when he touches the ,winter ,tropic4 ,for the same reason the ,full ,moon neither rises in ,summer1 nor sets in ,winter1 considering her as moving in the ,ecliptic4 ,for the ,winter ,full ,moon being as high in the ,ecliptic as the ,summer ,sun1 must therefore continue as long above the ,horizon2 and the ,summer ,full ,moon being as low in the ,ecliptic as the ,winter ,sun1 can no more rise than he does4 ,but these are only the two ,full ,moons which happen about the ,tropics1 for all the others rise and set4 ,in ,summer the ,full ,moons are low1 and their stay is short above the ,horizon1 when the nights are short1 and we have least occasion for ,moon-light3 in ,winter they go high1 and stay long1 above the ,horizon when the nights are long1 and we want the greatest quantity of ,moon-light4 ,sidenote3 ,the long continuance of ,moon-light at the ,poles4 ,fig4 ,v4 #bid4 ,at the ,poles1 one half of the ,ecliptic never sets1 and the other half never rises3 and therefore1 as the ,sun is always half a year in describing one half of the ,ecliptic1 and as long in going through the other half1 'tis natural to imagine that the ,sun continues half a year together above the ,horizon of each ,pole in it's turn1 and as long below it2 rising to one ,pole when he sets to the other4 ,this would be exactly the case if there were no refraction3 but by the ,atmosphere's refracting the ,sun's rays1 he becomes visible some days sooner #ahc1 and continues some days longer in sight than he would otherwise do3 so that he appears above the ,horizon of either ,pole before he has got below the ,horizon of the other4 ,and1 as he never goes more than #bc-a_/b degrees below the ,horizon of the ,poles1 they have very little dark night3 it being twilight there as well as at all other places till the ,sun be #ah degrees below the ,horizon1 #agg4 ,the ,full ,moon being always opposite to the ,sun1 can never be seen while the ,sun is above the ,horizon1 except when the ,moon falls in the northern half of her ,orbit2 for whenever any point of the ,ecliptic rises the opposite point sets4 ,therefore1 as the ,sun is above the ,horizon of the north ,pole from the #bjth of ,march till the #bc;d of ,september1 it is plain that the ,moon1 when ,full1 being opposite to the ,sun1 must be below the ,horizon during that half of the year4 ,but when the ,sun is in the southern half of the ,ecliptic he never rises to the north ,pole1 during which half of the year1 every ,full ,moon happens in some part of the northern half of the ,ecliptic1 which never sets4 ,consequently1 as the polar ,inhabitants never see the ,full ,moon in ,summer1 they have her always in the ,winter1 before1 at1 and after the ,full1 shining for #ad of our days and nights4 ,and when the ,sun is at his greatest depression below the ,horizon1 being then in ,capricorn1 the ,moon is at her ,first ,quarter in ,aries1 ,full in ,cancer1 and at her ,third ,quarter in ,libra4 ,and as the beginning of ,aries is the rising point of the ,ecliptic1 ,cancer the highest1 and ,libra the setting point1 the ,moon rises at her ,first ,quarter in ,aries1 is most elevated above the ,horizon1 and ,full in ,cancer1 and sets at the beginning of ,libra in her ,third ,quarter1 having continued visible for #ad diurnal rotations of the ,earth4 ,thus the ,poles are supplied one half of the winter time with constant ,moon-light in the ,sun's absence2 and only lose sight of the ,moon from her ,third to her ,first ,quarter1 while she gives but very little light2 and could be but of little1 and sometimes of no service to them4 ,a bare view of the ,figure will make this plain2 in which let ,s be the ,sun1 e the ,earth in ,summer when it's north ,pole n inclines toward the ,sun1 and ,e the ,earth in ,winter1 when it's north ,pole declines from him4 ,,sen and ,,nws is the ,horizon of the north ,pole1 which is coincident with the ,equator2 and1 in both these positions of the ,earth1 is the ,moon's ,orbit1 in which she goes round the ,earth1 according to the order of the letters abcd1 ,,abcd4 ,when the ,moon is at a she is in her ,third ,quarter to the ,earth at e1 and just rising to the north ,pole n2 at b she changes1 and is at the greatest height above the ,horizon1 as the ,sun likewise is2 at c she is in her ,first ,quarter1 setting below the ,horizon2 and is lowest of all under it at d1 when opposite to the ,sun1 and her enlightened side toward the ,earth4 ,but then she is full in view to the south ,pole p2 which is as much turned from the ,sun as the north ,pole inclines towards him4 ,thus in our ,summer1 the ,moon is above the ,horizon of the north ,pole whilst she describes the northern half of the ,ecliptic 1 or from her ,third ,quarter to her ,first2 and below the ,horizon during the progress through the southern half 2 highest at the ,change1 most depressed at the ,full4 ,but in winter1 when the ,earth is at ,e1 and it's north ,pole declines from the ,sun1 the ,new ,moon at ,d is at her greatest depression below the ,horizon ,,nws1 and the ,full ,moon at ,b at her greatest height above it2 rising at her ,first ,quarter ,a1 and keeping above the ,horizon till she comes to her ,third ,quarter ,c4 ,at a mean state she is #bc-a_/b degrees above the ,horizon at ,b and b1 and as much below it at ,d and d1 equal to the inclination of the ,earth's ,axis ,f4 ,s and ,s are1 as it were1 a ray of light proceeding from the ,sun to the ,earth2 and shews that when the ,earth is at e1 the ,sun is above the ,horizon1 vertical to the ,tropic of ,cancer2 and when the ,earth is at ,e1 he is below the ,horizon1 vertical to the ,tropic of ,capricorn4 ,illustration3 ,plate ,,viii4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 ,illustration3 ,plate ,,ix4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 ,,chap4 ,,xvii4 ,of the ebbing and flowing of the ,sea4 ,sidenote3 ,the cause of the ,tides discovered by ,,kepler4 ,,plate ,,ix4 ,their ,theory improved by ,sir ,,isaac ,,newton4 #bie4 ,the cause of the ,tides was discovered by ,,kepler1 who1 in his ,introduction to the ,physics of the ,heavens1 thus explains it3 8,the ,orb of the attracting power1 which is in the ,moon1 is extended as far as the ,earth2 and draws the waters under the torrid ,zone1 acting upon places where it is vertical1 insensibly on confined seas and bays1 but sensibly on the ocean whose beds are large1 and the waters have the liberty of reciprocation2 that is1 of rising and falling40 ,and in the #gjth page of his ,lunar ,astronomy----8,but the cause of the ,tides of the ,sea appears to be the bodies of the ,sun and ,moon drawing the waters of the ,sea40 ,this hint being given1 the immortal ,sir ,,isaac ,,newton improved it1 and wrote so amply on the subject1 as to make the ,theory of the ,tides in a manner quite his own2 by discovering the cause of their rising on the side of the ,earth opposite to the ,moon4 ,for ,,kepler believed that the presence of the ,moon occasioned an impulse which caused another in her absence4 ,sidenote3 ,explained on the ,newtonian principles4 ,fig4 ,i4 ,fig4 ,i4 #bif4 ,it has been already shewn #ajf1 that the power of gravity diminishes as the square of the distance increases2 and therefore the waters at ,z on the side of the ,earth ,,abcdefgh next the ,moon ,m are more attracted than the central parts of the ,earth ,o by the ,moon1 and the central parts are more attracted by her than the waters on the opposite side of the ,earth at n3 and therefore the distance between the ,earth's center and the waters on it's surface under and opposite to the ,moon will be increased4 ,for1 let there be three bodies at ,h1 ,o1 and ,d3 if they are all equally attracted by the body ,m1 they will all move equally fast toward it1 their mutual distances from each other continuing the same4 ,if the attraction of ,m is unequal1 then that body which is most strongly attracted will move fastest1 and this will increase it's distance from the other body4 ,therefore1 by the law of gravitation1 ,m will attract ,h more strongly than it does ,o1 by which1 the distance between ,h and ,o will be increased3 and a spectator on ,o will perceive ,h rising higher toward ,z4 ,in like manner1 ,o being more strongly attracted than ,d1 it will move farther towards ,m than ,d does3 consequently1 the distance between ,o and ,d will be increased2 and a spectator on ,o1 not perceiving his own motion1 will see ,d receding farther from him towards n3 all effects and appearances being the same whether ,d recedes from ,o or ,o from ,d4 ,sidenote3 ,,plate ,,ix4 #big4 ,suppose now there is a number of bodies1 as ,a1 ,b1 ,c1 ,d1 ,e1 ,f1 ,g1 ,h placed round ,o1 so as to form a flexible or fluid ring3 then1 as the whole is attracted towards ,m1 the parts at ,h and ,d will have their distance from ,o increased2 whilst the parts at ,b and ,f1 being nearly at the same distance from ,m as ,o is1 these parts will not recede from one another2 but rather1 by the oblique attraction of ,m1 they will approach nearer to ,o4 ,hence1 the fluid ring will form itself into an ellipse ,z,i,b,ln,k,f,n,z1 whose longer ,axis n,o,z produced will pass through ,m1 and it's shorter ,axis ,,bof will terminate in ,b and ,f4 ,let the ring be filled with bodies1 so as to form a flexible or fluid sphere round ,o2 then1 as the whole moves toward ,m1 the fluid sphere being lengthned at ,z and n1 will assume an oblong or oval form4 ,if ,m is the ,moon1 ,o the ,earth's center1 ,,abcdefgh the ,sea covering the ,earth's surface1 'tis evident by the above reasoning1 that whilst the ,earth by it's gravity falls toward the ,moon1 the ,water directly below her at ,b will swell and rise gradually towards her3 also1 the ,water at ,d will recede from the center strictly speaking1 the center recedes from ,d and rise on the opposite side of the ,earth3 whilst the ,water at ,b and ,f is depressed1 and falls below the former level4 ,hence1 as the ,earth turns round it's ,axis from the ,moon to the ,moon again in #bd-c_/d hours1 there will be two tides of flood and two of ebb in that time1 as we find by experience4 ,sidenote3 ,fig4 ,,ii4 #bih4 ,as this explanation of the ebbing and flowing of the ,sea is deduced from the ,earth's constantly falling toward the ,moon by the power of gravity1 some may find a difficulty in conceiving how this is possible when the ,moon is ,full1 or in opposition to the ,sun2 since the ,earth revolves about the ,sun1 and must continually fall towards it1 and therefore cannot fall contrary ways at the same time3 or if the ,earth is constantly falling towards the ,moon1 they must come together at last4 ,to remove this difficulty1 let it be considered1 that it is not the center of the ,earth that describes the annual orbit round the ,sun2 but the #fc;common center of gravity of the ,earth and ,moon together3 and that whilst the ,earth is moving round the ,sun1 it also describes a ,circle round that centre of gravity2 going as many times round it in one revolution about the ,sun as there are ,lunations or courses of the ,moon round the ,earth in a year3 and therefore1 the ,earth is constantly falling towards the ,moon from a tangent to the ,circle it describes round the said common center of gravity4 ,let ,m be the ,moon1 ,,tw part of the ,moon's ,orbit1 and ,c the center of gravity of the ,earth and ,moon3 whilst the ,moon goes round her ,orbit1 the center of the ,earth describes the ,circle ged round ,c1 to which ,circle gak is a tangent3 and therefore1 when the ,moon has gone from ,m to a little past ,w1 the ,earth has moved from g to e2 and in that time has fallen towards the ,moon1 from the tangent at a to e2 and so round the whole ,circle4 ,sidenote3 ,,plate ,,ix4 #bii4 ,the ,sun's influence in raising the ,tides is but small in comparison of the ,moon's3 ,for though the ,earth's diameter bears a considerable proportion to it's distance from the ,moon1 it is next to nothing when compared with the distance of the ,sun4 ,and therefore1 the difference of the ,sun's attraction on the sides of the ,earth under and opposite to him1 is much less than the difference of the ,moon's attraction on the sides of the ,earth under and opposite to her3 and therefore the ,moon must raise the ,tides much higher than they can be raised by the ,sun4 ,sidenote3 ,why the ,tides are not highest when the ,moon is on the ,meridian4 ,fig4 ,i4 #cjj4 ,on this ,theory so far as we have explained it1 the ,tides ought to be highest directly under and opposite to the ,moon2 that is1 when the ,moon is due north and south4 ,but we find1 that in open ,seas1 where the water flows freely1 the ,moon ,m is generally past the north and south ,meridian as at p when it is high water at ,z and at n4 ,the reason is obvious2 for though the ,moon's attraction was to cease altogether when she was past the ,meridian1 yet the motion of ascent communicated to the water before that time would make it continue to rise for some time after2 much more must it do so when the attraction is only diminished3 as a little impulse given to a moving ball will cause it still move farther than otherwise it could have done4 ,and as experience shews1 that the day is hotter about three in the afternoon1 than when the ,sun is on the ,meridian1 because of the increment made to the heat already imparted4 ,sidenote3 ,nor always answer to her being at the same distance from it4 #cja4 ,the ,tides answer not always to the same distance of the ,moon from the ,meridian at the same places2 but are variously affected by the action of the ,sun1 which brings them on sooner when the ,moon is in her first and third ,quarters1 and keeps them back later when she is in her second and fourth3 because1 in the former case1 the ,tide raised by the ,sun alone would be earlier than the ,tide raised by the ,moon2 and in the latter case later4 ,sidenote3 ,spring and neap ,tides4 ,,plate ,,ix4 ,fig4 ,,vi4 #cjb4 ,the ,moon goes round the ,earth in an elliptic ,orbit1 and therefore she approaches nearer to the ,earth than her mean distance1 and recedes farther from it1 in every ,lunar ,month4 ,when she is nearest3 she attracts strongest1 and so rises the ,tides most2 the contrary happens when she is farthest1 because of her weaker attraction4 ,when both ,luminaries are in the ,equator1 and the ,moon in ,perigeo1 or at her least distance from the ,earth1 she raises the ,tides highest of all1 especially at her ,conjunction and opposition2 both because the equatoreal parts have the greatest centrifugal force from their describing the largest ,circle1 and from the concurring actions of the ,sun and ,moon4 ,at the ,change1 the attractive forces of the ,sun and ,moon being united1 they diminish the gravity of the waters under the ,moon1 which is also diminished on the other side1 by means of a greater centrifugal force4 ,at the full1 whilst the ,moon raises the ,tide under and opposite to her1 the ,sun acting in the same line1 raises the ,tide under and opposite to him2 whence their conjoint effect is the same as at the ,change2 and in both cases1 occasion what we call the ,spring ,tides4 ,but at the ,quarters the ,sun's action on the waters at ,o and ,h diminishes the ,moon's action on the waters at ,z and ,n2 so that they rise a little under and opposite to the ,sun at ,o and ,h1 and fall as much under and opposite to the ,moon at ,z and ,n2 making what we call the ,neap ,tides1 because the ,sun and ,moon then act cross-wise to each other4 ,but1 strictly speaking1 these ,tides happen not till some time after2 because in this1 as in other cases1 #cjj1 the actions do not produce the greatest effect when they are at the strongest1 but some time afterward4 ,sidenote3 ,not greatest at the ,equinoxes1 and why4 #cjc4 ,the ,sun being nearer the ,earth in ,winter than in ,summer1 #bje1 is of course nearer to it in ,february and ,october than in ,march and ,september3 and therefore the greatest ,tides happen not till some time after the autumnal ,equinox1 and return a little before the vernal4 ,sidenote3 ,the ,tides would not immediately cease upon the annihilation of the ,sun and ,moon4 ,the ,sea being thus put in motion1 would continue to ebb and flow for several times1 even though the ,sun and ,moon were annihilated1 or their influence should cease3 as if a bason of water were agitated1 the water would continue to move for some time after the bason was left to stand still4 ,or like a ,pendulum1 which having been put in motion by the hand1 continues to make several vibrations without any new impulse4 ,sidenote3 ,the lunar day1 what4 ,the ,tides rise to unequal heights in the same day1 and why4 ,,plate ,,ix4 ,fig4 ,,iii1 ,,iv1 ,v4 ,fig4 ,,iii4 ,fig4 ,,iv4 ,fig4 ,v4 #cjd4 ,when the ,moon is in the ,equator1 the ,tides are equally high in both parts of the lunar day1 or time of the ,moon's revolving from the ,meridian to the ,meridian again1 which is #bd hours #dh minutes4 ,but as the ,moon declines from the ,equator towards either ,pole1 the ,tides are alternately higher and lower at places having north or south ,latitude4 ,for one of the highest elevations1 which is that under the ,moon1 follows her towards the same ,pole1 and the other declines towards the opposite2 each describing parallels as far distant from the ,equator1 on opposite sides1 as the ,moon declines from it to either side2 and consequently1 the parallels described by these elevations of the water are twice as many degrees from one another1 as the ,moon is from the ,equator2 increasing their distance as the ,moon increases her declination1 till it be at the greatest1 when the said parallels are1 at a mean state1 #dg degrees from one another3 and on that day1 the ,tides are most unequal in their heights4 ,as the ,moon returns toward the ,equator1 the parallels described by the opposite elevations approach towards each other1 until the ,moon comes to the ,equator1 and then they coincide4 ,as the ,moon declines toward the opposite ,pole1 at equal distances1 each elevation describes the same parallel in the other part of the lunar day1 which it's opposite elevation described before4 ,whilst the ,moon has north declination1 the greatest ,tides in the northern ,hemisphere are when she is above the ,horizon2 and the reverse whilst her declination is south4 ,let ,,nesq be the ,earth1 ,,ncs it's ,axis1 ,,eq the ,equator1 ,t the ,tropic of ,cancer1 t the ,tropic of ,capricorn1 ab the arctic ,circle1 cd the ,antarctic1 ,n the north ,pole1 ,s the south ,pole1 ,m the ,moon1 ,f and ,g the two eminences of water1 whose lowest parts are at a and d 7,fig4 ,,iii47 at ,n and ,s 7,fig4 ,,iv47 and at b and c 7,fig4 ,v47 always #ij degrees from the highest4 ,now when the ,moon is in her greatest north declination at ,m1 the highest elevation ,g under her1 is on the ,tropic of ,cancer ,t1 and the opposite elevation ,f on the ,tropic of ,capricorn t2 and these two elevations describe the ,tropics by the ,earth's diurnal rotation4 ,all places in the northern ,hemisphere ,,enq have the highest ,tides when they come into the position b,q1 under the ,moon2 and the lowest ,tides when the ,earth's diurnal rotation carries them into the position a,t,e1 on the side opposite to the ,moon2 the reverse happens at the same time in the southern ,hemisphere ,,esq1 as is evident to sight4 ,the ,axis of the ,tides a,cd has now it's ,poles a and d 7being always #ij degrees from the highest elevations7 in the arctic and antarctic ,circles2 and therefore 'tis plain1 that at these ,circles there is but one ,tide of ,flood1 and one of ,ebb1 in the lunar day4 ,for1 when the point a revolves half round to b1 in #ab lunar hours1 it has a ,tide of ,flood2 but when it comes to the same point a again in #ab hours more1 it has the lowest ebb4 ,in seven days afterward1 the ,moon ,m comes to the equinoctial ,circle1 and is over the ,equator ,,eq1 when both ,elevations describe the ,equator2 and in both ,hemispheres1 at equal distances from the ,equator1 the ,tides are equally high in both parts of the lunar day4 ,the whole ,phenomena being reversed when the ,moon has south declination to what they were when her declination was north1 require no farther description4 ,sidenote3 ,fig4 ,,vi4 ,when both ,tides are equally high in the same day1 they arrive at unequal intervals of ,time2 and vice versa4 #cje4 ,in the three last-mentioned ,figures1 the ,earth is orthographically projected on the plane of the ,meridian2 but in order to describe a particular ,phenomenon we now project it on the plane of the ,ecliptic4 ,let ,,hzon be the ,earth and ,sea1 ,,fed the ,equator1 ,t the ,tropic of ,cancer1 ,c the arctic ,circle1 ,p the north ,pole1 and the ,curves #a1 #b1 #c1 c4 #bd ,meridians1 or hour ,circles1 intersecting each other in the ,poles2 ,,agm is the ,moon's orbit1 ,s the ,sun1 ,m the ,moon1 ,z the ,water elevated under the ,moon1 and ,n the opposite equal ,elevation4 ,as the lowest parts of the ,water are always #ij degrees from the highest1 when the ,moon is in either of the ,tropics 7as at ,m7 the ,elevation ,z is on the ,tropic of ,capricorn1 and the opposite ,elevation ,n on the ,tropic of ,cancer1 the low-water ,circle ,,hco touches the polar ,circles at ,c2 and the high-water ,circle ,,etp#f goes over the ,poles at ,p1 and divides every parallel of ,latitude into two equal segments4 ,in this case the ,tides upon every parallel are alternately higher and lower2 but they return in equal times3 the point ,t1 for example1 on the ,tropic of ,cancer 7where the depth of the ,tide is represented by the breadth of the dark shade7 has a shallower ,tide of ,flood at ,t than when it revolves half round from thence to #f1 according to the order of the numeral ,figures2 but it revolves as soon from #f to ,t as it did from ,t to #f4 ,when the ,moon is in the ,equinoctial1 the ,elevations ,z and ,n are transferred to the ,equator at ,o and ,h1 and the high and low-water ,circles are got into each other's former places2 in which case the ,tides return in unequal times1 but are equally high in both parts of the lunar day3 for a place at #a 7under ,d7 revolving as formerly1 goes sooner from #a to #aa 7under ,f7 than from #aa to #a1 because the parallel it describes is cut into unequal segments by the high-water ,circle ,,hco3 but the points #a and #aa being equidistant from the ,pole of the ,tides at ,c1 which is directly under the ,pole of the ,moon's orbit ,,mga1 the ,elevations are equally high in both parts of the day4 #cjf4 ,and thus it appears1 that as the ,tides are governed by the ,moon1 they must turn on the ,axis of the ,moon's orbit1 which is inclined #bc-a_/b degrees to the ,earth's ,axis at a mean state3 and therefore the ,poles of the ,tides must be so many degrees from the ,poles of the ,earth1 or in opposite points of the polar ,circles1 going round these ,circles in every lunar day4 ',tis true that according to ,fig4 ,,iv4 when the ,moon is vertical to the ,equator ,,ecq1 the ,poles of the ,tides seem to fall in with the ,poles of the ,world ,n and ,s3 but when we consider that ,,fhg is under the ,moon's orbit1 it will appear1 that when the ,moon is over ,h1 in the ,tropic of ,capricorn1 the north ,pole of the ,tides1 7which can be no more than #ij degrees from under the ,moon7 must be at c in the arctic ,circle1 not at ,n2 the north ,pole of the ,earth2 and as the ,moon ascends from ,h to ,g in her orbit1 the north ,pole of the ,tides must shift from c to a in the arctic ,circle2 and the ,south ,pole as much in the antarctic4 ,it is not to be doubted1 but that the ,earth's quick rotation brings the poles of the ,tides nearer to the ,poles of the ,world1 than they would be if the ,earth were at rest1 and the ,moon revolved about it only once a month2 for otherwise the ,tides would be more unequal in their heights1 and times of their returns1 than we find they are4 ,but how near the ,earth's rotation may bring the ,poles of it's ,axis and those of the ,tides together1 or how far the preceding ,tides may affect those which follow1 so as to make them keep up nearly to the same heights1 and times of ebbing and flowing1 is a problem more fit to be solved by observation than by theory4 ,sidenote3 ,to know at what times we may expect the greatest and least ,tides4 #cjg4 ,those who have opportunity to make observations1 and choose to satisfy themselves whether the ,tides are really affected in the above manner by the different positions of the ,moon2 especially as to the unequal times of their returns1 may take this general rule for knowing1 when they ought to be so affected4 ,when the ,earth's ,axis inclines to the ,moon1 the northern ,tides1 if not retarded in their passage through ,shoals and ,channels1 nor affected by the ,winds1 ought to be greatest when the ,moon is above the ,horizon1 least when she is below it2 and quite the reverse when the ,earth's ,axis declines from her3 but in both cases1 at equal intervals of time4 ,when the ,earth's ,axis inclines sidewise to the ,moon1 both ,tides are equally high1 but they happen at unequal intervals of time4 ,in every ,lunation the ,earth's ,axis inclines once to the ,moon1 once from her1 and twice sidewise to her1 as it does to the ,sun every year2 because the ,moon goes round the ,ecliptic every month1 and the ,sun but once in a year4 ,in ,summer1 the ,earth's ,axis inclines towards the ,moon when ,new2 and therefore the day-tides in the north ought to be highest1 and night-tides lowest about the ,change3 at the ,full the reverse4 ,at the ,quarters they ought to be equally high1 but unequal in their returns2 because the ,earth's ,axis then inclines sidewise to the ,moon4 ,in winter the ,phenomena are the same at ,full-,moon as in ,summer at ,new4 ,in ,autumn the ,earth's ,axis inclines sidewise to the ,moon when ,new and ,full2 therefore the ,tides ought to be equally high1 and unequal in their returns at these times4 ,at the first ,quarter the ,tides of ,flood should be least when the ,moon is above the ,horizon1 greatest when she is below it2 and the reverse at her third ,quarter4 ,in ,spring1 ,phenomena of the first ,quarter answer to those of the third ,quarter in ,autumn2 and vice versa4 ,the nearer any time is to either of these seasons1 the more the ,tides partake of the ,phenomena of these seasons2 and in the middle between any two of them the ,tides are at a mean state between those of both4 ,sidenote3 ,why the ,tides rise higher in ,rivers than in the ,sea4 #cjh4 ,in open ,seas1 the ,tides rise but to very small heights in proportion to what they do in wide-mouthed rivers1 opening in the ,direction of the ,stream of ,tide4 ,for1 in ,channels growing narrower gradually1 the water is accumulated by the opposition of the contracting ,bank4 ,like a gentle wind1 little felt on an open plain1 but strong and brisk in a street2 especially if the wider end of the street be next the plain1 and in the way of the wind4 ,sidenote3 ,the ,tides happen at all distances of the ,moon from the ,meridian at different places1 and why4 #cji4 ,the ,tides are so retarded in their passage through different ,shoals and ,channels1 and otherwise so variously affected by striking against ,capes and ,headlands1 that to different places they happen at all distances of the ,moon from the ,meridian2 consequently at all hours of the lunar day4 ,the ,tide propagated by the ,moon in the ,german ocean1 when she is three hours past the ,meridian1 takes #ab hours to come from thence to ,london bridge2 where it arrives by the time that a new ,tide is raised in the ocean4 ,and therefore when the ,moon has north declination1 and we should expect the ,tide at ,london to be greatest when the ,moon is above the ,horizon1 we find it is least2 and the contrary when she has south declination4 ,at several places 'tis high water three hours before the ,moon comes to the ,meridian2 but that ,tide which the ,moon pushes as it were before her1 is only the ,tide opposite to that which was raised by her when she was nine hours past the opposite ,meridian4 ,sidenote3 ,the ,water never rises in ,lakes4 #caj4 ,there are no ,tides in ,lakes1 because they are generally so small that when the ,moon is vertical she attracts every part of them alike1 and therefore by rendering all the water equally light1 no part of it can be raised higher than another4 ,the ,mediterranean and ,baltic ,seas suffer very small elevations1 because the ,inlets by which they communicate with the ocean are so narrow1 that they cannot1 in so short a time1 receive or discharge enough to raise or sink their surfaces sensibly4 ,sidenote3 ,the ,moon raises ,tides in the ,air4 ,why the ,mercury in the ,barometer is not affected by the aerial ,tides4 #caa4 ,air being lighter than ,water1 and the surface of the ,atmosphere being nearer to the ,moon than the surface of the ,sea1 it cannot be doubted that the ,moon raises much higher ,tides in the ,air than in the ,sea4 ,and therefore many have wondered why the ,mercury does not sink in the ,barometer when the ,moon's action on the particles of ,air makes them lighter as she passes over the ,meridian4 ,but we must consider1 that as these particles are rendered lighter1 a greater number of them is accumulated1 until the deficiency of gravity be made up by the height of the column2 and then there is an equilibrium1 and consequently an equal pressure upon the ,mercury as before2 so that it cannot be affected by the aerial ,tides4 ,,chap4 ,,xviii4 ,of ,eclipses3 ,their ,number and ,periods4 ,a large ,catalogue of ,ancient and ,modern ,eclipses4 ,sidenote3 ,a shadow1 what4 #cab4 ,every ,planet and ,satellite is illuminated by the ,sun2 and casts a shadow towards that point of the ,heavens which is opposite to the ,sun4 ,this shadow is nothing but a privation of light in the space hid from the ,sun by the opake body that intercepts his rays4 ,sidenote3 ,eclipses of the ,sun and ,moon1 what4 #cac4 ,when the ,sun's light is so intercepted by the ,moon1 that to any place of the ,earth the ,sun appears partly or wholly covered1 he is said to undergo an ,eclipse2 though properly speaking1 'tis only an ,eclipse of that part of the ,earth where the ,moon's shadow or #fd,penumbra falls4 ,when the ,earth comes between the ,sun and ,moon1 the ,moon falls into the ,earth's shadow2 and having no light of her own1 she suffers a real ,eclipse from the interception of the ,sun's rays4 ,when the ,sun is eclipsed to us1 the ,moon's ,inhabitants on the side next the ,earth 7if any such there be7 see her shadow like a dark spot travelling over the ,earth1 about twice as fast as its equatoreal parts move1 and the same way as they move4 ,when the ,moon is in an ,eclipse1 the ,sun appears eclipsed to her1 total to all those parts on which the ,earth's shadow falls1 and of as long continuance as they are in the shadow4 ,illustration3 ,plate ,x4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 ,sidenote3 ,a proof that the ,earth and ,moon are globular bodies4 #cad4 ,that the ,earth is spherical 7for the hills take off no more from the roundness of the ,earth1 than grains of dust do from the roundness of a common ,globe7 is evident from the figure of its shadow on the ,moon2 which is always bounded by a circular line1 although the ,earth is incessantly turning its different sides to the ,moon1 and very seldom shews the same side to her in different ,eclipses1 because they seldom happen at the same hours4 ,were the ,earth shaped like a round flat plate1 its shadow would only be circular when either of its sides directly faced the ,moon2 and more or less elliptical as the ,earth happened to be turned more or less obliquely towards the ,moon when she is eclipsed4 ,the ,moon's different ,phases prove her to be round #bed2 for1 as she keeps still the same side towards the earth1 if that side were flat1 as it appears to be1 she would never be visible from the third ,quarter to the first2 and from the first ,quarter to the third1 she would appear as round as when we say she is ,full3 because at the end of her first ,quarter the ,sun's light would come as suddenly on all her side next the ,earth1 as it does on a flat wall1 and go off as abruptly at the end of her third ,quarter4 ,sidenote3 ,and that the ,sun is much bigger than the ,earth1 and the ,moon much less4 #cae4 ,if the ,earth and ,sun were equally big1 the ,earth's shadow would be infinitely extended1 and all of the same breadth2 and the ,planet ,mars1 in either of its nodes and opposite to the ,sun1 would be eclipsed in the ,earth's shadow4 ,were the ,earth bigger than the ,sun1 it's shadow would increase in breadth the farther it was extended1 and would eclipse the great ,planets ,jupiter and ,saturn1 with all their ,moons1 when they were opposite to the ,sun4 ,but as ,mars in opposition never falls into the ,earth's shadow1 although he is not then above #db millions of miles from the ,earth1 'tis plain that the ,earth is much less than the ,sun2 for otherwise it's shadow could not end in a point at so small a distance4 ,if the ,sun and ,moon were equally big1 the ,moon's shadow would go on to the ,earth with an equal breadth1 and cover a portion of the ,earth's surface more than #bjjj miles broad1 even if it fell directly against the ,earth's center1 as seen from the ,moon3 and much more if it fell obliquely on the ,earth3 but the ,moon's shadow is seldom #aej miles broad at the ,earth1 unless when it falls very obliquely on the ,earth1 in total ,eclipses of the ,sun4 ,in annular ,eclipses1 the ,moon's real shadow ends in a point at some distance from the ,earth4 ,the ,moon's small distance from the ,earth1 and the shortness of her shadow1 prove her to be less than the ,sun4 ,and1 as the ,earth's shadow is large enough to cover the ,moon1 if her diameter was three times as large as it is 7which is evident from her long continuance in the shadow when she goes through it's center7 'tis plain1 that the ,earth is much bigger than the ,moon4 ,sidenote3 ,the primary ,planets never eclipse one another4 ,,plate ,x4 #caf4 ,though all opake bodies on which the ,sun shines have their shadows1 yet such is the bulk of the ,sun1 and the distances of the ,planets1 that the primary ,planets can never eclipse one another4 ,a ,primary can eclipse only it's secondary1 or be eclipsed by it2 and never but when in opposition or conjunction with the ,sun4 ,the primary ,planets are very seldom in these positions1 but the ,sun and ,moon are so every month3 whence one may imagine that these two ,luminaries should be eclipsed every month4 ,but there are few ,eclipses in respect of the number of ,new and ,full ,moons2 the reason of which we shall now explain4 ,sidenote3 ,why there are so few ,eclipses4 ,the ,moon's ,nodes4 ,limits of ,eclipses4 #cag4 ,if the ,moon's ,orbit were coincident with the ,plane of the ,ecliptic1 in which the ,earth always moves and the ,sun appears to move1 the ,moon's shadow would fall upon the ,earth at every ,change1 and eclipse the ,sun to some parts of the ,earth4 ,in like manner the ,moon would go through the middle of the ,earth's shadow1 and be eclipsed at every ,full2 but with this difference1 that she would be totally darkened for above an hour and half2 whereas the ,sun never was above four minutes totally eclipsed by the interposition of the ,moon4 ,but one half of the ,moon's ,orbit1 is elevated #e-a_/c degrees above the ,ecliptic1 and the other half as much depressed below it3 consequently1 the ,moon's ,orbit intersects the ,ecliptic in two opposite points called the ,moon's ,nodes1 as has been already taken notice of #bhh4 ,when these points are in a right line with the center of the ,sun at ,new or ,full ,moon1 the ,sun1 ,moon1 and ,earth are all in a right line2 and if the ,moon be then ,new1 her shadow falls upon the ,earth2 if ,full the ,earth's shadow falls upon her4 ,when the ,sun and ,moon are more than #ag degrees from either of the ,nodes at the time of ,conjunction1 the ,moon is then too high or too low in her ,orbit to cast any part of her shadow upon the ,earth4 ,and when the ,sun is more than #ab degrees from either of the ,nodes at the time of ,full ,moon1 the ,moon is too high or too low in her ,orbit to go through any part of the ,earth's shadow3 and in both these cases there will be no ,eclipse4 ,but when the ,moon is less than #ag degrees from either ,node at the time of ,conjunction1 her shadow or ,penumbra falls more or less upon the ,earth1 as she is more or less within this limit4 ,and when she is less than #ab degrees from either ,node at the time of opposition1 she goes through a greater or less portion of the ,earth's shadow1 as she is more or less within this limit4 ,her ,orbit contains #cfj degrees2 of which #ag1 the limit of solar ,eclipses on either side of the ,nodes1 and #ab the limit of lunar ,eclipses1 are but small portions3 and as the ,sun commonly passes by the ,nodes but twice in a year1 it is no wonder that we have so many ,new and ,full ,moons without ,eclipses4 ,sidenote3 ,fig4 ,i4 ,,plate ,x4 ,line of the ,nodes4 ,to illustrate this1 let ,,abcd be the ,ecliptic1 ,,rstu a ,circle lying in the same ,plane with the ,ecliptic1 and ,,vwxy the ,moon's ,orbit1 all thrown into an oblique view1 which gives them an elliptical shape to the eye4 ,one half of the ,moon's ,orbit1 as ,,vwx1 is always below the ,ecliptic1 and the other half ,,xyv above it4 ,the points ,v and ,x1 where the ,moon's ,orbit intersects the ,circle ,,rstu1 which lies even with the ,ecliptic1 are the ,moon's ,nodes2 and a right line as ,,xev drawn from one to the other1 through the ,earth's center1 is the ,line of the ,nodes1 which is carried almost parallel to itself round the ,sun in a year4 ,if the ,moon moved round the ,earth in the ,orbit ,,rstu1 which is coincident with the ,plane of the ,ecliptic1 her shadow would fall upon the ,earth every time she is in conjunction with the ,sun2 and at every opposition she would go through the ,earth's shadow4 ,were this the case1 the ,sun would be eclipsed at every ,change1 and the ,moon at every ,full1 as already mentioned4 ,but although the ,moon's shadow ,n must fall upon the ,earth at a1 when the ,earth is at ,e1 and the ,moon in conjunction with the ,sun at i1 because she is then very near one of her ,nodes2 and at her opposition n she must go through the ,earth's shadow ,i1 because she is then near the other ,node2 yet1 in the time that she goes round the ,earth to her next ,change1 according to the order of the letters ,,xyvw1 the ,earth advances from ,e to e1 according to the order of the letters ,,efgh1 and the line of the ,nodes ,,vex being carried nearly parallel to itself1 brings the point f of the ,moon's ,orbit in conjunction with the ,sun at that next ,change2 and then the ,moon being at f is too high above the ,ecliptic to cast her shadow on the ,earth3 and as the ,earth is still moving forward1 the ,moon at her next opposition will be at g1 too far below the ,ecliptic to go through any part of the ,earth's shadow2 for by that time the point g will be at a considerable distance from the ,earth as seen from the ,sun4 ,sidenote3 ,fig4 ,i and ,,ii4 ,when the ,earth comes to ,f1 the ,moon in conjunction with the ,sun ,z is not at k1 in a ,plane coincident with the ,ecliptic1 but above it at ,y in the highest part of her ,orbit3 and then the point b of her shadow ,o goes far above the ,earth 7as in ,fig4 ,,ii1 which is an edge view of ,fig4 ,i47 ,the ,moon at her next opposition is not at o 7,fig ,i7 but at ,w where the ,earth's shadow goes far above her1 7as in ,fig4 ,,ii47 ,in both these cases the line of the ,nodes ,,vfx 7,fig4 ,i47 is about #ij degrees from the ,sun1 and both ,luminaries as far as possible from the limits of ,eclipses4 ,sidenote3 ,,plate ,x4 ,when the ,earth has gone half round the ,ecliptic from ,e to ,g1 the line of the ,nodes ,,vgx is nearly1 if not exactly1 directed towards the ,sun at ,z2 and then the ,new ,moon l casts her shadow ,p on the ,earth ,g2 and the ,full ,moon p goes through the ,earth's shadow ,l2 which brings on ,eclipses again1 as when the ,earth was at ,e4 ,when the ,earth comes to ,h the ,new ,moon falls not at m in a plane coincident with the ,ecliptic ,,cd1 but at ,w in her ,orbit below it3 and then her shadow ,q 7see ,fig4 ,,ii7 goes far below the ,earth4 ,at the next ,full she is not at q 7,fig4 ,i7 but at ,y in her orbit #e-a_/c degrees above q1 and at her greatest height above the ,ecliptic ,,cd2 being then as far as possible1 at any opposition1 from the ,earth's shadow ,m 7as in ,fig4 ,,ii47 ,so1 when the ,earth is at ,e and ,g1 the ,moon is about her ,nodes at ,new and ,full2 and in her greatest ,north and ,south ,declination1 7or ,latitude as it is generally called7 from the ,ecliptic at her ,quarters3 but when the ,earth is at ,f or ,h1 the ,moon is in her greatest ,north and ,south ,declination from the ,ecliptic at ,new and ,full1 and in the ,nodes about her ,quarters4 ,sidenote3 ,the ,moon's ascending and descending ,node4 ,her ,north and ,south ,latitude4 #cah4 ,the point ,x where the ,moon's ,orbit crosses the ,ecliptic is called the ,ascending ,node1 because the ,moon ascends from it above the ,ecliptic3 and the opposite point of intersection ,v is called the ,descending ,node1 because the ,moon descends from it below the ,ecliptic4 ,when the ,moon is at ,y in the highest point of her ,orbit1 she is in her greatest ,north ,latitude2 and when she is at ,w in the lowest point of her ,orbit1 she is in her greatest ,south ,latitude4 ,sidenote3 ,the ,nodes have a retrograde motion4 ,fig4 ,i4 ,which brings on the ,eclipses sooner every year than they would be if the ,nodes had not such a motion4 #cai4 ,if the line of the ,nodes1 like the ,earth's ,axis1 was carried parallel to itself round the ,sun1 there would be just half a year between the conjunctions of the ,sun and ,nodes4 ,but the ,nodes shift backward1 or contrary to the ,earth's annual motion1 #ai-a_/c degrees every year2 and therefore the same ,node comes round to the ,sun #ai days sooner every year than on the year before4 ,consequently1 from the time that the ascending ,node ,x 7when the ,earth is at ,e7 passes by the ,sun as seen from the ,earth1 it is only #agc days 7not half a year7 till the descending ,node ,v passes by him4 ,therefore1 in whatever time of the year we have ,eclipses of the ,luminaries about either ,node1 we may be sure that in #agc days afterward we shall have ,eclipses about the other ,node4 ,and when at any time of the year the line of the ,nodes is in the situation ,,vgx1 at the same time next year it will be in the situation r,gs2 the ascending ,node having gone backward1 that is1 contrary to the order of ,signs from ,x to s1 and the descending ,node from ,v to r2 each #ai-a_/c degrees4 ,at this rate the ,nodes shift through all the ,signs and degrees of the ,ecliptic in #ah years and #bbe days2 in which time there would always be a regular period of ,eclipses1 if any compleat number of ,lunations were finished without a fraction4 ,but this never happens1 for if the ,sun and ,moon should start from a conjunction with either of the ,nodes in any point of the ,ecliptic1 whilst the same ,node is going round to that point again the ,earth performs #ah annual revolutions about the ,sun and #bbb ,degrees 7or #g ,signs #ab ,degrees7 over2 and the ,moon #bcj ,lunations or ,courses from ,change to ,change and #he ,degrees 7or #b ,signs #be ,degrees7 over2 so that the ,sun will be #ach ,degrees from the same ,node when it comes round1 and the ,moon #he ,degrees from the ,sun4 ,hence1 the period of ,eclipses and revolution of the ,nodes are completed in different times4 ,sidenote3 ,a period of ,eclipses4 ,the defects of it4 #cbj4 ,in #ah years #aj days #g hours #dc minutes after the ,sun ,moon and ,nodes have been in a line of conjunction1 they come very near to a conjunction again3 only1 if the conjunction from which you reckon falls in a leap-year1 the return of the conjunction will be one day later4 ,therefore1 if to the #femean time of any ,eclipse of the ,sun or ,moon in leap-year1 you add #ah years #aa days #g hours #dc minutes2 or in a common year a day less1 you will have the mean time of that ,eclipse returned again for some ages2 though not always visible1 because the #g hours #dc minutes may shift a solar ,eclipse into the night1 and a lunar ,eclipse into the day4 ,in this period there are just #bbc ,lunations1 and the ,sun is again within half a degree of the same ,node1 but short of it4 ,therefore1 although this period will serve tolerably well for some ages to examine ,eclipses by1 it cannot hold long2 because half a degree from the ,node sets the ,moon #b-a_/b minutes of a degree from the ,ecliptic4 ,and as the ,moon's mean distance from the ,earth is equal to #fj ,semidiameters of the ,earth1 every minute of a degree at that distance is equal to #fj geographical miles1 or one degree on the ,earth2 consequently #b-a_/b minutes of declination from the ,ecliptic in the ,moon's ,orbit1 is equal to #aej such miles1 or #b-a_/b degrees on the ,earth4 ,consequently1 if the ,moon be passing by her ascending ,node at the end of this period1 her shadow will go #aej miles more southward on the ,earth than it did at the beginning thereof4 ,if the ,moon be passing by her descending ,node1 her shadow will go #aej miles more northward3 and in either case1 in #ejj years the shadow will have too great a ,latitude to touch the ,earth4 ,so that any ,eclipse of the ,sun1 which begins 7for example7 to touch the ,earth at the south ,pole 7and that must be when the ,moon is #ag degrees past her descending ,node7 will advance gradually northward in every return for about a thousand years1 and then go off at the north ,pole2 and cannot take such another course again in less than #aa1fhc years4 ,this falling back of the ,sun and ,moon in every period1 with respect to the ,nodes1 will occasion those ,eclipses which happen about the ascending ,node to go more southerly in each return2 and those which happen about the descending ,node to go more northerly3 for the farther the ,moon is short of the ascending ,node1 within the limits of ,eclipses1 the farther she is south of the ,ecliptic2 and on the contrary1 the more she is short of the descending ,node1 the farther she is northward of the ,ecliptic4 ,sidenote3 ,from ,mr4 ,g4 ,,smith's dissertation on ,eclipses1 printed at ,london1 by ,e4 ,,cave1 in the year #agdh4 #cba4 8,to illustrate this a little farther1 we shall examine some of the most remarkable circumstances of the returns of the ,eclipse which happened ,july #ad1 #agdh1 about noon3 ,this ,eclipse1 after traversing the voids of space from the ,creation1 at last began to enter the ,terra ,australis ,incognita1 about #hh years after the ,conquest1 which was the last of ,king ,,stephen's reign2 every #ff;,chaldean period it has crept more northerly1 but was still invisible in ,britain before the year #afbb2 when on the #cjth of ,april it began to touch the south parts of ,england about #b in the afternoon2 its central appearance rising in the ,american ,south ,seas1 and traversing ,peru and the ,amazon's country1 through the ,atlantic ocean into ,africa1 and setting in the thiopian continent1 not far from the beginning of the ,red ,sea4 8,its next visible period was after three ,chaldean revolutions in #afgf1 on the first of ,june1 rising central in the ,atlantic ocean1 passing us about #i in the morning1 with four #fg;,digits eclipsed on the under limb2 and setting in the gulf of ,cochinchina in the ,east-,indies4 8,it being now near the ,solstice1 this ,eclipse was visible the very next return in #afid1 in the evening2 and in two periods more1 which was in #agcj1 on the #dth of ,july1 was seen above half eclipsed just after ,sun-rise1 and observed both at ,wirtemberg in ,germany1 and ,pekin in ,china1 soon after which it went off4 8,eighteen years more afforded us the ,eclipse which fell on the #adth of ,july #agdh4 8,the next visible return will happen on ,july #be1 #agff1 in the evening1 about four ,digits eclipsed2 and after two periods more1 on ,august #afth1 #ahjb1 early in the morning1 about five ,digits1 the center coming from the north frozen continent1 by the capes of ,norway1 through ,tartary1 ,china1 and ,japan1 to the ,ladrone islands1 where it goes off4 8,again1 in #ahbj1 ,august #bf1 betwixt one and two1 there will be another great ,eclipse at ,london1 about #aj ,digits2 but happening so near the ,equinox1 the center will leave every part of ,britain to the ,west1 and enter ,germany at ,embden1 passing by ,venice1 ,naples1 ,grand ,cairo1 and set in the gulf of ,bassora near that city4 8,it will be no more visible till #ahgd1 when five ,digits will be obscured1 the center being now about to leave the ,earth on ,september #bh4 ,in #ahib the ,sun will go down eclipsed at ,london1 and again in #aibh the passage of the center will be in the expansum1 though there will be two ,digits eclipsed at ,london1 ,october the #cast of that year2 and about the year #bjij the whole ,penumbra will be wore off2 whence no more returns of this ,eclipse can happen till after a revolution of #aj thousand years4 8,from these remarks on the intire revolution of this ,eclipse1 we may gather1 that a thousand years1 more or less 7for there are some irregularities that may protract or lengthen this period #ajj years7 complete the whole terrestrial ,phenomena of any single ,eclipse3 and since #bj periods of #ed years each1 and about #cc days1 comprehend the intire extent of their revolution1 'tis evident that the times of the returns will pass through a circuit of one year and ten months1 every ,chaldean period being ten or eleven days later1 and of the equable appearances about #cb or #cc days4 ,thus1 though this ,eclipse happens about the middle of ,july1 no other subsequent ,eclipse of this period will return to the middle of the same month again2 but wear constantly each period #aj or #aa days forward1 and at last appear in ,winter1 but then it begins to cease from affecting us4 8,another conclusion from this revolution may be drawn1 that there will seldom be any more than two great ,eclipses of the ,sun in the interval of this period1 and these follow sometimes next return1 and often at greater distances4 ,that of #agae returned again in #agcc very great2 but this present ,eclipse will not be great till the arrival of #ahbj1 which is a revolution of four ,chaldean periods3 so that the irregularities of their circuits must undergo new computations to assign them exactly4 8,nor do all ,eclipses come in at the south ,pole3 that depends altogether on the position of the lunar ,nodes1 which will bring in as many from the expansum one way as the other2 and such ,eclipses will wear more southerly by degrees1 contrary to what happens in the present case4 8,the ,eclipse1 for example1 of #agcf1 in ,september1 had its center in the expansum1 and set about the middle of its obscurity in ,britain2 it will wear in at the north ,pole1 and in the year #bfjj1 or thereabouts1 go off into the expansum on the south side of the ,earth4 8,the ,eclipses therefore which happened about the ,creation are little more than half way yet of their etherial circuit2 and will be #djjj years before they enter the ,earth any more4 ,this grand revolution seems to have been entirely unknown to the antients4 ,sidenote3 ,why our present ,tables agree not with antient observations4 8#cbb4 ,it is particularly to be noted1 that ,eclipses which have happened many centuries ago1 will not be found by our present ,tables to agree exactly with antient observations1 by reason of the great ,anomalies in the lunar motions2 which appears an incontestable demonstration of the non-eternity of the ,universe4 ,for it seems confirmed by undeniable proofs1 that the ,moon now finishes her period in less time than formerly1 and will continue by the centripetal law to approach nearer and nearer the ,earth1 and to go sooner and sooner round it3 nor will the centrifugal power be sufficient to compensate the different gravitations of such an assemblage of bodies as constitute the solar system1 which would come to ruin of itself1 without some new regulation and adjustment of their original motions#fh4 ,sidenote3 ,,thales's ,eclipse4 8#cbc4 ,we are credibly informed from the testimony of the antients1 that there was a total ,eclipse of the ,sun predicted by ,,thales to happen in the fourth year of the #dhth #fi,olympiad1 either at ,sardis or ,miletus in ,asia1 where ,,thales then resided4 ,that year corresponds to the #eheth year before ,,christ2 when accordingly there happened a very signal ,eclipse of the ,sun1 on the #bhth of ,may1 answering to the present #ajth of that month#gj1 central through ,north ,america1 the south parts of ,france1 ,italy1 c4 as far as ,athens1 or the ,isles in the gean ,sea2 which is the farthest that even the ,caroline ,tables carry it2 and consequently make it invisible to any part of ,asia1 in the total character2 though ,i have good reasons to believe that it extended to ,babylon1 and went down central over that city4 ,we are not however to imagine1 that it was set before it past ,sardis and the ,asiatic towns1 where the predictor lived2 because an invisible ,eclipse could have been of no service to demonstrate his ability in ,astronomical ,sciences to his countrymen1 as it could give no proof of its reality4 ,sidenote3 ,,thucydides's ,eclipse4 8#cbd4 ,for a farther illustration1 ,,thucydides relates1 that a solar ,eclipse happened on a ,summer's day in the afternoon1 in the first year of the ,peloponnesian war1 so great that the ,stars appeared4 ,rhodius was victor in the ,olympic games the fourth year of the said war1 being also the fourth of the #hgth ,olympiad1 on the #dbhth year before ,,christ4 ,so that the ,eclipse must have happened in the #dcast year before ,,christ2 and by computation it appears1 that on the #c;d of ,august there was a signal ,eclipse which would have past over ,athens1 central about #f in the evening1 but which our present ,tables bring no farther than the antient ,syrtes on the ,african coast1 above #djj miles from ,athens2 which suffering in that case but #i ,digits1 could by no means exhibit the remarkable darkness recited by this historian2 the center therefore seems to have past ,athens about #f in the evening1 and probably might go down about ,jerusalem1 or near it1 contrary to the construction of the present ,tables4 ,i have only obviated these things by way of caution to the present ,astronomers1 in re-computing antient ,eclipses2 and refer them to examine the ,eclipse of ,nicias1 so fatal to the ,athenian fleet#ga2 that which overthrew the ,macedonian ,army#gb c40 ,so far ,mr4 ,,smith4 ,sidenote3 ,the number of ,eclipses4 #cbe4 ,in any year1 the number of ,eclipses of both ,luminaries cannot be less than two1 nor more than seven2 the most usual number is four1 and it is very rare to have more than six4 ,for the ,sun passes by both the ,nodes but once a year1 unless he passes by one of them in the beginning of the year2 and if he does1 he will pass by the same ,node again a little before the year be finished2 because1 as these points move #ai degrees backward every year1 the ,sun will come to either of them #agc days after the other #cai4 ,and when either ,node is within #ag degrees of the ,sun at the time of ,new ,moon1 the ,sun will be eclipsed4 ,at the subsequent opposition the ,moon will be eclipsed in the other ,node2 and come round to the next conjunction again ere the former ,node be #ag degrees past the ,sun1 and will therefore eclipse him again4 ,when three ,eclipses fall about either ,node1 the like number generally falls about the opposite2 as the ,sun comes to it in #agc days afterward3 and six ,lunations contain but four days more4 ,thus1 there may be two ,eclipses of the ,sun and one of the ,moon about each of her ,nodes4 ,but when the ,moon changes in either of the ,nodes1 she cannot be near enough the other ,node at the next ,full to be eclipsed2 and in six lunar months afterward she will change near the other ,node3 in these cases there can be but two ,eclipses in a year1 and they are both of the ,sun4 ,sidenote3 ,two periods of ,eclipses4 #cbf4 ,a longer1 and consequently more exact period than the above-mentioned #cbj1 for comparing and examining ,eclipses which happen at long intervals of time1 is #eg ,julian years #cbd days #ba hours #da minutes and #ce seconds2 in which time there are just #gaf mean ,lunations1 and the ,sun is again within #e minutes of the same ,node as before4 ,but a still better period is #eeg years #ba days #ah hours #cj minutes #ab seconds2 in which time there are #fhij mean ,lunations2 and the ,sun and ,node meet again so nearly as to be but #aa seconds distant4 ,sidenote3 ,an account of the following catalogue of ,eclipses4 #cbg4 ,we shall subjoin a catalogue of ,eclipses recorded in history1 from #gba years before ,,christ to ,a4 ,d4 #adhe2 of computed ,eclipses from #adhe to #agjj2 and of all the ,eclipses visible in ,europe from #agjj to #ahjj4 ,from the beginning of the catalogue to ,a4,d4 #adhe the ,eclipses are taken from ,,struyk's ,introduction to universal ,geography1 as that indefatigable author has1 with much labour1 collected them from ,ptolemy1 ,thucydides1 ,plutarch1 ,calvisius1 ,xenophon1 ,diodorus ,siculus1 ,justin1 ,polybius1 ,titus ,livius1 ,cicero1 ,lucanus1 ,theophanes1 ,dion ,cassius1 and many others4 ,from #adhe to #agjj the ,eclipses are taken from ,ricciolus's ,almagest3 and from #agjj to #ahjj from ,l'art de verifier les ,dates#gc4 ,those from ,struyk have all the places mentioned where they were observed3 ,those from the ,french authors1 viz4 the religious ,benedictines of the ,congregation of ,st4 ,maur1 are fitted to the ,meridian of ,paris3 ,and concerning those from ,ricciolus1 that author gives the following account4 ,because it is of great use for fixing the ,cycles or ,revolutions of ,eclipses1 to have at hand1 without the trouble of calculation1 a list of successive ,eclipses for many years1 computed by authors of ,ephemerides1 although from ,tables not perfect in all respects1 ,i shall for the benefit of ,astronomers give a summary collection of such4 ,the authors ,i extract from are1 an anonymous one who published ,ephemerides from #adhd to #aejf inclusive2 ,jacobus ,pflaumen and ,jo4 ,stflerinus1 to the ,meridian of ,ulm1 from #aejg to #aecd3 ,lucas ,gauricus1 to the ,latitude of #de degrees1 from #aecd to #aeea3 ,peter ,appian1 to the ,meridian of ,leysing1 from #aech to #aegh3 ,jo4 ,stflerus to the ,meridian of ,tubing1 from #aedc to #aeed3 ,petrus ,pitatus1 to the ,meridian of ,venice from #aedd to #aeef3 ,georgius-,joachimus ,rheticus1 for the year #aeea3 ,nicholaus ,simus1 to the ,meridian of ,bologna1 from #aeeb to #aefh3 ,michael ,mstlin1 to the ,meridian of ,tubing1 from #aeeg to #aeij3 ,jo4 ,stadius1 to the ,meridian of ,antwerp1 from #aeed to #aegd3 ,jo4 ,antoninus ,maginus1 to the ,meridian of ,venice1 from #aeha to #afcj3 ,david ,origan1 to the ,meridian of ,franckfort on the ,oder1 from #aeie to #affd3 ,andrew ,argol1 to the ,meridian of ,rome1 from #afcj to #agjj3 ,franciscus ,montebrunus1 to the ,meridian of ,bologna1 from #adfa to #affj3 ,among which1 ,stadius1 ,mstlin1 and ,maginus1 used the ,prutenic ,tables2 ,origan the ,prutenic and ,tychonic2 ,montebrunus the ,lansbergian1 as likewise those of ,duret4 ,almost all the rest the ,alphonsine4 ,but1 that the places may readily be known for which these ,eclipses were computed1 and from what ,tables1 consult the following list1 in which the years inclusive are also set down4 ,from #adhe to #aejf ,the place and author unknown4 #aejg #aeec ,ulm in ,suabia1 from the ,alphonsine4 #aeed #aegf ,antwerp1 from the ,prutenic4 #aegg #aehe ,tubing1 from the ,prutenic4 #aehf #aeid ,venice1 from the ,prutenic4 #aeie #afjj ,franckfort on ,oder1 from the ,prutenic4 #afja #afdj ,franckfort on ,oder1 from the ,tychonic4 #afda #affj ,bologna1 from the ,lansbergian4 #affa #agjj ,rome1 from the ,tychonic4 ,so far ,,ricciolus4 ,n4 ,b4 ,the ,eclipses marked with an ,asterisk are not in ,,ricciolus's catalogue2 but are supplied from ,l'art de verifier les ,dates4 ,from the beginning of the catalogue to ,a4 ,d4 #agjj1 the time is reckoned from the noon of the day mentioned to the noon of the following day2 but from #agjj to #ahjj the time is set down according to our common way of reckoning4 ,those marked ,pekin and ,canton are ,eclipses from the ,chinese chronology according to ,,struyk2 and throughout the ,table this mark signifies ,sun1 and this ,moon4 ,,struyk's ,catalogue of ,,eclipses4 ---------------------------------------- -------------------- ,bef4 ,eclipses of the ,sun ,m4 ,d4 ,middle ,digits ,chr4 and ,moon seen at ,h4 ,m4 eclipsed ---------------------------------------- -------------------- #gba ,babylon ,mar4 #ai #aj #cd ,total #gbj ,babylon ,mar4 #h #aa #ef #a #e #gbj ,babylon ,sept4 #a #aj #ah #e #d #fba ,babylon ,apr4 #ba #ah #bb #b #cf #ebc ,babylon ,july #af #ab #dg #g #bd #ejb ,babylon ,nov4 #ai #ab #ba #a #eb #dia ,babylon ,apr4 #be #ab #ab #a #dd #dca ,athens ,aug4 #c #f #ce #aa #j #dbe ,athens ,oct4 #i #f #de ,total #dbd ,athens ,mar4 #bj #bj #ag #i #j #dac ,athens ,aug4 #bg #aj #ae ,total #djf ,athens ,apr4 #ae #h #ej ,total #djd ,athens ,sept4 #b #ba #ab #h #dj #djc ,pekin ,aug4 #bh #e #ec #aj #dj #cid ,gnide ,aug4 #ac #bb #ag #aa #j #chc ,athens ,dec4 #bb #ai #f #b #a #chb ,athens ,june #ah #h #ed #f #ae #chb ,athens ,dec4 #ab #aj #ba ,total #cfd ,thebes ,july #ab #bc #ea #f #aj #ceg ,syracuse ,feb4 #bh #bb -- #c #cc #ceg ,zant ,aug4 #bi #g #bi #d #ba #cdj ,zant ,sept4 #ad #ah -- #i #j #cca ,arbela ,sept4 #bj #aj #i ,total #caj ,sicily ,island ,aug4 #ad #bj #e #aj #bb #bai ,mysia ,mar4 #ai #ad #e ,total #bah ,pergamos ,sept4 #a rising ,total #bag ,sardinia ,feb4 #aa #a #eg #i #f #bjc ,frusini ,may #f #b #eb #e #dj #bjb ,cumis ,oct4 #ah #bb #bd #a #j #bja ,athens ,sept4 #bb #g #ad #h #eh #bjj ,athens ,mar4 #ai #ac #i ,total #bjj ,athens ,sept4 #aa #ad #dh ,total #aih ,rome ,aug4 #f ---- ---- #aij ,rome ,mar4 #ac #ah -- #aa #j #ahh ,rome ,july #af #bj #ch #aj #dh #agd ,athens ,apr4 #cj #ad #cc #g #a #afh ,macedonia ,june #ba #h #b ,total #ada ,rhodes ,jan4 #bg #aj #h #c #bf #ajd ,rome ,july #ah #bb #j #aa #eb #fc ,rome ,oct4 #bg #f #bb ,total #fj ,gibralter ,mar4 #af setting ,central #ed ,canton ,may #i #c #da ,total #ea ,rome ,mar4 #g #b #ab #i #j #dh ,rome ,jan4 #ah #aj #j ,total #de ,rome ,nov4 #f #ad -- ,total #cf ,rome ,may #ai #c #eb #f #dg #ca ,rome ,aug4 #bj setting ,gr4 ,ecl4 #bi ,canton ,jan4 #e #d #b #aa #j #bh ,pekin ,june #ah #bc #dh ,total #bf ,canton ,oct4 #bc #d #af #aa #ae #bd ,pekin ,april #g #d #aa #b #j #af ,pekin ,nov4 #a #e #ac #b #h #b ,canton ,feb4 #a #bj #h #aa #db ---------------------------------------- -------------------- ---------------------------------------- -------------------- ,aft4 ,eclipses of the ,sun ,m4 ,d4 ,middle ,digits ,chr4 and ,moon seen at ,h4 ,m4 eclipsed ---------------------------------------- -------------------- #a ,pekin ,june #aj #a #aj #aa #dc #e ,rome ,mar4 #bh #d #ac #d #de #ad ,panonia ,sept4 #bf #ag #ae ,total #bg ,canton ,july #bb #h #ef ,total #cj ,canton ,nov4 #ac #ai #bj #aj #cj #dj ,pekin ,apr4 #cj #e #ej #g #cd #de ,rome ,july #ca #bb #a #e #ag #df ,pekin ,july #ba #bb #be #b #aj #df ,rome ,dec4 #ca #i #eb ,total #di ,pekin ,may #bj #g #af #aj #h #ec ,canton ,mar4 #h #bj #db #aa #f #ee ,pekin ,july #ab #ba #ej #f #dj #ef ,canton ,dec4 #be #j #bh #i #bj #ei ,rome ,apr4 #cj #c #h #aj #ch #fj ,canton ,oct4 #ac #c #ca #aj #cj #fe ,canton ,dec4 #ae #ba #ej #aj #bc #fi ,rome ,oct4 #ah #aj #dc #aj #di #gj ,canton ,sept4 #bb #ba #ac #h #bf #ga ,rome ,mar4 #d #h #cb #f #j #ie ,ephesus ,may #ba ---- #a #j #abe ,alexandria ,april #e #i #af #a #dd #acc ,alexandria ,may #f #aa #dd ,total #acd ,alexandria ,oct4 #bj #aa #e #aj #ai #acf ,alexandria ,mar4 #e #ae #ef #e #ag #bcg ,bologna ,apr4 #ab ---- ,total #bch ,rome ,april #a #bj #bj #h #de #bij ,carthage ,may #ae #c #bj #aa #bj #cjd ,rome ,aug4 #ca #i #cf ,total #caf ,constantinople ,dec4 #cj #ai #ec #b #ah #ccd ,toledo ,july #ag at noon ,central #cdh ,constantinople ,oct4 #h #ai #bd #h #j #cfj ,ispahan ,aug4 #bg #ah #j ,central #cfd ,alexandria ,nov4 #be #ae #bd ,total #dja ,rome ,june #aa ---- ,total #dja ,rome ,dec4 #f #ab #ae ,total #djb ,rome ,june #a #h #dc #aj #b #djb ,rome ,nov4 #aj #bj #cc #aj #cj #ddg ,compostello ,dec4 #bc #j #df #a -- #dea ,compostello ,april #a #af #cd #ai #eb #dea ,compostello ,sept4 #bf #f #cj #j #b #deh ,chaves ,may #bg #bc #af #ah #ec #dfb ,compostello ,mar4 #a #ac #b #aa #aa #dfd ,chaves ,july #ai #ai #a #aj #ae #dhd ,constantinople ,jan4 #ac #ai #ec #j #j #dhf ,constantinople ,may #ai #a #aj #e #ae #dig ,constantinople ,apr4 #ah #f #e #ag #eg #eab ,constantinople ,june #bh #bc #h #a #ej #ech ,england ,feb4 #ad #ai -- #h #bc #edj ,london ,june #ai #bj #ae #h -- #egg ,tours ,dec4 #aj #ag #bh #f #df #eha ,paris ,april #d #ac #cc #f #db #ehb ,paris ,sept4 #ag #ab #da ,total #eij ,paris ,oct4 #ah #f #cj #i #be #eib ,constantinople ,mar4 #ah #bb #f #aj #j #fjc ,paris ,aug4 #ab #c #c #aa #bj #fbb ,constantinople ,febr4 #a #aa #bh ,total #fdd ,paris ,nov4 #e #j #cj #i #ec #fhj ,paris ,june #ag #ab #cj ,total #fhc ,paris ,april #af #aa #cj ,total #fic ,constantinople ,oct4 #d #bc #ed #aa #ed #gaf ,constantinople ,jan4 #ac #g -- ,total #gah ,constantinople ,june #c #a #ae ,total #gcc ,england ,aug4 #ac #bj -- #aa #a #gcd ,england ,jan4 #bc #ad -- ,total #geb ,england ,july #cj #ac -- ,total #gec ,england ,june #h #bb -- #aj #ce #gec ,england ,jan4 #bc #ac -- ,total #gfj ,england ,aug4 #ae #d -- #h #ae #gfj ,london ,aug4 #cj #e #ej #aj #dj #gfd ,england ,june #d at noon #g #ae #ggj ,london ,feb4 #ad #g #ab ,total #ggd ,rome ,nov4 #bb #ad #cg #aa #eh #ghd ,london ,nov4 #a #ad #b ,total #ghg ,constantinople ,sept4 #ad #bj #dc #i #dg #gif ,constantinople ,mar4 #bg #af #bb ,total #hjj ,rome ,jan4 #ae #i #j #aj #ag #hjg ,angoulesme ,feb4 #aj #ba #bd #i #db #hjg ,paris ,feb4 #be #ac #dc ,total #hjg ,paris ,aug4 #ba #aj #bj ,total #hji ,paris ,july #ae #ba #cc #h #h #hji ,paris ,dec4 #be #h -- ,total #haj ,paris ,june #bj #h -- ,total #haj ,paris ,nov4 #cj #j #ab ,total #haj ,paris ,dec4 #ad #h -- ,total #hab ,constantinople ,may #ad #b #ac #i -- #hac ,cappadocia ,may #c #ag #e #aj #ce #hag ,paris ,feb4 #e #e #db ,total #hah ,paris ,july #f #ah -- #f #ee #hbj ,paris ,nov4 #bc #f #bf ,total #hbd ,paris ,mar4 #ah #g #ee ,total #hbh ,paris ,june #cj #ae -- ,total #hbh ,paris ,dec4 #bd #ac #de ,total #hca ,paris ,april #cj #f #ai #aa #h #hca ,paris ,may #ae #bc -- #d #bd #hca ,paris ,oct4 #bd #aa #ah ,total #hcb ,fulda ,apr4 #ah #i #j ,total #hdj ,paris ,may #d #bc #bb #i #bj #hda ,paris ,oct4 #ag #ah #eh #e #bd #hdb ,paris ,mar4 #bi #ad #ch ,total #hdc ,paris ,mar4 #ai #g #a ,total #hfa ,paris ,mar4 #bi #ae #g ,total #hgh ,paris ,oct4 #ad #af -- ,total #hgh ,paris ,oct4 #bi #a -- #aa #ad #hhc ,arracta ,july #bc #g #dd #aa -- #hhi ,constantinople ,april #c #ag #eb #i #bc #hia ,constantinople ,aug4 #g #bc #dh #aj #cj #ija ,arracta ,aug4 #b #ae #g ,total #ijd ,london ,may #ca #aa #dg ,total #ijd ,london ,nov4 #be #i #j ,total #iab ,london ,jan4 #f #ae #ab ,total #ibf ,paris ,mar4 #ca #ae #ag ,total #icd ,paris ,apr4 #af #d #cj #aa #cf #ici ,paris ,july #ah #ai #de #aj #g #iee ,paris ,sept4 #d #aa #ah ,total #ifa ,rhemes ,may #af #bj #ac #i #ah #igj ,constantinople ,may #g #ah #ch #aa #bb #igf ,london ,july #ac #ae #g ,total #ihe ,messina ,july #bj #c #eb #d #aj #ihi ,constantinople ,may #bh #f #ed #h #dj #iij ,fulda ,apr4 #ab #aj #bb #i #e #iij ,fulda ,oct4 #f #ae #d #aa #aj #iij ,constantinople ,oct4 #ba #j #de #aj #e #iie ,augsburgh ,july #ad #aa #bg ,total #ajji ,ferrara ,oct4 #f #aa #ch ,total #ajaj ,messina ,mar4 #ah #e #da #i #ab #ajaf ,nimeguen ,nov4 #af #af #ci ,total #ajag ,nimeguen ,oct4 #bb #b #h #f -- #ajbj ,cologne ,sept4 #d #aa #ch ,total #ajbc ,london ,jan4 #bc #bc #bi #aa -- #ajcj ,rome ,feb4 #bj #aa #dc ,total #ajca ,paris ,feb4 #i #aa #ea ,total #ajcc ,paris ,dec4 #h #aa #aa #i #ag #ajcd ,milan ,june #d #i #h ,total #ajcg ,paris ,apr4 #ag #bj #de #aj #de #ajci ,auxerre ,aug4 #ba #bc #dj #aa #e #ajdb ,rome ,jan4 #h #af #ci ,total #ajdd ,auxerre ,nov4 #g #af #ab #aj #a #ajdd ,cluny ,nov4 #ba #bb #ab #aa -- #ajef ,nuremburg ,april #b #ab #i ,total #ajfc ,rome ,nov4 #h #ab #af ,total #ajgd ,augsburgh ,oct4 #g #aj #ac ,total #ajhj ,constantinople ,nov4 #bi #aa #ab #i #cf #ajhb ,london ,may #ad #aj #cb #aj #b #ajhf ,constantinople ,feb4 #af #d #g ,total #ajhi ,naples ,june #be #f #f ,total #ajic ,augsburgh ,sept4 #bb #bb #ce #aj #ab #ajif ,gemblours ,feb4 #aj #af #d ,total #ajif ,augsburgh ,aug4 #f #h #ba ,total #ajih ,augsburgh ,dec4 #be #a #be #aj #ab #ajii ,naples ,nov4 #cj #d #eh ,total #aajc ,rome ,sept4 #ag #aj #ah ,total #aajf ,erfurd ,july #ag #aa #bh #aa #ed #aajg ,naples ,jan4 #aj #ac #af ,total #aaji ,erfurd ,may #ca #a #cj #aj #bj #aaaj ,london ,may #e #aj #ea ,total #aaac ,jerusalem ,mar4 #ah #ai #j #i #ab #aaad ,london ,aug4 #ag #ae #e ,total #aaag ,trier ,june #ae #ac #bf ,total #aaag ,trier ,dec4 #aj #ab #ea ,total #aaah ,naples ,nov4 #bi #ae #df #d #aa #aaba ,trier ,sept4 #bg #af #dg ,total #aabb ,prague ,mar4 #bd #aa #bj #c #di #aabd ,erfurd ,feb4 #a #f #dc #h #ci #aabd ,london ,aug4 #aj #bc #bi #i #eh #aacb ,erfurd ,march #c #h #ad ,total #aacc ,prague ,feb4 #bj #af #da #c #bc #aace ,london ,dec4 #bb #bj #aa ,total #aadb ,rome ,feb4 #aa #ad #ag #h #cj #aadc ,rome ,feb4 #a #f #cf ,total #aadg ,auranches ,oct4 #be #bb #ch #g #bj #aadi ,bary ,mar4 #be #ac #ed #e #bi #aaea ,eimbeck ,aug4 #bh #ab #d #d #bi #aaec ,augsburgh ,jan4 #bf #j #db #aa -- #aaed ,paris ,june #bf #af #a ,total #aaed ,paris ,dec4 #ba #h #cj #d #db #aaee ,auranches ,june #aj #h #de #j #ec #aafj ,rome ,aug4 #ah #g #ec #f #di #aafa ,rome ,aug4 #g #h #ae ,total #aafb ,erfurd ,feb4 #a #f #dj #e #ef #aafb ,erfurd ,july #bg #ab #cj #d #aa #aafc ,mont ,cassin4 ,july #c #g #dj #b #j #aafd ,milan ,june #f #aj #j ,total #aafh ,london ,sept4 #ah #ad #j ,total #aagb ,cologne ,jan4 #aa #ac #ca ,total #aagf ,auranches ,april #be #g #b #h #f #aagf ,auranches ,oct4 #ai #aa #bj #h #ec #aagh ,cologne ,march #e setting #g #eb #aagh ,auranches ,aug4 #bi #ac #eb #e #ca #aagh ,cologne ,sept4 #ab -- -- #aj #ea #aagi ,cologne ,aug4 #ah #ad #bh ,total #aahj ,auranches ,jan4 #bh #d #ad #aj #cd #aaha ,auranches ,july #ac #c #ae #c #dh #aaha ,auranches ,dec4 #bb #h #eh #d #dj #aahe ,rhemes ,may #a #a #ec #i #j #aahf ,cologne ,april #e #f -- ,total #aahf ,franckfort ,april #bj #g #ai #d #j #aahg ,paris ,mar4 #be #af #ag #h #db #aahg ,england ,sept4 #c #ba #ed #h #f #aahi ,england ,feb4 #b #aj -- #i -- #aaia ,england ,june #bc #j #bj #aa #cb #aaib ,france ,nov4 #bj #ad -- #f -- #aaic ,france ,nov4 #aj #e #bg ,total #aaid ,london ,april #bb #b #ae #f #di #abjj ,london ,jan4 #b #ag #b #d #ce #abja ,london ,june #ag #ae #d ,total #abjd ,england ,april #ae #ab #ci ,total #abjd ,saltzburg ,oct4 #aj #f #cb ,total #abjg ,rhemes ,feb4 #bg #aj #ej #aj #bj #abjh ,rhemes ,feb4 #b #e #aj ,total #abaa ,vienna ,nov4 #ba #ac #eg ,total #abae ,cologne ,mar4 #af #ae #ce ,total #abaf ,acre ,feb4 #ah #ba #ae #aa #cf #abaf ,acre ,march #e #i #ch #g #d #abah ,damietta ,july #i #i #df #aa #ca #abbb ,rome ,oct4 #bb #ad #bh ,total #abbc ,colmar ,april #af #h #ac #aa #j #abbh ,naples ,dec4 #bg #i #ee #i #ai #abcj ,naples ,may #ac #ag -- ,total #abcj ,london ,nov4 #ba #ac #ba #i #cd #abcb ,rhemes ,oct4 #ae #d #bi #d #be #abde ,rhemes ,july #bd #ag #dg #f -- #abdh ,london ,june #g #h #di ,total #abee ,london ,july #bj #i #dg ,total #abee ,constantinople ,dec4 #cj #b #eb ,annul4 #abeh ,augsburgh ,may #ah #aa #ag ,total #abfa ,vienna ,mar4 #ca #bb #dj #i #h #abfb ,vienna ,march #g #e #ej ,total #abfb ,vienna ,aug4 #cj #ad #ci ,total #abfc ,vienna ,feb4 #bd #f #eb #f #bi #abfc ,augsburgh ,aug4 #e #c #bd #aa #ag #abfc ,vienna ,aug4 #bj #g #ce #i #g #abfe ,vienna ,dec4 #bc #af #be ,total #abfg ,constantinople ,may #bd #bc #aa #aa #dj #abgj ,vienna ,mar4 #bb #ah #dg #aj #dj #abgb ,vienna ,aug4 #aj #g #bg #h #ec #abgd ,vienna ,jan4 #bc #aj #ci #i #be #abge ,lauben ,dec4 #d #f #bj #d #bi #abgf ,vienna ,nov4 #bb #ae -- ,total #abgg ,vienna ,may #ah -- -- ,total #abgi ,franckfort ,apr4 #ab #f #ee #aj #f #abhj ,london ,mar4 #ag #ab #ab ,total #abhd ,reggio ,dec4 #bc #af #aa #i #ac #abij ,wittemburg ,sept4 #d #ai #cg #aj #cj #abia ,london ,feb4 #ad #aj #b ,total #acjb ,constantinople ,jan4 #ad #aj #be ,total #acjg ,ferrara ,april #b #bb #ah #j #ed #acji ,london ,feb4 #bd #ag #dd ,total #acji ,lucca ,aug4 #ba #aj #cb ,total #acaj ,wittemburg ,jan4 #ca #b #b #aj #aj #acaj ,torcello ,feb4 #ad #d #h #aj #bj #acaj ,torcello ,aug4 #aj #ae #cc #g #af #acab ,wittemburg ,july #d #ai #di #c #bc #acab ,plaisance ,dec4 #ad #g #ai ,total #acac ,torcello ,dec4 #c #h #eh #i #cd #acaf ,modena ,oct4 #a #ad #ee ,total #acba ,wittemburg ,june #be #ah #a #aa #ag #acbc ,florence ,may #bj #ae #bd ,total #acbd ,florence ,may #i #f #c ,total #acbd ,wittemburg ,apr4 #bc #f #ce #h #h #acbg ,constantinople ,aug4 #ca #ah #bf ,total #acbh ,constantinople ,feb4 #be #ac #dg #aa -- #accj ,florence ,june #cj #ae #aj #g #cd #accj ,constantinople ,july #af #d #e #aj #dc #accj ,prague ,dec4 #be #ae #di ,total #acca ,prague ,nov4 #bi #bj #bf #g #da #acca ,prague ,dec4 #ad #ah -- #aa -- #accc ,wittemburg ,may #ad #c -- #aj #ah #accd ,cesena ,apr4 #ai #aj #cc ,total #acda ,constantinople ,nov4 #bc #ab #bc ,total #acda ,constantinople ,dec4 #h #bb #ae #f #cj #acdb ,constantinople ,may #bj #ad #bg ,total #acdd ,alexandria ,oct4 #f #ah #dj #h #ee #acdi ,wittemburg ,june #cj #ab #bj ,total #aced ,wittemburg ,sept4 #af #bj #de #h #dc #acef ,florence ,feb4 #af #aa #dc ,total #acfa ,constantinople ,may #d #bb #ae #h #ed #acfg ,in ,china ,jan4 #af #h #bg ,total #achi ,eugibin ,nov4 #c #ag #e ,total #acif ,augsburg ,jan4 #aa #j #af #f #bb #acif ,augsburg ,june #ba #aa #aj ,total #acii ,forli ,oct4 #bi #j #dc #i -- #adjf ,constantinople ,june #a #ac -- #aj #ca #adjf ,constantinople ,june #ae #ah #a #aa #ch #adjh ,forli ,oct4 #ah #ba #dg #i #cb #adji ,constantinople ,apr4 #ae #c #a #aj #dh #adaj ,vienna ,mar4 #bj #ac #ac ,total #adae ,wittemburg ,june #f #f #dc ,total #adai ,franckfort ,mar4 #be #bb #e #a #de #adba ,forli ,feb4 #ag #h #b ,total #adbb ,forli ,feb4 #f #h #bf #aa #g #adbd ,wittemburg ,june #bf #c #eg #aa #bj #adca ,forli ,feb4 #ab #b #d #a #ci #adcc ,wittemburg ,june #ag #e -- ,total #adch ,wittemburg ,sept4 #ah #bj #ei #h #g #addb ,rome ,dec4 #ag #c #ef ,total #addh ,tubing ,aug4 #bh #bb #bc #h #ec #adej ,constantinople ,july #bd #g #ai ,total #adeg ,vienna ,sept4 #c #aa #ag ,total #adfj ,austria ,july #c #g #ca #e #bc #adfj ,austria ,july #ag #ag #cb #aa #ai #adfj ,vienna ,dec4 #bg #ac #cj ,total #adfa ,vienna ,june #bb #aa #ej ,total #adfa ,rome ,dec4 #ag -- -- ,total #adfb ,viterbo ,june #aa #ae -- #g #ch #adfb ,viterbo ,nov4 #ba #j #aj #b #f #adfd ,padua ,apr4 #ba #ab #dc ,total #adfe ,rome ,sept4 #bj #e #ae #h #df #adfe ,rome ,oct4 #d #e #ab ,total #adfi ,rome ,jan4 #bg #g #i ,total #adhe ,norimburg ,mar4 #af #c #ec #aa -- ---------------------------------------- -------------------- ,the following ,,eclipses are all taken from ,,ricciolus1 except those marked with an ,asterisk1 which are from ,l',art de verifier les ,dates4 ---------------------------------------- - ,aft4 ,m4 ,d4 ,middle ,digits ,chr4 ,h4 ,m4 eclipsed ---------------------------------------- - #adhf ,feb4 #ah #e #da ,total #adhf ,mar4 #e #ag #dc #i #j #adhg ,feb4 #g #ae #di ,total #adhg ,july #bj #b #f #g #j #adhh ,jan4 #bh #f -- 99 #adhh ,july #h #ag #cj #d #j #adhi ,dec4 #g #ag #da ,total #adij ,may #ai ,noon 99 #adij ,june #b #aj #f ,total #adij ,nov4 #bf #ah #be ,total #adia ,may #h #b #ai #i #j #adia ,nov4 #ae #ah -- 99 #adib ,apr4 #bf #g -- 99 #adib ,oct4 #bj #bc -- 99 #adic ,april #a #ad #j ,total #adic ,oct4 #aj #b #dj #h #j #adid ,mar4 #g #d #ab #d #j #adid ,mar4 #ba #ad #ch ,total #adid ,sept4 #ad #ai #de ,total #adie ,mar4 #aj #af -- 99 #adie ,aug4 #ai #ag -- 99 #adif ,jan4 #bi #ad -- 99 #adig ,jan4 #ah #f #ch ,total #adig ,july #bi #c #b #c #j #adii ,june #bb #ag -- 99 #adii ,aug4 #bc #ah -- 99 #adii ,nov4 #ag #aj -- 99 #aejj ,mar4 #bg ,in the ,night #aejj ,apr4 #aa ,at ,noon #aejj ,oct4 #e #ad #b #aj #j #aeja ,may #b #ag #di ,total #aejb ,sept4 #cj #ai #de #aj #j #aejb ,oct4 #ae #ab #bj #b #j #aejc ,mar4 #ab #i -- 99 #aejc ,sept4 #ai #bb -- 99 #aejd ,feb4 #bi #ac #cf ,total #aejd ,mar4 #af #c -- 99 #aeje ,aug4 #ad #h #ah ,total #aejf ,feb4 #g #ae -- 99 #aejf ,july #bj #c #aa #b #j #aejf ,aug4 #c #aj -- 99 #aejg ,jan4 #ab #ai -- 99 #aejh ,jan4 #b #d -- 99 #aejh ,may #bi #f -- 99 #aejh ,june #ab #ag #dj ,total #aeji ,june #b #aa #aa #g #j #aeji ,nov4 #aa #bb -- 99 #aeaj ,oct4 #af #ai -- 99 #aeaa ,oct4 #f #aa #ej ,total #aeab ,sept4 #be #c #ef ,total #aeac ,mar4 #g #j #cj #f #j #aeac ,aug4 #cj #a -- 99 #aeae ,jan4 #bi #ae #ah ,total #aeaf ,jan4 #ai #f #j ,total #aeaf ,july #ac #aa #cg ,total #aeaf ,dec4 #bc #c #dg #c #j #aeag ,june #ah #af -- 99 #aeag ,nov4 #bg #ai -- 99 #aeah ,may #bd #aa #ai #i #aa #aeah ,june #g #ag #ef #aa #j #aeai ,may #bh #a -- 99 #aeai ,oct4 #bc #d #cc #f #j #aeai ,nov4 #f #f #bd ,total #aebj ,may #b #g -- 99 #aebj ,oct4 #aa #e #bb #c #aebj ,oct4 #be #ai -- 99 #aebj ,mar4 #ba #ag -- 99 #aeba ,april #f #ai -- 99 #aeba ,sept4 #cj #c -- 99 #aebb ,sept4 #e #ab #ag ,total #aebc ,mar4 #a #h #bf ,total #aebc ,aug4 #be #ae #bd ,total #aebd ,feb4 #d #a -- 99 #aebd ,aug4 #af #af -- 99 #aebe ,jan4 #bc #d -- 99 #aebe ,july #d #aj #aj ,total #aebe ,dec4 #bi #aj #df ,total #aebf ,dec4 #ah #aj #cj ,total #aebg ,jan4 #b #c -- 99 #aebg ,dec4 #g #aj -- 99 #aebh ,may #ag #bj -- 99 #aebi ,oct4 #af #bj #bc #aa #ee #aecj ,mar4 #bh #ah #bc #h #bd #aecj ,oct4 #f #ab #aa ,total #aeca ,april #a #g -- 99 #aecb ,aug4 #cj #j #di #c #ce #aecc ,aug4 #d #aa #ej ,total #aecc ,aug4 #ai #ag -- 99 #aecd ,jan4 #ad #a #db #e #de #aecd ,jan4 #bi #ad #be ,total #aece ,june #cj ,noon 99 #aece ,july #ad #h -- 99 #aece ,dec4 #bd #b -- 99 #aecf ,june #ah #b #b #h #j #aecf ,nov4 #bg #f #ba #aj #ae #aecg ,may #bd #h #c ,total #aecg ,june #g #g -- 99 #aecg ,nov4 #af #ad #ef ,total #aech ,may #ac #ad #bd #c #j #aech ,nov4 #f #e #ca #c #cg #aeci ,apr4 #ah #d #cc #i #j #aedj ,april #f #ag #ae ,total #aeda ,mar4 #aa #af #cd ,total #aeda ,aug4 #ba #j #ef #c #j #aedb ,mar4 #a #h #df #a #ch #aedb ,aug4 #aj #ag -- 99 #aedc ,july #ae #af -- 99 #aedd ,jan4 #i #ah #ac ,total #aedd ,jan4 #bc #ba #af #aa #ag #aedd ,july #d #h #ca ,total #aedd ,dec4 #bh #ah #bg ,total #aede ,june #h #bj #dh #c #de #aede ,dec4 #ag #ah -- 99 #aedf ,may #cj #e -- 99 #aedf ,nov4 #bb #bc -- 99 #aedg ,may #d #aj #bg #h #j #aedg ,oct4 #bh #d #ef #aa #cd #aedg ,nov4 #ab #b #i #i #cj #aedh ,april #h #c -- 99 #aedh ,apr4 #bb #aa #bd ,total #aedi ,apr4 #aa #ae #ai #b #j #aedi ,oct4 #f #f -- 99 #aeej ,mar4 #af #bj -- 99 #aeea ,feb4 #bj #h #ba ,total #aeea ,aug4 #ca #b #j #a #eb #aeec ,jan4 #ab #bb #ed #a #bb #aeec ,july #aj #g -- 99 #aeec ,july #bd #af #j #j #ca #aeed ,june #bi #f -- 99 #aeed ,dec4 #h #ac #g #aj #ab #aeee ,june #d #ae #j ,total #aeee ,nov4 #ac #ai -- 99 #aeef ,nov4 #a #ah #j #i #da #aeef ,nov4 #af #ab #dd #f #ee #aeeg ,oct4 #bj #bj -- 99 #aeeh ,april #b #aa #j #i #ej #aeeh ,apr4 #ah #a -- 99 #aeei ,apr4 #af #d #ej ,total #aefj ,mar4 #aa #ae #dj #d #ac #aefj ,aug4 #ba #a #j #f #bb #aefj ,sept4 #d #g -- 99 #aefa ,feb4 #ac #ai -- 99 #aefb ,feb4 #c #e -- 99 #aefb ,july #ae #ae #ej ,total #aefc ,jan4 #bb #ai -- 99 #aefc ,june #bj #d #ej #h #ch #aefc ,july #e #h #d #aa #cd #aefe ,mar4 #g #ab #ec ------ #aefe ,may #ad #af -- 99 #aefe ,nov4 #g #ab #df #aa #df #aeff ,oct4 #bh #e #ch ,total #aefg ,april #h #bc #d #i #cd #aefg ,oct4 #ag #ac #dc #b #dj #aefh ,mar4 #bh #e -- 99 #aefi ,mar4 #b #ae #ah ,total #aegj ,feb4 #bj #e #df ,total #aegj ,aug4 #ae #i #ag ,total #aega ,jan4 #be #d -- 99 #aegb ,jan4 #ad #ai -- 99 #aegb ,june #be #i #j #e #bf #aegc ,june #bh #ah -- 99 #aegc ,nov4 #bd #d -- 99 #aegc ,dec4 #h #f #ea ,total #aegd ,nov4 #ac #c #ej #e #ba #aege ,may #ai #h -- 99 #aege ,nov4 #b #e -- 99 #aegf ,oct4 #g #i #de ------ #aegg ,april #b #h #cc ,total #aegg ,sept4 #bf #ac #d ,total #aegh ,sept4 #ae #ac #d #b #bj #aegi ,feb4 #ae #e #da #h #cf #aegi ,aug4 #bj #ai #j 99 #aehj ,jan4 #ca #aj #g ,total #aeha ,jan4 #ai #i #bb ,total #aeha ,july #ae #ag #ea ,total #aehb ,jan4 #h #aj #bi #j #ec #aehb ,june #ai #ag #e #g #e #aehc ,nov4 #bh #ba #ea ,total #aehd ,may #i #ah #bj #c #cf #aehd ,nov4 #ag #ad #ae ,total #aehe ,apr4 #bi #g #ec #aa #g #aehe ,may #ac #e #b #f #ed #aehf ,sept4 #bg #h -- 99 #aehf ,oct4 #ab ,noon 99 #aehg ,sept4 #af #i #bh #aj #b #aehh ,feb4 #bf #a #bc #a #c #aehh ,mar4 #ab #ad #ad ,total #aehh ,sept4 #d #ag #cj ,total #aehi ,aug4 #aj #ah -- 99 #aehi ,aug4 #be #h #a #c #ed #aeij ,feb4 #d #e -- 99 #aeij ,july #af #ag #d #c #ed #aeij ,july #cj #ai #eg #aj #bg #aeia ,jan4 #i #f #ba #i #dj #aeia ,july #f #e #h ,total #aeia ,july #bj #d #b #a #j #aeia ,dec4 #bi #af #aa ,total #aeib ,june #bd #aj #ac #h #eh #aeib ,dec4 #ah #g #bd #e #ed #aeic ,may #cj #b #cj #b #ch #aeid ,may #ai #ad #eh #aj #bc #aeid ,oct4 #bh #ai #ae #i #dj #aeie ,april #i ,ter4 de ,fuego #aeie ,apr4 #bd #d #ab ,total #aeie ,may #g #bb -- 99 #aeie ,oct4 #c #b #d #e #ah #aeie ,oct4 #ah #bj #dg ,total #aeif ,mar4 #bh ,in ,chili #aeif ,apr4 #ab #h #eb #f #d #aeif ,sept4 #ba ,in ,china #aeif ,oct4 #f #ba #ae #c #cc #aeig ,mar4 #ag ,st4 ,pet4 ,isle #aeig ,sept4 #aa ,picora #i #di #aeih ,feb4 #bj #ah #ab #aj #ee #aeih ,mar4 #f #bb #ab #aa #eg #aeih ,aug4 #af #h #ae ,total #aeih ,aug4 #ca ,magel4 #h #cd #aeii ,feb4 #aj #ag #ba ,total #aeii ,july #bb #d #ca #d #ah #aeii ,aug4 #f ------ ,total #afjj ,jan4 #ae ,java #aa #dh #afjj ,jan4 #cj #f #dj #b #eh #afjj ,july #aj #b #aj #e #ci #afja ,jan4 #d ,ethiop4 #i #dj #afja ,june #ae #f #ah #d #eb #afja ,june #bi ,china #d #bi #afja ,dec4 #i #g #f #aj #ec #afja ,dec4 #bd #b #df #i #eb #afjb ,may #ba ,greenl4 #b #da #afjb ,june #d #g #ah ,total #afjb ,june #ai ,n4 ,gra4 #e #dc #afjb ,nov4 #ac ,magel4 #c -- #afjb ,nov4 #bh #aj #b ,total #afjc ,may #aj ,china #aa #ba #afjc ,may #bd #aa #da #g #ei #afjc ,nov4 #c ,rom4 ,i4 #aa #ag #afjc ,nov4 #ah #g #ca #c #bf #afjd ,apr4 #bi ,arabia #i #cb #afjd ,oct4 #bb ,peru #f #di #afje ,april #c #i #ai #aa #di #afje ,apr4 #ah ,madag4 #e #ca #afje ,sept4 #bg #d #bg #i #bf #afje ,oct4 #ab #b #cb #i #bd #afjf ,mar4 #h ,mexico #f #j #afjf ,mar4 #bd #aa #ag ,total #afjf ,sept4 #b ,magel4 #f #dj #afjf ,sept4 #af #ae #f ,total #afjg ,feb4 #be #ba #dh #a #ac #afjg ,mar4 #ac #f #cf #a #bb #afjg ,sept4 #e #ae #dj #d #g #afjh ,feb4 #ae at the ,antipo4 #afjh ,july #bg #j #cj #a #ec #afjh ,aug4 #i #d #ci #j #dj #afji ,jan4 #ai #ae #ba #aj #cb #afji ,feb4 #d ,fuego #e #bb #afji ,july #af #ab #h ,total #afji ,july #cj ,canada #d #aj #afji ,dec4 #bf #ai -- #e #ej #afaj ,jan4 #i #a #ca ,total #afaj ,june #bj ,java #aj #df #afaj ,july #e #af #eh #aa #ac #afaj ,dec4 #ae ,cyprus #d #ej #afaj ,dec4 #bi #af #dg #d #bc #afaa ,june #aj ,califor4 #aa #cj #afab ,may #ad #aj #ch #g #bb #afab ,may #bi #bc #ch #g #ad #afab ,nov4 #h #c #bb #i #di #afab ,nov4 #bb ,magel4 #i #j #afac ,apr4 #bj ,magel lanica #afac ,may #d #j #ce ,total #afac ,may #ai ,east ,tartary #afac ,oct4 #ac ,south ,amer4 #afac ,oct4 #bh #d #ai ,total #afad ,april #h ,n4 ,gui4 #h #dd #afad ,apr4 #bc #ag #cf #e #be #afad ,oct4 #c #j #eg #e #b #afad ,oct4 #ag #d #ch #d #ef #afae ,mar4 #bi ,goa #aj #ch #afae ,sept4 #bb ,salom ,isle #afaf ,mar4 #c #a #eh ,total #afaf ,mar4 #ag ,mexico #f #dg #afaf ,aug4 #bf #ae #cc ,total #afaf ,sept4 #aj ,magel4 #aj #cc #afag ,feb4 #e ,magel lanica #afag ,feb4 #bj #a #di ,total #afag ,mar #f #bb -- 99 #afag ,aug4 #a ,biarmia #afag ,aug4 #af #h #bb ,total #afah ,jan4 #bf ,magel lanica #afah ,feb4 #i #c #bi #b #eg #afah ,july #ba ,mexico ------ #afai ,jan4 #ae ,califor nia #afai ,june #bf #ab #dj #c #aj #afai ,july #aa ,africa #aa #ci #afai ,dec4 #bj #ae #ec #aj #dg #afbj ,may #ca ,arctic ,circle #afbj ,june #ad #ac #dg ,total #afbj ,june #bi ,magel4 #g #bj #afbj ,dec4 #i #f #ci ,total #afbj ,dec4 #bc ,magel lanica #afba ,may #bj #ad #ed #aj #dd #afba ,june #c #ai #db #i #ec #afba ,nov4 #ac ,magel lanica #afba ,nov4 #bh #ae #dc #c #ch #afbb ,may #aj ,c4 ,verd #aa #eb #afbb ,nov4 #b ,malac ca ,in4 #afbc ,apr4 #ad #g #ai #aj #ed #afbc ,apr4 #bi ------ ------ #afbc ,oct4 #h #j #bb #h #ce #afbc ,oct4 #bc ,califor4 #aj #df #afbd ,may #ah ,n4 ,zem4 #f #j #afbd ,apr4 #c #g #i ,total #afbd ,apr4 #ag ,antar4 ,circle #afbd ,sept4 #ab ,magel lanica #afbd ,sept4 #bf #h #ee ,total #afbe ,mar4 #h ,florida #afbe ,mar4 #bc #ad #aa #b #aa #afbe ,sept4 #a ,st4 ,pete r's ,isl4 #afbe ,sept4 #af #aa #da #e #f #afbf ,feb4 #be ,madag4 #h #bg #afbf ,aug4 #g #g #dh #j #be #afbf ,aug4 #ba ,in ,mexico #afbg ,jan4 #cj #aa #ch #aj #ba #afbg ,feb4 #ae ,magel lanica #afbg ,july #bg #i #d ,total #afbg ,aug4 #aa ,tenduc #aj #j #afbh ,jan4 #f ,tenduc #e #dj #afbh ,jan4 #bj #aj #aa ,total #afbh ,july #a ,c ,good ,hope #afbh ,july #af #aa #bf ,total #afbh ,dec4 #be ,in ,england #afbi ,jan4 #i #a #cf #d #bg #afbi ,june #ba ,ganges #aa #be #afbi ,dec4 #ad ,peru #aj #ad #afcj ,may #be #ag #ef #f #j #afcj ,june #aj #g #dg #i #h #afcj ,nov4 #ai #aa #bd #i #bg #afcj ,dec4 #c ,n4 ,gui4 #aj #aj #afca ,apr4 #cj ,antar4 ,circle #afca ,may #ae #h #ae ,total #afca ,oct4 #bd ,c ,good ,hope #afca ,nov4 #h #ab #j ,total #afcb ,apr4 #ai ,c ,good ,hope #afcb ,may #d #a #bd #f #ce #afcb ,oct4 #ac ,mexico #h #cg #afcb ,oct4 #bg #ab #bc #e #ca #afcc ,april #h #e #ad #d #cj #afcc ,oct4 #c ,maldiv4 ,total #afcd ,mar4 #ad #i #ce #aa #ah #afcd ,mar4 #bh ,japan #aj #ai #afcd ,sept4 #g #e #j ,total #afcd ,sept4 #bb ,c4,g4,h4 #i #ed #afce ,feb4 #ag ,antar4 ,circle #afce ,mar4 #c #i #bf ,total #afce ,mar4 #ah ,mexico #j #af #afce ,aug4 #ab ,iceland #e #j #afce ,aug4 #bg #af #d ,total #afcf ,feb4 #f ,in ,peru #afcf ,feb4 #bj #aa #cd #c #bc #afcf ,aug4 #a ,tartary #aa #bj #afcf ,aug4 #af #d #cd #a #be #afcg ,jan4 #bf ,camboya #afcg ,july #ba ,jucutan #afcg ,dec4 #ca #j #dd #aj #de #afch ,jan4 #ad ,persia #i #de #afch ,june #be #bj #ag ,total #afch ,july #aa ,magellan #i #e #afch ,dec4 #e ,magellan #b #aj #afch ,dec4 #bj #ae #af ,total #afci ,jan4 #d ,tartary #j #cj #afci ,june #a #e #ei #aj #dj #afci ,june #ae #b #da #aa #i #afci ,nov4 #bd ,magel4 #aa #j #afci ,dec4 #i #aa #eg #c #df #afdj ,may #bj ,n4 ,spa4 #aj #cj #afdj ,nov4 #ac ,peru #aj #cf #afda ,apr4 #be #a #b #i #di #afda ,may #i ,peru #aj #af #afda ,oct4 #ah #h #ai #f #ca #afda ,nov4 #b #ah #df ------ #afdb ,mar4 #cj ,estotl4 #d #j #afdb ,apr4 #ad #ad #ca ,total #afdb ,sept4 #be ,magel lan #afdb ,oct4 #g #af #de ,total #afdc ,mar4 #ai #ac #ec ------ #afdc ,april #c #ba #aj #c #i #afdc ,sept4 #ab #ag #j ------ #afdc ,sept4 #bg #g #ch #f #j #afdd ,mar4 #h #f #bj ------ #afdd ,aug4 #ca #ah #aj ------ #afde ,feb4 #aj #g #de #h #eb #afde ,feb4 #bf ,rom4 ,i4 #aj #df #afde ,aug4 #g #b #d ,total #afde ,aug4 #ba #j #ce #d #dj #afdf ,jan4 #af ,str4 of ,anian4 #afdf ,jan4 #cj #ah #aa ,total #afdf ,july #ab #f #eg ------ #afdf ,july #bg #f #b ,total #afdg ,jan4 #e #ab #aj ------ #afdg ,jan4 #bj #i #dc #d #dg #afdg ,july #b #j #i ------ #afdg ,dec4 #be #ac #ch ------ #afdh ,june #e #j #ee #d #bh #afdh ,june #bj #ac #bh ------ #afdh ,nov4 #bi #ai #ag #g #dj #afdh ,dec4 #ac #ba #dh ------ #afdi ,may #be #ae #bj ,total #afdi ,june #i ,arct4 ,c4 #d #j #afdi ,nov4 #d #b #aj #e #ai #afdi ,nov4 #ah #ai #ef ,total #afej ,apr4 #cj #e #ed ------ #afej ,may #ae #h #cg #g #eg #afej ,oct4 #bd #ag #ag ------ #afej ,nov4 #g #bj #bi #e #c #afea ,apr4 #ai ,tuber4 ------ #afea ,oct4 #ad #b #ae ------ #afeb ,mar4 #bd #af #eb #h #ej #afeb ,april #g #bb #dj #i #ei #afeb ,sept4 #ag #g #bg #i #di #afeb ,oct4 #b #e #b ------ #afec ,feb4 #bg -- -- ------ #afec ,mar4 #ac #ag #i ,total #afec ,aug4 #bb -- -- ------ #afec ,sept4 #f #bc #de ,total #afed ,feb4 #af #i #aj ------ #afed ,mar4 #b #ai #be #c #ad #afed ,aug4 #aa #bb #bd #b #bh #afed ,aug4 #bg #aa #di #a #ec #afee ,feb4 #f #b #cg #d #bj #afee ,aug4 #a #ad #ai ------ #afee ,aug4 #af #af -- 99 #afef ,jan4 #aa #i #d #aj #j #afef ,july #f #c #ag ,total #afef ,july #ba #aa #dh ------ #afef ,dec4 #cj #bc #cj ,total #afeg ,june #aa #aa #bj ------ #afeg ,june #be #i #ce ,total #afeg ,dec4 #d #bj #j ------ #afeg ,dec4 #bj #g #dg #c #i #afeh ,may #ca #af #j ------ #afeh ,june #ad #bb #eh ------ #afeh ,nov4 #i #ac #ef #j #aj #afeh ,nov4 #bd #aa #cf ------ #afei ,may #f #h #cd #h #e #afei ,may #bj #ag #d ------ #afei ,oct4 #bi #af #af #e #eb #afei ,nov4 #ad #d #be #i #ea #affj ,apr4 #bd #ba #eh ,total #affj ,oct4 #c #bb #cd ------ #affj ,oct4 #ah #j #cb ,total #affj ,nov4 #b #ac #dh ------ #affa ,mar4 #bi #bb #cb ------ #affa ,apr4 #ad #d #bh ------ #affa ,sept4 #bc #a #cf #aa #ai #affa ,oct4 #g #ad #ea #g #d #affb ,mar4 #ai #ae #h ------ #affb ,apr4 #ab #a #h ------ #affc ,feb4 #ba #af #aa #c #ad #affc ,mar4 #i #e #dg ------ #affc ,aug4 #ah #h #de ,total #affc ,sept4 #a #h #h ------ #affd ,jan4 #bg #bj #dj ------ #affd ,feb4 #aa #c #af ------ #affd ,july #bb #ad #dh ------ #affd ,aug4 #bj #bb #aj ------ #affe ,jan4 #cj #ah #dg #d #cd #affe ,july #ab #g #dh ------ #affe ,july #bf #ac #ca #j #aj #afff ,jan4 #d #ba #cc ------ #afff ,july #a #ai #j #aa #aj #affg ,june #e ,noon ------ #affg ,july #ba #b #cb ------ #affg ,nov4 #ae #aa #cj ------ #affh ,may #aj ,setting ------ #affh ,may #be #af #bf #i #cb #affh ,nov4 #d #b #ec #i #ej #affh ,nov4 #ah #c #ed #f #de #affi ,apr4 #bi #ah #ah ------ #affi ,oct4 #bd #aj #ac ------ #afgj ,apr4 #ai #g #j ------ #afgj ,sept4 #aj #ai #j ------ #afgj ,sept4 #bh #ae #dc #i #g #afgj ,oct4 #ac #ab #e ------ #afga ,april #h #bc #bi ------ #afga ,sept4 #b #ba #be ------ #afga ,sept4 #ah #g #dd ,total #afgb ,feb4 #bh #c #ch ------ #afgb ,mar4 #ac #c #ag ------ #afgb ,aug4 #bb #f #dc ------ #afgb ,sept4 #f #ah #ed ------ #afgc ,feb4 #af #g #bi ------ #afgc ,aug4 #aa #ba #dd ------ #afgd ,jan4 #ba #ah #bb #aa #ba #afgd ,feb4 #e #i #d ------ #afgd ,july #ag #i #dj ,total #afge ,jan4 #aa #h #bi ,total #afge ,jan4 #be #aj #cf ------ #afge ,july #f #af #ca ,total #afgf ,june #aj #ba #bf #d #cd #afgf ,june #be #f #bf ------ #afgf ,dec4 #d #bj #eb ------ #afgg ,nov4 #bd #ab #e ------ #afgg ,may #af #af #be #h #ae #afgh ,may #f #e #cj ------ #afgh ,oct4 #bi #i #ag ,total #afgi ,apr4 #aj #ba #j ------ #afgi ,apr4 #be #aa #ec #e #dg #afhj ,mar4 #bi #bc #bb ------ #afhj ,sept4 #bb #g #eg ------ #afha ,mar4 #d ,noon ------ #afha ,mar4 #aj #ac #dc ------ #afha ,aug4 #bh #ae #bb #aj #ce #afha ,sept4 #aa #ae #dc ------ #afhb ,feb4 #ba #ab #bh ,total #afhb ,aug4 #ag #ah #ef ,total #afhc ,jan4 #bg #a #ce #aj #cj #afhc ,feb4 #i #c #ci ------ #afhc ,aug4 #f #bj #cf ------ #afhd ,jan4 #af #f #cd ------ #afhd ,june #bf #ae #ah #a #ce #afhd ,july #ab #c #bf ,total #afhd ,dec4 #ba #aa #ah #i #de #afhe ,jan4 #d #af #j ------ #afhe ,june #af #f #j ------ #afhe ,dec4 #aj #aa #bf ,total #afhf ,may #ba #ag #i ------ #afhf ,june #f ,noon ------ #afhf ,nov4 #bi #ab #bb ,total #afhg ,may #aa #a -- 99 #afhg ,may #bf #ad -- 99 #afhg ,apr4 #ae #g #d #f #di #afhh ,apr4 #bi #af #bg ------ #afhh ,oct4 #i ,noon ------ #afhh ,oct4 #be #ai #dj ------ #afhi ,april #d #g #db ,total #afhi ,sept4 #bh #ae #df ,total #afij ,mar4 #aj -- -- ------ #afij ,mar4 #bd #aa #ad #e #dc #afij ,sept4 #c -- -- ------ #afij ,sept4 #ah #b #db ------ #afia ,feb4 #bg #ag #cj ------ #afia ,aug4 #bc #e #ea ------ #afib ,feb4 #b #c #bj ------ #afib ,feb4 #af #ag #ca ------ #afib ,july #bg #af #i ,total #afic ,jan4 #ba #ag #be ,total #afic ,july #ag ,noon ------ #afid ,jan4 #aa ,noon ------ #afid ,june #bb #d #bb #f #bb #afid ,july #f #ac #ea #j #dg #afie ,may #aa #f #c ------ #afie ,may #bh ,noon ------ #afie ,nov4 #bj #h #j #f #ee #afie ,dec4 #e #ag #g ------ #afif ,may #af #ab #de ,total #afif ,may #cj #ab #ef ------ #afif ,nov4 #h #ag #cj ,total #afif ,nov4 #bc #ag #cb ------ #afig ,apr4 #bj #ad #cb ------ #afig ,may #e #ah #bg ------ #afig ,oct4 #bi #h #dd #h #ed #afih ,apr4 #aj #i #ac ------ #afih ,oct4 #c #ae #bi ------ #afii ,mar4 #ae #h #ad #i #g #afii ,mar4 #cj #bb #j ------ #afii ,sept4 #h #bc #bb ------ #afii ,sept4 #bc #bb #ch #i #eh #agjj ,mar4 #d #bj #aa ------ #agjj ,aug4 #bi #a #db ------ ---------------------------------------- - ,the ,eclipses from ,,struyk were observed3 those from ,,ricciolus calculated3 the following from ,l',art de verifier les ,dates1 are only those which are visible in ,europe for the present century3 those which are total are marked with a ,t2 and ,m signifies ,morning1 ,a ,afternoon4 ,visible ,,eclipses from #agjj to #ahjj4 --------------------------------- ,aft4 ,months ,time of ,chr4 and the ,day ,days4 or ,night4 --------------------------------- #agja ,feb4 #bb #aa ,a4 #agjc ,jan4 #c #g ,m4 #agjc ,june #bi #a ,m4 ,t4 #agjc ,dec4 #bc #g ,m4 ,t4 #agjd ,dec4 #aa #g ,m4 #agjf ,apr4 #bh #b ,m4 #agjf ,may #ab #aj ,m4 #agjf ,oct4 #ba #g ,a4 #agjg ,apr4 #ag #b ,m4 ,t4 #agjh ,april #e #f ,m4 #agjh ,dec4 #ad #h ,m4 #agjh ,sept4 #bi #i ,a4 #agji ,mar4 #aa #b ,a4 #agaj ,feb4 #ac #aa ,a4 #agaj ,feb4 #bh #a ,a4 #agaa ,july #ae #h ,a4 #agaa ,july #bi #f ,a4 ,t4 #agab ,jan4 #bc #h ,a4 #agac ,june #h #f ,a4 #agac ,dec4 #b #d ,m4 #agae ,may #c #i ,m4 ,t4 #agae ,nov4 #aa #e ,m4 #agag ,mar4 #bg #c ,m4 #agag ,may #bj #f ,a4 #agah ,sept4 #i #h ,a4 ,t4 #agai ,aug4 #bi #i ,a4 #agba ,jan4 #ac #c ,a4 #agbb ,june #bi #c ,m4 #agbb ,dec4 #h #c ,a4 #agbb ,dec4 #bb #d ,a4 #agbd ,may #bb #g ,a4 ,t4 #agbd ,nov4 #a #d ,m4 #agbe ,oct4 #ba #g ,a4 #agbf ,sept4 #be #f ,a4 #agbf ,oct4 #aa #e ,m4 #agbg ,sept4 #ae #g ,m4 #agbi ,feb4 #ac #i ,a4 ,t4 #agbi ,aug4 #i #a ,m4 #agcj ,feb4 #d #d ,m4 #agca ,june #bj #b ,m4 #agcb ,dec4 #a #aj ,a4 ,t4 #agcc ,may #ac #g ,a4 #agcc ,may #bh #g ,a4 #agce ,oct4 #b #a ,m4 #agcf ,mar4 #bf #ab ,a4 ,t4 #agcf ,sept4 #bj #c ,m4 ,t4 #agcf ,oct4 #d #f ,a4 #agcg ,mar4 #a #d ,a4 #agcg ,sept4 #i #d ,m4 #agch ,aug4 #ae #aa ,m4 #agci ,jan4 #bd #aa ,a4 #agci ,aug4 #d #e ,a4 #agci ,dec4 #cj #i ,m4 #agdj ,jan4 #ac #aa ,a4 ,t4 #agda ,jan4 #a #ab ,a4 #agdc ,nov4 #b #c ,m4 ,t4 #agdd ,aug4 #bf #i ,a4 #agdf ,aug4 #cj #ab ,a4 #agdg ,feb4 #ad #e ,m4 ,t4 #agdh ,july #be #aa ,m4 #agdh ,aug4 #h #ab ,a4 #agdi ,dec4 #bc #h ,a4 #agej ,jan4 #h #i ,m4 #agej ,june #ai #i ,a4 ,t4 #agej ,dec4 #ac #g ,m4 #agea ,june #i #b ,m4 #agea ,dec4 #b #aj ,a4 #ageb ,may #ac #h ,a4 #agec ,apr4 #ag #g ,a4 #agec ,oct4 #bf #aj ,m4 #agee ,mar4 #bh #a ,m4 #ageg ,feb4 #d #f ,m4 #ageg ,july #cj #ab ,a4 #ageh ,jan4 #bd #g ,m4 ,t4 #ageh ,dec4 #cj #g ,m4 #agei ,june #bd #g ,a4 #agei ,dec4 #ai #b ,a4 #agfj ,may #bi #i ,a4 #agfj ,june #ac #g ,m4 #agfj ,nov4 #bb #i ,a4 #agfa ,may #ah #aa ,a4 ,t4 #agfb ,may #h #d ,m4 #agfb ,oct4 #ag #h ,m4 #agfb ,nov4 #a #h ,a4 #agfc ,apr4 #ac #h ,m4 #agfd ,apr4 #a #aj ,m4 #agfd ,apr4 #af #a ,m4 #agfe ,mar4 #ba #b ,a4 #agfe ,aug4 #af #e ,a4 #agff ,feb4 #bd #g ,a4 #agff ,aug4 #e #g ,a4 #agfh ,jan4 #d #e ,m4 #agfh ,june #cj #d ,m4 ,t4 #agfh ,dec4 #bc #d ,a4 ,t4 #agfi ,june #d #h ,m4 #agfi ,dec4 #ac #g ,m4 #aggj ,nov4 #ag #aj ,m4 #agga ,apr4 #bh #b ,m4 #agga ,oct4 #bc #e ,a4 #aggb ,oct4 #aa #f ,a4 ,t4 #aggb ,oct4 #bf #aj ,m4 #aggc ,mar4 #bc #e ,m4 #aggc ,sept4 #cj #g ,a4 #aggd ,mar4 #ab #aj ,m4 #aggf ,july #ca #a ,m4 ,t4 #aggf ,aug4 #ad #e ,m4 #aggg ,jan4 #i #e ,a4 #aggh ,june #bd #d ,a4 #aggh ,dec4 #d #f ,m4 #aggi ,may #cj #e ,m4 ,t4 #aggi ,june #ad #h ,m4 #aggi ,nov4 #bc #h ,a4 #aghj ,oct4 #bg #f ,a4 #aghj ,nov4 #ab #d ,m4 #agha ,apr4 #bc #f ,a4 #agha ,oct4 #ag #h ,m4 #aghb ,apr4 #ab #g ,a4 #aghc ,mar4 #ah #i ,a4 ,t4 #aghc ,sept4 #aj #aa ,a4 ,t4 #aghd ,mar4 #g #c ,m4 #aghe ,feb4 #i #a ,a4 #aghg ,jan4 #c #ab ,a4 ,t4 #aghg ,jan4 #ai #aj ,m4 #aghg ,june #ae #e ,a4 #aghg ,dec4 #bd #c ,a4 #aghh ,june #d #i ,m4 #aghi ,nov4 #b #ab ,a4 #agij ,apr4 #bh #ab ,a4 ,t4 #agij ,oct4 #bc #a ,m4 ,t4 #agia ,april #c #a ,a4 #agia ,oct4 #ab #c ,m4 #agib ,sept4 #af #aa ,m4 #agic ,feb4 #be #aj ,a4 #agic ,sept4 #e #c ,a4 #agid ,jan4 #ca #d ,a4 #agid ,feb4 #ad #aa ,a4 ,t4 #agid ,aug4 #be #e ,a4 #agie ,feb4 #d #a ,m4 #agie ,july #af #i ,m4 #agie ,july #ca #h ,a4 #agig ,june #be #h ,a4 #agig ,dec4 #d #f ,m4 #agih ,may #bg #g ,a4 ,t4 #ahjj ,oct4 #b #aa ,a4 --------------------------------- #cbh4 ,a ,list of ,eclipses1 and historical ,events1 which happened about the same ,times1 from ,,ricciolus4 ,sidenote3 ,historical ,eclipses4 ,before ,,christ4 #ged ,july #e ,but according to an old ,calendar this ,eclipse of the ,sun was on the #bast of ,april1 on which day the ,foundations of ,rome were laid if we may believe ,taruntius ,firmanus4 #gba ,march #ai ,a total ,eclipse of the ,moon4 ,the ,assyrian ,empire at an end2 the ,babylonian established4 #ehe ,may #bh ,an ,eclipse of the ,sun foretold by ,,thales1 by which a peace was brought about between the ,medes and ,lydians4 #ebc ,july #af ,an ,eclipse of the ,moon1 which was followed by the death of ,,cambyses4 #ejb ,nov4 #ai ,an ,eclipse of the ,moon1 which was followed by the slaughter of the ,sabines1 and death of ,valerius ,publicola4 #dfc ,april #cj ,an ,eclipse of the ,sun4 ,the ,persian war1 and the falling off of the ,persians from the ,egyptians4 #dca ,april #be ,an ,eclipse of the ,moon1 which was followed by a great famine at ,rome2 and the beginning of the ,peloponnesian war4 #dca ,august #c ,a total ,eclipse of the ,sun4 ,a ,comet and ,plague at ,athens#gd4 #dac ,aug4 #bg ,a total ,eclipse of the ,moon4 ,nicias with his ship destroyed at ,syracuse4 #cid ,aug4 #ad ,an ,eclipse of the ,sun4 ,the ,persians beat by ,conon in a sea engagement4 #afh ,june #ba ,a total ,eclipse of the ,moon4 ,the next day ,perseus ,king of ,macedonia was conquered by ,paulus ,emilius4 ,after ,,christ4 #ei ,april #cj ,an ,eclipse of the ,sun4 ,this is reckoned among the prodigies1 on account of the murther of ,agrippinus by ,nero4 #bcg ,april #ab ,a total ,eclipse of the ,sun4 ,a sign that the reign of the ,gordiani would not continue long4 ,a sixth persecution of the ,christians4 #cjf ,july #bg ,an ,eclipse of the ,sun4 ,the ,stars were seen1 and the ,emperor ,constantius died4 #hdj ,may #d ,a dreadful ,eclipse of the ,sun4 ,and ,lewis the ,pious died within six months after it4 #ajji ---- ,an ,eclipse of the ,sun4 ,and ,jerusalem taken by the ,saracens4 #aacc ,aug4 #b ,a terrible ,eclipse of the ,sun4 ,the ,stars were seen4 ,a schism in the church1 occasioned by there being three ,popes at once4 ,illustration3 ,plate ,,xi4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 ,sidenote3 ,the superstitious notions of the antients with regard to ,eclipses4 ,,plate ,,xi4 #cbi4 ,i have not cited one half of ,,ricciolus's list of potentous ,eclipses2 and for the same reason that he declines giving any more of them than what that list contains3 namely1 that 'tis most disagreeable to dwell any longer on such nonsense1 and as much as possible to avoid tiring the reader3 the superstition of the antients may be seen by the few here copied4 ,my author farther says1 that there were treatises written to shew against what regions the malevolent effects of any particular ,eclipse was aimed3 and the writers affirmed1 that the effects of an ,eclipse of the ,sun continued as many years as the ,eclipse lasted hours2 and that of the ,moon as many months4 ,sidenote3 ,very fortunate once for ,,christopher ,,columbus4 #ccj4 ,yet such idle notions were once of no small advantage to ,,christopher ,,columbus2 who1 in the year #adic1 was driven on the island of ,jamaica1 where he was in the greatest distress for want of provisions1 and was moreover refused any assistance from the inhabitants2 on which he threatened them with a plague1 and that in token of it there should be an ,eclipse3 which accordingly fell on the day he had foretold1 and so terrified the ,barbarians1 that they strove who should be first in bringing him all sorts of provisions2 throwing them at his feet1 and imploring his forgiveness4 ,,ricciolus's ,almagest1 ,vol4 ,i4 #a4 v4 c4 ii4 ,sidenote3 ,why there are more visible ,eclipses of the ,moon than of the ,sun4 #cca4 ,eclipses of the ,sun are more frequent than of the ,moon1 because the ,sun's ecliptic limits are greater than the ,moon's #cag3 yet we have more visible ,eclipses of the ,moon than of the ,sun1 because ,eclipses of the ,moon are seen from all parts of that ,hemisphere of the ,earth which is next her1 and equally great to each of these parts2 but the ,sun's ,eclipses are visible only to that small portion of the ,hemisphere next him whereon the ,moon's shadow falls2 as shall be explained by and by at large4 ,sidenote3 ,fig4 ,i4 ,total and annular ,eclipses of the ,sun4 ,,plate ,,xi4 #ccb4 ,the ,moon's ,orbit being elliptical1 and the ,earth in one of its focuses1 she is once at her least distance from the ,earth1 and once at her greatest in every ,lunation4 ,when the ,moon changes at her least distance from the ,earth1 and so near the ,node that her dark shadow falls on the ,earth1 she appears big enough to cover the whole #ge;,disc of the ,sun from that part on which her shadow falls2 and the ,sun appears totally eclipsed there1 as at ,a1 for some minutes3 ,but when the ,moon changes at her greatest distance from the ,earth1 and so near the ,node that her dark shadow is directed towards the ,earth1 her diameter subtends a less angle than the ,sun's2 and therefore she cannot hide his whole ,disc from any part of the ,earth1 nor does her shadow reach it at that time2 and to the place over which the point of her shadow hangs1 the ,eclipse is annular as at ,b2 the ,sun's edge appearing like a luminous ring all around the body of the ,moon4 ,when the ,change happens within #ag degrees of the ,node1 and the ,moon at her mean distance from the ,earth1 the point of her shadow just touches the ,earth1 and she eclipseth the ,sun totally to that small spot whereon her shadow falls2 but the darkness is not of a moment's continuance4 ,sidenote3 ,the longest duration of total ,eclipses of the ,sun4 #ccc4 ,the ,moon's apparent diameter when largest exceeds the ,sun's when least only #a minute #ch seconds of a degree3 ,and in the greatest ,eclipse of the ,sun that can happen at any time and place1 the total darkness continues no longer than whilst the ,moon is going #a minute #ch seconds from the ,sun in her ,orbit2 which is about #c minutes and #ac seconds of an hour4 ,sidenote3 ,to how much of the ,earth the ,sun may be totally or partially eclipsed at once4 #ccd4 ,the ,moon's dark shadow covers only a spot on the ,earth's surface1 about #ahj ,english miles broad1 when the ,moon's diameter appears largest and the ,sun's least2 and the total darkness can extend no farther than the dark shadow covers4 ,yet the ,moon's partial ,shadow or ,penumbra may then cover a circular space #dijj miles in diameter1 within all which the ,sun is more or less eclipsed as the places are less or more distant from the ,center of the ,penumbra4 ,when the ,moon changes exactly in the ,node1 the ,penumbra is circular on the ,earth at the middle of the general ,eclipse2 because at that time it falls perpendicularly on the ,earth's surface3 ,but at every other moment it falls obliquely1 and will therefore be elliptical2 and the more so1 as the time is longer before or after the middle of the general ,eclipse2 and then1 much greater portions of the ,earth's surface are involved in the ,penumbra4 ,sidenote3 ,duration of general and particular ,eclipses4 ,the ,moon's dark shadow4 ,and ,penumbra4 #cce4 ,when the ,penumbra first touches the ,earth the general ,eclipse begins3 when it leaves the ,earth the general ,eclipse ends3 from the beginning to the end the ,sun appears eclipsed in some part of the ,earth or other4 ,when the ,penumbra touches any place the ,eclipse begins at that place1 and ends when the ,penumbra leaves it4 ,when the ,moon changes in the ,node1 the ,penumbra goes over the center of the ,earth's ,disc as seen from the ,moon2 and consequently1 by describing the longest line possible on the ,earth1 continues the longest upon it2 namely1 at a mean rate1 #e hours #ej minutes3 more1 if the ,moon be at her greatest distance from the ,earth1 because she then moves slowest2 less1 if she be at her least distance1 because of her quicker motion4 ,sidenote3 ,fig4 ,,ii4 #ccf4 ,to make the last five articles and several other ,phenomena plainer1 let ,s be the ,sun1 ,e the ,earth1 ,m the ,moon1 and ,,amp the ,moon's ,orbit4 ,draw the right line ,wc #ab from the western edge of the ,sun at ,w1 touching the western edge of the ,moon at c and the ,earth at #ab3 draw also the right line ,vd #ab from the eastern edge of the ,sun at ,v1 touching the eastern edge of the ,moon at d and the ,earth at #ab3 the dark space ce #ab d included between those lines is the ,moon's shadow1 ending in a point at #ab where it touches the ,earth2 because in this case the ,moon is supposed to change at ,m in the middle between ,a the ,apogee1 or farthest point of her ,orbit from the ,earth1 and ,p the ,perigee1 or nearest point to it4 ,for1 had the point ,p been at ,m1 the ,moon had been nearer the ,earth2 and her dark shadow at e would have covered a space upon it about #ahj miles broad1 and the ,sun would have been totally darkened as at ,a 7,fig ,i7 with some continuance3 but had the point ,a 7,fig4 ,,ii7 been at ,m1 the ,moon would have been farther from the ,earth1 and her shadow would have ended in a point about e1 and therefore the ,sun would have appeared as at ,b 7,fig4 ,i7 like a luminous ring all around the ,moon4 ,draw the right lines ,w,xdh and ,v,xcg1 touching the contrary sides of the ,sun and ,moon1 and ending on the ,earth at a and b3 draw also the right line ,,sxm #ab1 from the center of the ,sun's ,disc1 through the ,moon's center1 to the ,earth at #ab2 and suppose the two former lines ,w,xdh and ,v,xcg to revolve on the line ,,sxm #ab as an ,axis1 and their points a and b will describe the limits of the ,penumbra ,,tt on the ,earth's surface1 including the large space a#j;b#ab;a2 within which the ,sun appears more or less eclipsed as the places are more or less distant from the verge of the ,penumbra a#j;b4 ,sidenote3 ,digits1 what4 ,draw the right line y #ab across the ,sun's ,disc1 and parallel to the plane of the ,moon's ,orbit2 divide this line into twelve equal parts1 as in the ,figure1 for the twelve #gf;,digits of the ,sun's diameter3 and at equal distances from the center of the ,penumbra ,,tt to its edge on the ,earth1 or from #ab to #j1 draw twelve concentric ,circles1 as marked with the numeral ,figures #a #b #c #d c4 and remember that the ,moon's motion in her ,orbit ,,amp is from west to east1 as from s to t4 ,then1 ,sidenote3 ,the different phases of a solar ,eclipse4 ,,plate ,,xi4 ,fig4 ,,iii4 ,to an observer on the ,earth at b1 the eastern limb of the ,moon at d seems to touch the western limb of the ,sun at ,w1 when the ,moon is at ,m2 and the ,sun's ,eclipse begins at b2 appearing as at ,a in ,fig4 ,,iii at the left hand2 but at the same moment of absolute time to an observer at a in ,fig4 ,,ii the western edge of the ,moon at c leaves the eastern edge of the ,sun at ,v1 and the ,eclipse ends1 as at the right hand ,c of ,fig4 ,,iii4 ,at the very same instant1 to all those who live on the ,circle marked #a on the ,earth ,e in ,fig4 ,,ii1 the ,moon ,m cuts off or darkens a twelfth part of the ,sun ,s1 and eclipses him one ,digit1 as at #a in ,fig4 ,,iii3 to those who live on the ,circle marked #b in ,fig4 ,,ii the ,moon cuts off two twelfth parts of the ,sun1 as at #b in ,fig4 ,,iii3 to those on the ,circle #c1 three parts2 and so on to the center at #ab in ,fig4 ,,ii1 where the ,sun is centrally eclipsed as at ,b in the middle of ,fig4 ,,iii3 under which ,figure there is a scale of hours and minutes1 to shew at a mean state how long it is from the beginning to the end of a central ,eclipse of the ,sun on the parallel of ,london2 and how many ,digits are eclipsed at any particular time from the beginning at ,a to the middle at ,b1 or the end at ,c4 ,thus in #af minutes from the beginning1 the ,sun is two ,digits eclipsed2 in an hour and five minutes1 #h ,digits2 and in an hour and thirty-seven minutes1 #ab ,digits4 ,sidenote3 ,fig4 ,,ii4 ,the ,velocity of the ,moon's shadow on the ,earth4 ,fig4 ,,iv4 #ccg4 ,by ,fig4 ,,ii it is plain1 that the ,sun is totally or centrally eclipsed but to a small part of the ,earth at any time2 because the dark conical shadow e of the ,moon ,m falls but on a small part of the ,earth3 and that the partial ,eclipse is confined at that time to the space included by the ,circle a #j b1 of which only one half can be projected in the ,figure1 the other half being supposed to be hid by the convexity of the ,earth ,e3 and likewise1 that no part of the ,sun is eclipsed to the large space ,,yy of the ,earth1 because the ,moon is not between the ,sun and that part of the ,earth3 and therefore to all that part the ,eclipse is invisible4 ,the ,earth turns eastward on its ,axis1 as from g to h1 which is the same way that the ,moon's shadow moves2 but the ,moon's motion is much swifter in her ,orbit from s to t3 and therefore1 altho' ,eclipses of the ,sun are of longer duration on account of the ,earth's motion on its ,axis1 than they would be if that motion was stopt1 yet in #c minutes and #ac seconds of time1 the ,moon's swifter motion carries her dark shadow quite over any place that its center touches at the time of greatest obscuration4 ,the motion of the shadow on the ,earth's ,disc is equal to the ,moon's motion from the ,sun1 which is about #cj-a_/b minutes of a degree every hour at a mean rate2 but so much of the ,moon's ,orbit is equal to #cj-a_/b degrees of a great ,circle on the ,earth1 #cbj2 and therefore the ,moon's shadow goes #cj-a_/b degrees or #ahcj geographical miles on the ,earth in an hour1 or #cj-a_/b miles in a minute1 which is almost four times as swift as the motion of a cannon-ball4 ,sidenote3 ,,plate ,,xi4 ,fig4 ,,iv4 ,phenomena of the ,earth as seen from the ,sun or ,new ,moon at different times of the year4 #cch4 ,as seen from the ,sun or ,moon1 the ,earth's ,axis appears differently inclined every day of the year1 on account of keeping its parallelism throughout its annual course4 ,let ,e1 ,d1 ,o1 ,n1 be the ,earth at the two ,equinoxes and the two ,solstices2 ,n ,s its ,axis1 ,n the ,north ,pole1 ,s the ,south ,pole1 ,q the ,equator1 ,t the ,tropic of ,cancer1 t the ,tropick of ,capricorn1 and ,,abc the ,circumference of the ,earth's enlightened ,disc as seen from the ,sun or ,new ,moon at these times4 ,the ,earth's ,axis has the position ,,nes at the vernal ,equinox1 lying towards the right hand1 as seen from the ,sun or ,new ,moon2 its ,poles ,n and ,s being then in the ,circumference of the ,disc2 and the ,equator and all its parallels seem to be straight lines1 because their planes pass through the observer's eye looking down upon the ,earth from the ,sun or ,moon directly over ,e1 where the ,ecliptic ,,fg intersects the ,equator 4 ,at the ,summer ,solstice1 the ,earth's ,axis has the position ,,nds2 and that part of the ,ecliptic ,,fg in which the ,moon is then ,new1 touches the ,tropic of ,cancer ,t at ,d4 ,the ,north ,pole ,n at that time inclining #bc-a_/b degrees towards the ,sun1 falls so many degrees within the ,earth's enlightened ,disc1 because the ,sun is then vertical to ,d1 #bc-a_/b degrees north of the ,equator ,q2 and the ,equator with all its parallels seem elliptic curves bending downward1 or towards the ,south ,pole as seen from the ,sun3 which ,pole1 together with #bc-a_/b degrees all round it1 is hid behind the ,disc in the dark ,hemisphere of the ,earth4 ,at the autumnal ,equinox the ,earth's ,axis has the position ,,nos1 lying to the left hand as seen from the ,sun or ,new ,moon1 which are then vertical to ,o1 where the ,ecliptic cuts the ,equator ,q4 ,both ,poles now lie in the circumference of the ,disc1 the ,north ,pole just going to disappear behind it1 and the ,south ,pole just entering into it2 and the ,equator with all its parallels seem to be straight lines1 because their planes pass through the observer's eye1 as seen from the ,sun1 and very nearly so as seen from the ,moon4 ,at the ,winter ,solstice the ,earth's ,axis has the position ,,nns2 when its ,south ,pole ,s inclining #bc-a_/b degrees toward the ,sun falls #bc-a_/b degrees within the enlightened ,disc1 as seen from the ,sun or ,new ,moon which are then vertical to the ,tropic of ,capricorn t1 #bc-a_/b degrees south of the ,equator ,q2 and the ,equator with all its parallels seem elliptic curves bending upward2 the ,north ,pole being as far hid behind the ,disc in the dark ,hemisphere1 as the ,south ,pole is come into the light4 ,the nearer that any time of the year is to the ,equinoxes or ,solstices1 the more it partakes of the ,phenomena relating to them4 ,sidenote3 ,,plate ,,xi4 ,various positions of the ,earth's ,axis1 as seen from the ,sun at different times of the year4 #cci4 ,thus it appears1 that from the vernal equinox to the autumnal1 the ,north ,pole is enlightened2 and the ,equator and all its parallels appear ,semi-ellipses as seen from the ,sun1 more or less curved as the time is nearer to or farther from the ,summer ,solstice2 and bending downwards or towards the ,south ,pole2 the reverse of which happens from the autumnal ,equinox to the vernal4 ,a little consideration will be sufficient to convince the reader1 that the ,earth's ,axis inclines towards the ,sun at the ,summer ,solstice2 from the ,sun at the ,winter ,solstice2 and sidewise to the ,sun at the ,equinoxes2 but towards the right hand1 as seen from the ,sun at the vernal ,equinox2 and towards the left hand at the autumnal4 ,from the ,winter to the ,summer ,solstice1 the ,earth's ,axis inclines more or less to the right hand1 as seen from the ,sun2 and the contrary from the ,summer to the ,winter ,solstice4 ,sidenote3 ,how these positions affect solar ,eclipses4 #cdj4 ,the different positions of the ,earth's ,axis1 as seen from the ,sun at different times of the year1 affect solar ,eclipses greatly with regard to particular places2 yea so far as would make central ,eclipses which fall at one time of the year invisible if they fell at another1 even though the ,moon should always change in the ,nodes and at the same hour of the day3 of which indefinitely various affections1 we shall only give ,examples for the times of the ,equinoxes and ,solstices4 ,sidenote3 ,fig4 ,,iv4 ,in the same ,diagram1 let ,,fg be part of the ,ecliptic1 and ,,ik ik ik ik part of the ,moon's ,orbit2 both seen edgewise1 and therefore projected into right lines2 and let the intersections ,n1 ,o1 ,d1 ,e be one and the same ,node at the above times1 when the ,earth has the forementioned different positions2 and let the spaces included by the ,circles ,p1 p1 p1 p be the ,penumbra at these times1 as its center is passing over the center of the ,earth's ,disc4 ,at the ,winter ,solstice1 when the ,earth's ,axis has the position ,,nns1 the center of the ,penumbra ,p touches the ,tropic of ,capricorn t in ,n at the middle of the general ,eclipse2 but no part of the ,penumbra touches the ,tropic of ,cancer ,t4 ,at the ,summer ,solstice1 when the ,earth's ,axis has the position ,,nds 7i,dk being then part of the ,moon's ,orbit whose ,node is at ,d7 the ,penumbra p has its center on the ,tropic of ,cancer ,t at the middle of the general ,eclipse1 and then no part of it touches the ,tropic of ,capricorn t4 ,at the autumnal ,equinox the ,earth's ,axis has the position ,,nos 7i,ok being then part of the ,moon's ,orbit7 and the ,penumbra equally includes part of both ,tropics ,t and t at the middle of the general ,eclipse3 at the vernal ,equinox it does the same1 because the ,earth's ,axis has the position ,,nes3 ,but1 in the former of these two last cases1 the ,penumbra enters the ,earth at ,a1 north of the ,tropic of ,cancer ,t1 and leaves it at m1 south of the ,tropic of ,capricorn t2 having gone over the ,earth obliquely southward1 as its center described the line ,a,om3 whereas in the latter case the ,penumbra touches the ,earth at n1 south of the ,equator ,q1 and describing the line n,eq 7similar to the former line ,a,om in open space7 goes obliquely northward over the ,earth1 and leaves it at q1 north of the ,equator4 ,in all these circumstances1 the ,moon has been supposed to change at noon in her descending ,node3 had she changed in her ascending ,node1 the ,phenomena would have been as various the contrary way1 with respect to the ,penumbra's going northward or southward over the ,earth4 ,but because the ,moon changes at all hours1 as often in one ,node as the other1 and at all distances from them both at different times as it happens1 the variety of the ,phases of ,eclipses are almost innumerable1 even at the same places1 considering also how variously the same places are situated on the enlightened ,disc of the ,earth1 with respect to the ,penumbra's motion1 at the different hours that ,eclipses happen4 ,sidenote3 ,how much of the ,penumbra falls on the ,earth at different distances from the ,nodes4 #cda4 ,when the ,moon changes #ag degrees short of her descending ,node1 the ,penumbra ,p #ah just touches the northern part of the ,earth's ,disc1 near the ,north ,pole ,n2 and1 as seen from that place the ,moon appears to touch the ,sun1 but hides no part of him from sight4 ,had the ,change been as far short of the ascending ,node1 the ,penumbra would have touched the southern part of the ,disc near the ,south ,pole ,s4 ,when the ,moon changes #ab degrees short of the descending ,node1 more than a third part of the ,penumbra ,p #ab falls on the northern parts of the ,earth at the middle of the general ,eclipse3 had she changed as far past the same ,node1 as much of the other side of the ,penumbra about ,p would have fallen on the southern part of the ,earth2 all the rest in the expansum1 or open space4 ,when the ,moon changes #f degrees from the ,node1 almost the whole ,penumbra ,p#f falls on the ,earth at the middle of the general ,eclipse4 ,and lastly1 when the ,moon changes in the ,node1 the ,penumbra ,,pn takes the longest course possible on the ,earth's ,disc2 its center falling on the middle thereof1 at the middle of the general ,eclipse4 ,the farther the ,moon changes from either ,node within #ag degrees of it1 the shorter is the ,penumbra's continuance on the ,earth1 because it goes over a less portion of the ,disc1 as is evident by the ,figure4 ,sidenote3 ,the ,earth's diurnal motion lengthens the duration of solar ,eclipses1 which fall without the polar ,circles4 #cdb4 ,the nearer that the ,penumbra's center is to the ,equator at the middle of the general ,eclipse1 the longer is the duration of the ,eclipse at all those places where it is central2 because1 the nearer that any place is to the ,equator1 the greater is the ,circle it describes by the ,earth's motion on its ,axis3 and so1 the place moving quicker keeps longer in the ,penumbra whose motion is the same way with that of the place1 tho' faster as has been already mentioned #ccg4 ,thus1 7see the ,earth at ,d and the ,penumbra at #ab7 whilst the point b in the polar ,circle abcd is carried from b to c by the ,earth's diurnal motion1 the point d on the ,tropick of ,cancer ,t is carried a much greater length from d to ,d3 and therefore1 if the ,penumbra's center goes one time over c and another time over ,d1 the ,penumbra will be longer in passing over the moving place d than it was in passing over the moving place b4 ,consequently1 central ,eclipses about the ,poles are of the shortest duration2 and about the ,equator of the longest4 ,sidenote3 ,and shortens the duration of some which fall within these ,circles4 #cdc4 ,in the middle of ,summer the whole frigid ,zone included by the polar ,circle abcd is enlightened2 and if it then happens that the ,penumbra's center goes over the north ,pole1 the ,sun will be eclipsed much the same number of ,digits at a as at c2 but whilst the ,penumbra moves eastward over c it moves westward over a1 because with respect to the ,penumbra1 the motions of a and c are contrary3 for c moves the same way with the ,penumbra towards d1 but a moves the contrary way towards b2 and therefore the ,eclipse will be of longer duration at c than at a4 ,at a the ,eclipse begins on the ,sun's eastern limb1 but at c on his western3 at all places lying without the polar ,circles1 the ,sun's ,eclipses begin on his western limb1 or near it1 and end on or near his eastern4 ,at those places where the ,penumbra touches the ,earth1 the ,eclipse begins with the rising ,sun1 on the top of his western or uppermost edge2 and at those places where the ,penumbra leaves the ,earth1 the ,eclipse ends with the setting ,sun1 on the top of his eastern edge which is then the uppermost1 just at its disappearing in the ,horizon4 ,sidenote3 ,the ,moon has no ,atmosphere4 #cdd4 ,if the ,moon were surrounded by an ,atmosphere of any considerable ,density1 it would seem to touch the ,sun a little before the ,moon made her appulse to his edge1 and we should see a little faintness on that edge before it were eclipsed by the ,moon3 ,but as no such faintness has been observed1 at least so far as ,i ever heard1 it seems plain1 that the ,moon has no such ,atmosphere as that of the ,earth4 ,the faint ring of light surrounding the ,sun in total ,eclipses1 called by ,,cassini la ,chevelure du ,soleil1 seems to be the ,atmosphere of the ,sun2 because it has been observed to move equally with the ,sun1 not with the ,moon4 ,sidenote3 ,,plate ,,xi4 #cde4 ,having been so prolix concerning ,eclipses of the ,sun1 we shall drop that subject at present1 and proceed to the doctrine of lunar ,eclipses2 which1 being more simple1 may be explained in less time4 ,sidenote3 ,eclipses of the ,moon4 ,fig4 ,,ii4 ,that the ,moon can never be eclipsed but at the time of her being ,full1 and the reason why she is not eclipsed at every ,full1 have been shewn already #caf1 #cag4 ,let ,s be the ,sun1 ,e the ,earth1 ,,rr the ,earth's shadow1 and ,b the ,moon in opposition to the ,sun3 in this situation the ,earth intercepts the ,sun's light in its way to the ,moon2 and when the ,moon touches the ,earth's shadow at v she begins to be eclipsed on her eastern limb x1 and continues eclipsed until her western limb y leaves the shadow at w3 at ,b she is in the middle of the shadow1 and consequently in the middle of the ,eclipse4 ,sidenote3 ,why the ,moon is visible in a total ,eclipse4 #cdf4 ,the ,moon when totally eclipsed1 is not invisible if she be above the ,horizon and the ,sky be clear2 but appears generally of a dusky colour like tarnished copper1 which some have thought to be the ,moon's native light4 ,but the true cause of her being visible is the scattered beams of the ,sun1 bent into the ,earth's shadow by going through the ,atmosphere2 which1 being more dense near the ,earth than at considerable heights above it1 refracts or bends the ,sun's rays more inward #agi1 the nearer they are passing by the ,earth's surface1 than those rays which go through higher parts of the ,atmosphere1 where it is less dense according to its height1 until it be so thin or rare as to lose its refractive power4 ,let the ,circle fghi1 concentric to the ,earth1 include the ,atmosphere whose refractive power vanishes at the heights f and i2 so that the rays ,wfw and ,viv go on straight without suffering the least refraction3 ,but all those rays which enter the ,atmosphere between f and k1 and between i and l1 on opposite sides of the ,earth1 are gradually more bent inward as they go through a greater portion of the ,atmosphere1 until the rays ,wk and ,vl1 touching the ,earth at m and n1 are bent so as to meet at q1 a little short of the ,moon2 and therefore the dark shadow of the ,earth is contained in the space moqpn where none of the ,sun's rays can enter3 all the rest ,,rr1 being mixed by the scattered rays which are refracted as above1 is in some measure enlightened by them2 and some of those rays falling on the ,moon give her the colour of tarnished copper1 or of iron almost red hot4 ,so that if the ,earth had no ,atmosphere1 the ,moon would be as invisible in total ,eclipses as she is when ,new4 ,if the ,moon were so near the ,earth as to go into its dark shadow1 suppose about po1 she would be invisible during her stay in it2 but visible before and after in the fainter shadow ,,rr4 ,sidenote3 ,,plate ,,xi4 ,why the ,sun and ,moon are sometimes visible when the ,moon is totally eclipsed4 #cdg4 ,when the ,moon goes through the center of the ,earth's shadow she is directly opposite to the ,sun3 yet the ,moon has been often seen totally eclipsed in the ,horizon when the ,sun was also visible in the opposite part of it3 for1 the horizontal refraction being almost #cd minutes of a degree #aha1 and the diameter of the ,sun and ,moon being each at a mean state but #cb minutes1 the refraction causes both ,luminaries to appear above the ,horizon when they are really below it #agi4 ,sidenote3 ,fig4 ,v4 ,duration of central ,eclipses of the ,moon4 #cdh4 ,when the ,moon is ,full at #ab degrees from either of her ,nodes1 she just touches the ,earth's shadow but enters not into it4 ,let ,,gh be the ,ecliptic1 ef the ,moon's ,orbit where she is #ab degrees from the ,node at her ,full2 cd her ,orbit where she is #f degrees from the ,node1 ab her ,orbit where she is ,full in the ,node1 ,,ab the ,earth's shadow1 and ,m the ,moon4 ,when the ,moon describes the line ef she just touches the shadow but does not enter into it2 when she describes the line cd she is totally though not centrally immersed in the shadow2 and when she describes the line ab she passes by the ,node at ,m in the center of the shadow1 and takes the longest line possible1 which is a diameter1 through it3 and such an ,eclipse being both total and central is of the longest duration1 namely1 #c hours #eg minutes #f seconds from the beginning to the end1 if the ,moon be at her greatest distance from the ,earth3 and #c hours #cg minutes #bf seconds1 if she be at her least distance4 ,the reason of this difference is1 that when the ,moon is farthest from the ,earth she moves slowest2 and when nearest to it1 quickest4 ,sidenote3 ,digits4 #cdi4 ,the ,moon's diameter1 as well as the ,sun's1 is supposed to be divided into twelve equal parts called ,digits2 and so many of these parts as are darkened by the ,earth's shadow1 so many ,digits is the ,moon eclipsed4 ,all that the ,moon is eclipsed above #ab ,digits1 shew how far the shadow of the ,earth is over the body of the ,moon1 on that edge to which she is nearest at the middle of the ,eclipse4 ,sidenote3 ,why the beginning and end of a lunar ,eclipse is so difficult to be determined by observation4 #cej4 ,it is difficult to observe exactly either the beginning or ending of a lunar ,eclipse1 even with a good ,telescope2 because the ,earth's shadow is so faint1 and ill defined about the edges1 that when the ,moon is either just touching or leaving it1 the obscuration of her limb is scarce sensible2 and therefore the nicest observers can hardly be certain to four or five seconds of time4 ,but both the beginning and ending of solar ,eclipses are visibly instantaneous2 for the moment that the edge of the ,moon's ,disc touches the ,sun's1 his roundness seems a little broke on that part2 and the moment she leaves it he appears perfectly round again4 ,sidenote3 ,the use of ,eclipses in ,astronomy1 ,geography1 and ,chronology4 #cea4 ,in ,astronomy1 ,eclipses of the ,moon are of great use for ascertaining the periods of her motions2 especially such ,eclipses as are observed to be alike in all circumstances1 and have long intervals of time between them4 ,in ,geography1 the ,longitudes of places are found by ,eclipses1 as already shewn in the eleventh chapter3 but for this purpose ,eclipses of the ,moon are more useful than those of the ,sun1 because they are more frequently visible1 and the same lunar ,eclipse is of equal largeness and duration at all places where it is seen4 ,in ,chronology1 both solar and lunar ,eclipses serve to determine exactly the time of any past event3 for there are so many particulars observable in every ,eclipse1 with respect to its quantity1 the places where it is visible 7if of the ,sun7 and the time of the day or night2 that 'tis impossible there can be two ,eclipses in the course of many ages which are alike in all circumstances4 ,sidenote3 ,the darkness at our ,,saviour's crucifixion supernatural4 #ceb4 ,from the above explanation of the doctrine of ,eclipses it is evident1 that the darkness at our ,,saviour's crucifixion was supernatural4 ,for he suffered on the next day after eating his last ,passover-,supper1 on which day it was impossible that the ,moon's shadow could fall on the ,earth1 for the ,jews kept the ,passover at the time of ,full ,moon3 nor does the darkness in total ,eclipses of the ,sun last four minutes in any place #ccc1 whereas the darkness at the crucifixion lasted three hours1 ,matt4 xxviii4 #ae4 and overspread at least all the land of ,judea4 ,,chap4 ,,xix4 ,the ,calculation of ,new and ,full ,moons and ,eclipses4 ,the geometrical ,construction of ,solar and ,lunar ,eclipses4 ,the examination of antient ,eclipses4 #cec4 ,to construct an ,eclipse of the ,sun1 we must collect these ten ,elements or ,requisites from the following ,astronomical ,tables4 ,sidenote3 ,requisites for a solar ,eclipse4 ,i4 ,the true time of conjunction of the ,sun and ,moon3 to know at what conjunctions the ,sun must be eclipsed2 and to the times of those conjunctions1 ,,ii4 ,the ,moon's horizontal parallax1 or angle which the semi-diameter of the ,earth subtends as seen from the ,moon4 ,,iii4 ,the ,sun's true place1 and distance from the solstitial colure to which he is then nearest1 either in coming to it or going from it4 ,,iv4 ,the ,sun's declination4 ,v4 ,the angle of the ,moon's visible path with the ,ecliptic4 ,,vi4 ,the ,moon's ,latitude or ,declination from the ,ecliptic4 ,,vii4 ,the ,moon's true hourly motion from the ,sun4 ,,viii4 ,the ,angle of the ,sun's semi-diameter as seen from the ,earth4 ,,ix4 ,the ,angle of the ,moon's semi-diameter as seen from the ,earth4 ,x4 ,the semi-diameter of the ,penumbra4 ,and for an ,eclipse of the ,moon1 the following ,elements4 ,sidenote3 ,requisites for a lunar ,eclipse4 ,i4 ,the true time of opposition of the ,sun and ,moon2 and for that time1 ,,ii4 ,the ,moon's horizontal parallax4 ,,iii4 ,the ,sun's semi-diameter4 ,,iv4 ,the semi-diameter of the ,earth's shadow4 ,v4 ,the ,moon's semi-diameter4 ,,vi4 ,the ,moon's ,latitude4 ,,vii4 ,the ,moon's true hourly motion from the ,sun4 ,,viii4 ,the ,angle of the ,moon's visible path with the ,ecliptic4 ,these ,elements are easily found from the following ,tables and ,precepts1 by the common ,rules of ,arithmetic4 ,note1 #fj minutes make a ,degree1 #cj degrees a ,sign1 and #ab ,signs a ,circle4 ,a ,sign is marked thus s1 a ,degree thus 1 and a ,minute thus 4 ,when you exceed #ab ,signs1 always reject them and set down the remainder4 ,when the number of ,signs to be subtracted is greater than the number you subtract from1 add #ab ,signs to that which you subtract from2 and then you will have a remainder to set down4 ,sidenote3 ,how the ,signs are reckoned4 #ced4 ,as we fix arbitrarily upon the beginning of the ,sign ,aries to reckon from1 when we speak of the places of the ,sun1 ,moon1 and ,nodes2 we call ,aries #j ,signs1 ,taurus #a ,sign1 ,gemini #b ,signs1 ,cancer #c ,signs1 c4 ,so1 when the ,sun is in the #ajth degree of ,aries1 we say his ,place or ,longitude is #j ,signs #aj ,degrees1 because he is only #aj ,degrees from the beginning of ,aries3 if he is in the #eth1 #ajth1 c4 ,degree of ,taurus1 we say his ,place or ,longitude is #a ,sign1 #e1 #aj1 c4 ,degrees3 and so on1 till he comes quite round again4 ,but in reckoning the ,anomalies of the ,sun and ,moon1 and their distance from the ,nodes1 we only consider the number of ,signs and ,degrees the ,luminaries are gone past their ,apogee or ,nodes2 not how far they have to go to these points1 were the distance ever so little4 ,the ,sun1 ,moon1 and ,apogee move according to the order of ,signs1 but the ,nodes contrary4 ,we shall now give the ,precepts and ,examples for the above ,requisites in their due order4 ,to calculate the time of ,new and ,full ,moon4 ,sidenote3 ,first ,element or ,requisite4 #cee4 ,,precept ,i4 ,for any proposed year in the #ahth ,century1 take out the mean time of the ,new ,moon in ,march from ,table ,i41 and the mean time of ,full ,moon from ,table ,,iii41 for the ,old ,stile2 or from ,tables ,,ii and ,,iv for ,new ,stile2 with the mean ,anomalies of the ,sun and ,moon for these times1 and set them by themselves4 ,then1 from ,table ,,vi1 take out as many ,lunations as the proposed ,month is after ,march1 with the days1 hours1 and minutes belonging to them2 and also the mean ,anomalies of the ,sun and ,moon for these ,lunations4 ,,ii4 ,add the days1 hours1 and minutes of these ,lunations to the time of ,new or ,full ,moon in ,march1 and the ,anomalies for the ,lunations to the ,anomalies for ,march3 the sums give the hours and minutes of the mean ,new or ,full ,moon required1 and the mean ,anomalies of the ,sun and ,moon for that time4 ,,iii4 ,then1 with the number of days enter ,table ,,vii1 under the given ,month1 and right against this number1 in the left hand column you have the day of ,new or ,full ,moon2 which set before the hours and minutes above-mentioned4 ,,iv4 ,but1 7as it will sometimes happen7 if the number of days fall short of all those under the given ,month1 add one ,lunation with its ,anomalies from ,table ,,vi to the foresaid sums2 so you will have a new sum of days wherewith to enter the #gth ,table under the given ,month1 where you are sure to find that sum the second time1 if the first falls short4 ,v4 ,with the ,signs and ,degrees of the ,sun's ,anomaly enter ,table ,,viii1 ,the ,moon's annual ,equation1 and take out the minutes of time of that ,equation by the ,anomaly2 remembring1 that if the ,signs are at the head of the ,table1 the degrees are at the left hand1 in which case the ,equation found in the ,angle of meeting must be subtracted from the mean time of ,new or ,full ,moon1 as the title ,subtract1 at the head of the ,table directs3 but if the ,signs are at the foot of the ,table their degrees are in the right-hand column1 and the ,equation where the ,signs and ,degrees meet in the ,table is to be added to the mean time1 as the title ,add1 at the foot of the ,table directs2 which ,equation1 so applied1 gives the mean time of ,new or ,full ,moon corrected4 ,,vi4 ,with the ,signs and ,degrees of the ,sun's ,anomaly enter ,table ,,ix1 ,equation of the ,moon's mean ,anomaly1 and take out the ,equation thereof2 adding it to the mean ,anomaly or subtracting it therefrom1 as the titles at the head or foot of the ,table direct2 and it gives the mean ,anomaly corrected4 ,then1 with the ,sun's ,anomaly enter ,table ,,xii1 ,equation of the ,sun's mean ,place1 and take out that ,equation1 applying it to the ,moon's corrected ,anomaly as the titles direct2 and it will give the ,moon's ,anomaly equated#gg4 ,n4 ,b4 ,in all these ,equations1 care must be taken to make proper allowance for the odd minutes of ,anomaly2 the ,tables having the ,equations only for compleat ,degrees4 ,,vii4 ,with the ,moon's equated ,anomaly enter ,table ,x1 ,the ,moon's elliptic ,equation1 and take out that ,equation in the same manner as the preceding3 adding it to the former corrected time if the ,signs be at the head of the ,table1 or subtracting it if they be at the foot1 as the ,table directs2 and this gives the mean time equated4 ,,viii4 ,lastly1 enter ,table ,,xi1 ,the ,sun's ,equation at ,new and ,full ,moon1 with the ,sun's ,anomaly1 and take out the ,sun's ,equation in the same manner as the others2 adding it to1 or subtracting it from the former equated time1 as the titles direct3 and by this last ,equation you have the true time of ,new or ,full ,moon1 agreeing with well regulated ,clocks and ,watches4 ,but to make it agree with true ,sun-,dials1 the ,equation of time must be applied as taught #bbe4 ,,example ,i4 ,to find the time of ,new ,moon in ,april #agfd1 ,n4 ,s4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,,ii4 ,mean time of ,new ,moon in ,march #b #h #eg #h #b #bc #aj #ac #cb ,add1 for ,lunation1 from ,tab4 ,,vi4 #bi #ab #dd #j #bi #f #j #be #di -------- ---------- ---------- ,mean ,new ,moon and ,anomaly #ca #ba #da #j #a #bi #aa #i #ba ,to which ,time add the ,moon's ------------- ,ann4 ,equ4 ,tab4 ,,viii4 #j #bb ,equ4 ,moon's ,anom4 - #bj ,and it gives the ,mean time -------- ---------- corrected #ca #bb #c ,anom4 cor4 #aa #i #a ,from which subtract the ,moon's ,sun's ,equat4 #a #ef elliptic ,equ4 ,tab4 ,x4 - #c #aj ---------- -------- ,moon's ,ano4 #aa #aj #eg ,and it gives the ,mean time equated #ca #ah #ec --------------------------- ,to which add the ,sun's ,equation1 h4 m4 ,tab4 ,,xi4 #c #cb ,moon's ann4 ,equ4 #j #bb add ,and it gives the true time -------- ,her ellipt4 ,equ4 #c #aj sub4 of ,conjunction #ca #bb #be ,sun's ,equation #c #cb add ------------------------------------- ,which true time answers to the first of ,april1 at #be minutes past #aj in the forenoon3 for1 as the ,astronomical ,day begins at ,noon1 then #bb hours #be min4 after the ,noon of ,march #ca1 is ,april #a1 at #aj hours #be min4 in the ,forenoon4 ---------------------------------------- ----------------------------------- ,,example ,,ii4 ,to find the time of ,full ,moon in ,may #agfa1 ,n4 ,s4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,mean time of ,full ,moon in ,march #bj #ab #i #h #bj #b #i #a #ac ,add1 for two ,lunations #ei #a #bh #a #bh #ac #a #ba #ch -------- ---------- ---------- ,the several sums are #gi #ac #cg #aj #ah #ae #aj #bb #ea ----------------------- ,the days1 in ,tab4 ,,vii1 answer to ,equ4 ,moon's ,anom4 - #ac ,may #ah #ah #ac #cg ---------- ,moon's annual ,equation add #ad ,anom4 cor4 #aj #bb #ch -------- ,sun's ,equat4 #a #ae ,mean time corrected #ah #ac #ea ---------- ,moon's elliptic ,equation subtract - #e #ch ,moon's ,ano4 #aj #bc #ec -------- --------------------------- ,mean time equated #ah #h #ac h4 m4 ,sun's ,equation add #b #ai ,moon's ann4 ,equ4 #j #ad add -------- ,her ellipt4 ,equ4 #e #ch sub4 ,true time of ,opposition1 ,may #ah #aj #cb ,sun's ,equation #b #ai add ------------------------------------- ,namely1 the #ahth day1 at #cb minutes past #aj at night4 ---------------------------------------- ----------------------------------- ,the ,leap-years are allowed for in the ,tables1 so as to give no ,trouble in these ,calculations4 ,to compute the time of ,new and ,full ,moon in a given year and month1 of any particular ,century1 between the ,christian ra#gh and #ahth ,century4 ,,precept ,i4 ,find the like year of the #ahth ,century in ,table ,i41 for ,new ,moon1 or ,table ,,iii41 for ,full ,moon2 and take out the ,new or ,full ,moon in ,march for that year1 with the ,anomalies of the ,sun and ,moon4 ,,ii4 ,from ,table ,v1 take as many compleat ,centuries1 as when subtracted from the above year of the #ahth ,century1 will answer to the given year2 and take out the ,conjunctions and ,anomalies of these ,centuries4 ,,iii4 ,subtract the ,conjunctions and ,anomalies of these ,centuries from those of the ,new or ,full ,moon in ,march above taken out1 and the remainders will shew the mean time of ,new or ,full ,moon in ,march the given year1 with the ,anomalies of the ,sun and ,moon at that time4 ,then1 work in all respects for the true time of the proposed ,new or ,full ,moon1 as taught by the ,precepts already given #cee4 ,,example ,i4 ,to find the time of ,new ,moon in ,july #aeha1 ,o4 ,s4 ,from #agha subtract #bjj years1 and there remains #aeha4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------- ,table ,i4 ,mean time of ,new ,moon in ,march #agha #ac #g #eb #h #bc #cg #j #j #ec ,tab4 ,v4 ,conj4 and ,anom4 for #bjj years subtract #h #af #bb #j #f #db #e #j #dd --------- ---------- ---------- ,remain the ,conj4 and ,anom4 for ,march #aeha #d #ae #cj #h #af #ee #g #j #i ,tab4 ,,vi4 ,add1 for five ,lunations1 to bring it to ,july #adg #ae #dj #d #be #cb #d #i #e --------- ---------- ---------- ,the sums are #aeb #g #aj #a #ab #bg #aa #i #ad ------------------------ ,the ,days in ,tab4 ,,vii4 answer ,equ4 ,moon's ,anom4 #ac to ,july #cjth #cj #g #aj ----------- ,sum of the three ,equations ,anom4 cor4 #aa #i #bg subtract - #g #i ,sun's ,equat4 - #a #af --------- ----------- ,true time of ,conjunction1 ,july #cj #j #a ,moon's ,ano4 #aa #h #aa ------------------------------------- ,which is the #cjth day1 at one minute ,moon's ann4 ,eq4 #j;h #adm sub4 past noon1 as shewn by well ,her ellipt4 ,equ4 #c #ce sub4 regulated ,clocks or ,watches ,sun's ,equation #c #bj sub4 ------------- ,sum #g #i sub4 ---------------------------------------- ---------------------------------- ,,example ,,ii4 ,to find the time of ,full ,moon in ,april ,a4 ,d4 #cj1 ,o4 ,s4 ,from #agcj subtract #agjj1 and there remains #cj4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,,iii4 ,mean time of ,full ,moon in ,march #agcj #bb #f #eh #i #b #dj #c #ac #bc ,tab4 ,v4 ,conj4 and ,anom4 for #agjj years subtract #ad #ag #cg #aa #bh #df #aj #bi #cf -------- ---------- ---------- ,rem4 the ,opposition and ,anom4 in ,march ,a4 ,d4 #cj #g #ac #ba #i #c #ed #d #ac #dg ,tab4 ,v4 ,add1 for one ,lunation1 to bring it into ,april #bi #ab #dd #j #bi #f #j #be #di -------- ---------- ---------- ,the sums are #cg #b #e #aj #c #j #e #i #cf ----------------------- ,the ,days in ,tab4 ,,vii4 answer to ,equ4 ,moon's ,anom4 - #ag ,april #f #f #b #e ---------- ,to which add the sum of the three ,anom4 cor4 #e #i #ai ,equations #f #a ,sun's ,equat4 #a #ce -------- ---------- ,true time of ,opposition ,moon's ,ano4 #e #aj #ed ,april ,a4 ,d4 #cj #f #h #f ------------------------------------ ,which is the #fth day1 at #f minutes past ,moon's ann4 ,eq4 #j;h #ahm add #h in the ,evening4 ,and thus1 the time ,her ellipt4 ,equ4 #b #df add of ,new or ,full ,moon may be found for ,sun's ,equat4 #b #eg add any given year and month after the ------------- ,christian ra4 ,sum #f #a add ---------------------------------------- ---------------------------------- ,sidenote3 ,remark4 ,n4 ,b4 ,sometimes it happens that the days annexed to the ,centuries in ,table ,v are more in number than the days on which the ,new or ,full ,moon happens in ,march the year of the #ahth ,century1 with which the computation begins2 as in the third following ,example1 viz4 for the ,full ,moon in ,march the year before ,,christ #gba3 in which case1 a ,lunation and it's ,anomalies must be added1 from ,table ,,vi1 to the days and ,anomalies of the ,new or ,full ,moon in ,march2 and then1 subtraction can be made3 and having gained a remainder1 work in all respects as taught in #cee4 ,to find the time of ,new or ,full ,moon in any given year and month before the ,christian ra4 #cef4 ,,precept ,i4 ,find a year of the #ahth ,century1 which added to the given number of years before ,,christ1 diminished by one1 shall make a number of whole ,centuries4 ,,ii4 ,find this number of ,centuries in ,table ,v1 and subtract the ,time and ,anomalies answering to it from the ,time and ,anomalies answering to the mean ,new or ,full ,moon in ,march the year of the #ahth ,century thus found2 and they will give the mean time of ,new or ,full ,moon in ,march the given year before ,,christ1 with the ,anomalies answering thereto4 ,whence the true time of that ,new or ,full ,moon may be had by the ,precepts already delivered #cee4 ,,iii4 ,the ,tables are calculated for the ,meridian of ,london3 therefore1 in computing for any place westward of ,london1 four minutes of time must be subtracted from the time shewn by the ,tables1 for every degree the place is westward2 and added for every degree it is eastward4 ,see #baj4 ,,example ,i4 ,to find the time of ,new ,moon at ,london and ,athens in ,march1 the year before ,christ #dbd4 ,the years #dbc added to #aggg make #bbjj1 or #bb ,centuries4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,i4 ,mean ,new ,moon in ,march ,a4 ,d4 #aggg #bg #g #ec #i #g #bg #e #be #ea ,from which subtract #bbjj years in ,tab4 ,v4 #f #ba #dg #aa #af #bf #d #bj #cg -------- ---------- ---------- ,mean ,conj4 and ,anom4 in ,march before ,chr4 #dbd #bj #aj #f #i #ba #a #a #e #ad ,which with1 the total of the three ------------- ,equations added #i #bj ,equ4 ,moon's ,anom4 - #ai -------- ---------- ,gives the true time of ,conjunction #bj #ai #bf ,anom4 cor4 #a #d #ee ---------- ,sun's ,equat4 #a #dh ,which was the #bast day of ,march1 at --------- #bf minutes past #g in the morning at ,moon's ,ano4 #a #f #dc ,london3 and if #a hour #ce minutes ------------------------------ be added for ,athens1 which is #bc #eb ,moon's ann4 ,eq4 #j;h #bjm add east of the meridian of ,london1 we ,her ellipt4 ,equ4 #e #dc add have the time at ,athens2 namely1 ,sun's ,equation #c #ag add #a minute past #i in the morning4 ,total #i #bj add ---------------------------------------- ---------------------------------- ,,example ,,ii4 ,to find the time of ,full ,moon in ,october1 the year before ,christ #djcj4 ,the years #agga added to #djbi make #ehjj1 or #eh ,centuries4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------- ,tab4 ,,iii4 ,from the mean ,full ,moon in ,march #agga #ai #g #aa #h #bi #f #g #bb #cj ------------------------------------- ,tab4 ,v4 ,subtr4 the numbers for #ehjj years #ejjj #aj #g #ef #aj #bc #ef #j #ag #cf #hjj #e #d #dc #aa #bg #dc #g #g #g --------- ---------- ---------- ,which collected make #ae #ab #ci #aj #ba #ci #g #bd #dc --------- ---------- ---------- ,rem4 the mean ,full ,moon c4 ,march before ,chr4 #djcj #c #ah #cb #aj #g #bg #aa #bg #dg ,to which add eight ,lunations to carry it to ,october #bcf #e #eb #g #bb #ej #f #bf #cb --------- ---------- ---------- ,and the several sums will be #bdj #j #bd #f #j #ag #f #bd #ai ------------------------------------- ,which1 for ,full ,moon day1 ,tab4 ,,vii1 is ,october #bf #bf #j #bd h4 m4 ,moon's ellipt4 ,equation subtr4 there being none besides #c #bh ,moon's ,ann4 ,eq4 #j #j add --------- ,moon's ellipt4 ,rem4 the true time of ,full ,moon1 ,eq4 #c #bh sub4 ,october #be #bj #ef ,sun's ,equation #j #j add ----------- --------- ,which is the #bfth day1 at #h hours ,total #c #bh sub4 #bf minutes in the forenoon#gi4 ---------------------------------------- ---------------------------------- ,sidenote3 ,age of the world uncertain4 ,by the method prescribed #bdh it will be found1 that the ,autumnal ,equinox in the year before ,,christ #djcj1 fell on the #bfth of ,october2 as this ,example shews the ,full ,moon to have been on the same day3 and by working as hereafter taught1 it will appear that the ,dominical ,letter was then ,g1 which shews the #bfth of that ,october to have been on a ,friday2 namely our sixth day of the week1 but the ,ante-,mosaic fifth day4 ,and as1 according to ,genesis1 chap4 i4 ver4 #ad4 the ,sun and ,moon were created on the fourth day of the week1 those who are of opinion that the world was made at the time of the ,autumnal ,equinox1 and that the ,moon at her first appearance was in full lustre1 opposite to the ,sun1 or nearly so1 may perhaps look upon this as a ,criterion for ascertaining the year of the creation2 since it shews the ,moon to have been ,full the next day after she was made3 and this is only #i years sooner than ,rheinholt makes it1 and #aa years later than according to ,lange4 ,whereas1 they who maintain that the world was created in the #djjgth year before ,,christ1 with the ,sun on the ,autumnal ,equinoctial ,point1 ,october #bf1 and the ,moon then ,full2 will find1 if they compute by the best ,tables extant1 that the ,moon was ,new1 instead of being ,full1 on that day4 ,if it could be proved from the writings of ,moses that the ,sun was created on the point of the ,autumnal ,equinox1 and the ,moon in opposition2 as well as it can be proved that these ,luminaries were made 7or according to some1 did not shine out till7 on the fourth day of the creation-week1 there would be ,data enough for ascertaining the age of the world3 for supposing the ,moon to have been ,full on an ,equinoctial ,day1 which was the fourth day of the week1 it would require many thousands of years to bring these three characters together again4 ,for1 the soonest in which the ,moon returns to be ,new or ,full on the same days of the ,months as before1 is #ai years wanting an hour and half1 but then the days of the week return not to the same days of the months in less than #bh years1 in which time the ,moon has gone through one ,course of ,lunations1 and #i years over2 therefore a co-incidence of the ,full ,moon and day of the ,week and ,month cannot happen in that time1 and if we multiply #ai by #bh1 which is the nearest co-incidence of these three characters1 namely #ecb years2 the ,moon's falling back an hour and half every #ai years will amount to #db hours in so many years2 and the ,equinox will have anticipated five days4 ,from all which we may venture to say1 that #bjjjjj years would not be sufficient to bring all these circumstances together again4 ,,example ,,iii4 ,to find the time of ,full ,moon at ,babylon in ,march1 the year before ,christ #gba4 ,the years #gbj added to #aghj make #bejj1 or #be ,centuries4 ---------------------------------------- -------------------------------- ,sun's ,anom4 ,moon's ,ano4 ,d4 ,h4 ,m4 -------------------------- s s ------------------------------------ ,tab4 ,i4 ,to the mean ,f4 ,moon and ,anom4 in ,mar4 #aghj #i #d #da #h #ai #dh #g #h #aj ,add one ,lunation and it's ,anomalies from ,tab4 ,,vi#hj #bi #ab #dd #j #bi #f #j #be #di -------- ---------- ---------- ,the several sums are #ch #ag #be #i #ah #ed #h #c #ei ,fr4 which subt4 the ,days ,anom4 of #bejj years1 ,tab4 ,v #ai #bb #bj #aa #bf #ai #f #f #dc -------- --------- ---------- ,rem4 the mean time and ,anom4 of ,f4,m4 in ,mar4 b4,c4 #gba #ah #ai #e #i #bb #be #a #bg #af ,to which add the sum of the ------------- three ,equations #aa #cf ,equ4 ,moon's ,anom4 - #ah -------- ,anom4 cor4 #a #bf #dh ,and it gives the true time of ,sun's ,equat4 #a #dg ,full ,moon1 ,mar4 b4,c4 #gba #ah #f #da ---------- --------- ,moon's ,anom4 #a #bh #ce ,which was the #aith day1 at #da minutes ------------------------------- past #f in the evening1 at ,london2 ,moon's ann4 ,eq4 #j;h #bjm add to which time1 if#ha #b hours #ea ,her ellipt4 ,equ4 #h #a add minutes be added1 we shall have ,sun's ,equation #c #ae add the time at ,babylon1 namely1 ,sum #aa #cf add #i hours #ea minutes4 ---------------------------------------- ---------------------------------- #ceg4 ,to know whether the ,sun will be eclipsed or no1 at the time of any given ,new ,moon2 collect the ,sun's distance from the ,node at that time1 and if it be less than #ag degrees he will be eclipsed1 otherwise not4 ,,example4 ,for the time of ,new ,moon in ,april #agfd4 ,sun from ,node s ,table ,,ii1 mean ,new ,moon in ,march #agfd1 ,new ,stile1 #aa #d #eg ,table ,,vi1 add for #a ,lunation to carry it to ,april #a #j #dj -------- ,sun's distance from the ,node at ,new ,moon in ,april #j #e #cg -------- ,which1 being within the above limit1 the ,sun must be eclipsed3 and therefore1 we proceed to find the rest of the ,elements for computing this ,eclipse4 ,to find the ,moons ,horizontal ,parallax1 or the ,angle of the ,earth's semi-diameter as seen from the ,moon4 ,sidenote3 ,second ,element4 #ceh4 ,,precept4 ,having found the ,moon's mean ,anomaly for the above time1 by the first and second ,precepts of #cee1 enter the ,x,vth ,table with the signs and degrees of that ,anomaly1 and thereby take out the ,moon's ,horizontal ,parallax3 only note1 that this is given but to every #fth degree of ,anomaly in the ,table1 because it is very easy to make proper allowance by sight4 ,so the ,moon's ,horizontal ,parallax ,april the #ast #agfd1 at #aj hours #be minutes in the ,forenoon1 answering to her mean ,anomaly at that time 7namely #aas #i #ba7 is #ee #g2 which1 diminished by #aj1 the ,sun's constant ,horizontal ,parallax1 gives for the semi-diameter of the ,earth's ,disc #ed #eg4 ,to find the ,sun's true ,place1 and his distance from the nearest ,solstice4 ,sidenote3 ,third ,element4 #cei4 ,,precept ,i4 ,we are to consider1 that the beginning of ,aries and of ,libra1 which are the ,equinoctial ,points1 are equidistant from the beginning of ,cancer and of ,capricorn1 which are the ,solstitial ,points4 ,hence1 when we know in what ,sign and ,degree the ,sun is1 we can easily find his distance from the nearest ,solstice4 ,now1 to find the ,sun's ,place1 or ,longitude from ,aries1 ,april the #ast1 #agfd1 at #aj hours #ba minutes in the ,forenoon2 being the equated time of ,new ,moon4 ,,precept ,,ii4 ,this being to the time of ,new ,moon1 take out the ,sun's mean ,place and ,anomaly from ,table ,,ii4 for that time1 and the ,equation of his mean ,place from ,table ,,xii by his ,anomaly2 adding the ,equation to his mean ,place or subtracting it from the same1 as the ,table directs1 will give his true ,place4 ,,example4 ---------------------------------------- ------------------------------- ,sun's ,long4 ,sun's mean from ,aries4 ,anomaly4 ------------------------- s s ,table ,i4 ,to the ,sun's mean ,place and ------------------------- ,anomaly at the mean time of ,new ,moon in ,march #agfd1 ,n4 ,s4 #aa #ag #g #h #b #bc ,add the same from ,tab4 ,,vi4 for one ,lunation1 to carry it to ,april #j #bi #f #j #bi #f --------- ---------- ,mean ,place and ,anomaly at the time of ,new ,moon in ,april #j #aj #ac #i #a #bi ,to which place add the ,sun's ,equation ------------ from ,tab4 ,,xii4 #a #ef ,equal --------- #a #ef ,and it gives the ,sun's true place #j #ab #i ,additive4 ------------------------- ,which is ,aries #ab #i2 and this1 when taken from three ,signs1 or the beginning of ,cancer1 leaves #b signs #ag deg4 #ea min41 or #gg #ea for the ,sun's distance from the then nearest ,solstice4 ---------------------------------------- --------------------------------- #cfj4 ,but because the ,sun's true ,place is often wanted when the ,moon is neither ,new nor ,full1 we shall next shew how it may be found for any given moment of time3 though this be digressing from our present purpose4 ,in ,table ,,xvi find the nearest lesser year to that in which the ,sun's ,place is sought2 and take out the ,sun's mean ,longitude and ,anomaly answering thereto2 to which add his mean motion and ,anomaly for the compleat residue of the years1 with the month1 day1 hour1 and minute1 all taken from the same ,table1 and you have the ,sun's mean ,longitude and ,anomaly for the given time4 ,then1 from ,table ,,xii take out the ,sun's ,equation by means of his ,anomaly 7making proportions for the odd minutes of ,anomaly7 which ,equation being added to or subtracted from the ,sun's mean ,longitude from ,aries1 as the titles in the ,table direct1 gives his true ,place1 or ,longitude from the beginning of ,aries1 reckoned according to the order of the ,signs #ced4 ,,example4 ,to find the ,sun's true ,place ,april #cjth1 ,a4 ,d4 #ageg1 at #ah minutes #dj seconds past #aj in the morning4 ---------------------------------------- ------------------------------- ,sun's ,long4 ,sun's ,anom4 ,the year next less than #ageg in the ,table -------------------------- is #agec1 at the beginning of which1 the s s ,sun's mean ,longitude from the beginning -------------------------- of ,aries1 and his mean ,anomaly1 is #i #aj #af #eb #f #a #ch ,to which add his mean ,mot4 and ,anom4 for four years to make #ageg #j #j #a #di #aa #bi #eh ,april #b #bh #db #cj #b #bh #db days #bi #j #bh #ce #b #j #bh #ce ,and likewise his mean ,mot4 and hours #bb #j #ed #ac #j #ed ,anom4 for min4 #ah #j #dd #a sec4 #di #b #j ----------- ------------- ,sun's mean ,longitude and ,anomaly for the given time is #a #h #ca #ab #i #bi #dh ,to which add the ,equation of the ,sun's mean ,place #a #dj #ad ------------- ----------- ,sun's ,eq4 ,and it gives his true ,place1 viz4 #a #dj #ad ,taurus #aj #aa #bf #a #aj #aa #bf ---------------------------------------- ------------------------------- ,n4 ,b4 ,in leap-years after ,february1 the ,sun's mean ,motion and ,anomaly must be taken out for the day next after the given one4 #cfa4 ,to calculate the ,sun's true ,place for any time in a given year before the first year of ,,christ3 subtract the mean ,motions and ,anomalies for the compleat hundreds next above the given year2 to the remainder add those for the residue of years1 months1 c4 and then work in all respects as above taught4 ,,example4 ,to find the ,suns true ,place ,may the #bhth at #d hours #c min4 #db sec4 in the afternoon1 the year before ,christ #ehe1 which was a ,leap year#hb4 ---------------------------------------- ------------------------------- ,sun's ,long4 ,sun's ,anom4 -------------------------- s s ,from the ,sun's mean ,longitude and ,anomaly -------------------------- at the beginning of the year ,christ #a #i #g #ec #aj #f #bi #ed ,subtract his mean ,motion and ,anomaly for #fjj years #j #d #cb #j #aa #bd #b ----------- ---------- ,and the remainder1 or radix1 is #i #c #ba #aj #g #e #eb ,to which add what #ehe wants of #fjj1 viz4 #ae years #aa #bi #bb #bg #aa #bi #g ,may #c #bh #af #dj #c #bh #ag days #bh ,bissextile #j #bh #ce #b #j #bh #ce ,and also those of hours #d #j #i #ea #j #aj min4 #c #j #g ---------- sec4 #db #b #j #b #a ----------- ,sun's ,anom4 ,sun's mean ,long4 ,may #bhth1 at #d hour ------------- #c min4 #bd sec4 afternoon #a #bi #de #ai ,equation of the ,sun's mean ,place subtract #b #b #b #bb ----------- ,sun's ,equat4 ,rem4 his true ,place for the same time1 subtract4 viz4 ,taurus #bi #dc #ag #a #bi #dc #ag ---------------------------------------- ------------------------------- ,n4 ,b4 ,as the ,longitudes or ,places of all the visible ,stars in the ,heavens are well known1 we have an easy method of finding the ,sun's true ,place in the ,ecliptic3 for the ,sun is directly opposite to that ,point of the ,ecliptic which comes to the ,meridian at mid-night4 ,to find the ,sun's ,declination4 ,sidenote3 ,fourth ,element4 #cfb4 ,,precept4 ,enter ,table ,,xvii with the ,signs and ,degrees of the ,sun's ,place2 and making proportions1 take out his ,declination answering thereto4 ,if the ,signs are at the head of the ,table1 the ,degrees are at the left hand2 but if the ,signs are at the foot of the ,table1 the ,degrees are at the right hand4 ,so1 the ,sun's ,declination answering to his true ,place 7found by #cei to be #js #ab #i7 is #d degrees #dh minutes #ed seconds1 making allowance for the #i that his ,place exceeds #ab4 ,to find the ,angle of the ,moon's visible ,path with the ,ecliptic4 ,sidenote3 ,fifth ,element4 ,,precept4 ,this we may state at #e degrees #ch minutes1 as near enough for the purpose2 since it is never above #h minutes of a degree more or less4 ,to find the ,moon's ,latitude4 ,sidenote3 ,sixth ,element4 #cfc4 ,,precept4 ,having found the ,sun's distance from the ,ascending ,node by #ceg1 at the mean time of ,new ,moon1 and his ,anomaly for that time by #cei1 find the ,equation of the ,node in ,table ,,xiii1 by the ,sun's ,anomaly1 and the ,equation of the ,sun's mean ,place in ,table ,,xii by his ,anomaly3 these two ,equations applied 7as the titles direct7 to the ,sun's mean distance from the ,ascending ,node1 give his true distance from it1 and also the ,moon's true distance at the time of ,change3 but when the ,moon is ,full1 this distance must be increased by the addition of #f ,signs1 which will then be the ,moon's true distance from the same ,node4 ,the ,moon's true distance from the ,ascending ,node is called the ,argument of the ,moon's ,latitude2 with the ,signs of which1 at the head of ,table ,,xiv1 and ,degrees at the left hand1 or with the ,signs at the foot of the ,table and ,degrees at the right hand1 take out the ,moon's ,latitude3 which is ,north ,ascending1 ,north ,descending1 ,south ,ascending1 or ,south ,descending1 according to the letters ,,na1 ,,nd1 ,,sa or ,,sd1 annexed to the ,signs of the said ,argument4 ,illustration3 ,plate ,,xii4 ,the ,geometrical ,construction of ,solar and ,lunar ,eclipses4 ,j4 ,ferguson delin4 ,j4 ,mynde ,sculp4 ,,example4 s ,sun's mean ,dist4 from the #hc,node at ,new ,moon in ,april #agfd #j #e #cg ,to which add the ,equation of the ,node #aj ---------- ,and it gives the ,sun's corrected ,distance from the ,node #j #e #dg ,to which cor4 ,dist4 add the ,eq4 of the ,sun's mean ,place #a #ef ---------- ,and it gives the ,sun's true ,distance from the ,node #j #g #dc ,which1 being at the time of ,new ,moon1 is the ,argument of ,latitude2 and in ,table ,,xiv1 7making proportions for the #dc7 shews the ,moon's ,latitude to be #dj #i ,north ,ascending#hd4 ,to find the ,moon's true hourly ,motion from the ,sun4 ,sidenote3 ,seventh ,element4 #cfd4 ,,precept4 ,with the ,moon's ,anomaly enter ,table ,,xv1 and thereby take out her true hourly ,motion3 then with the ,sun's ,anomaly take out his true hourly ,motion from the same ,table3 which done1 subtract the ,sun's hourly ,motion from the ,moon's1 and the remainder will be the ,moon's true hourly ,motion from the ,sun2 which1 for the above time #cei1 is #bg #ej4 ,to find the ,semi-diameters of the ,sun and ,moon as seen from the ,earth at the above-mentioned time4 ,sidenote3 ,eighth and ,ninth ,elements4 #cfe4 ,,precept4 ,enter the ,x,vth ,table with the ,sun's ,anomaly1 and thereby take out his ,semi-diameter2 and in the same manner take out the ,moon's ,semi-diameter by her ,anomaly4 ,the former of which for the above time will be found to be #af #f2 the latter #ad #eh4 ,to find the ,semi-diameter of the ,penumbra4 ,sidenote3 ,tenth ,element4 #cff4 ,,precept4 ,add the ,sun's semi-diameter to the ,moon's1 and their ,sum will be the ,semi-diameter of the ,penumbra2 namely1 at the above time #ca #d4 ,sidenote3 ,pl4 ,,xii4 #cff4 ,having found the proper ,elements or ,requisites for the ,sun's ,eclipse ,april #a1 #agfd1 and intending to project this ,eclipse ,geometrically1 we shall now collect them under the eye1 that they may be the more readily found as they are wanted in order for the ,projection4 ,sidenote3 ,the proper ,elements collected4 ,d ,h ,m #cfg4 ,i4 ,the true time of ,conj4 or ,new ,moon ,april #a #aj #be ,,ii4 ,the ,earth's ,semi-,disc1 which is equal to the ,moon's ,horizontal ,parallax #ee #g diminished by the ,sun's ,horizontal ,parallax which is always #aj #j #ed #eg ,,iii4 ,the ,sun's distance from the nearest ,solstice1 viz4 #gg #ea #j ,,iv4 ,the ,sun's ,declination1 ,north #d #dh #ed ,v4 ,the ,angle of the ,moon's vis4 path with the ,eclipt4 #e #ch #j ,,vi4 ,the ,moon's true ,latitude1 ,north ,ascending #dj #i ,,vii4 ,the ,moon's true ,horary ,motion from the ,sun #bg #ej ,,viii4 ,the ,sun's ,semi-diameter #af #f ,,ix4 ,the ,moon's ,semi-diameter #ad #eh ,x4 ,the ,semi-diameter of the ,penumbra #ca #d #cfh4 ,having collected these ,elements or ,requisites1 the following part of the work may be very much facilitated by means of a good ,sector1 with the use of which the reader should be so well acquainted1 as to know how to open it to any given ,radius1 as far as it will go2 and to take off the ,chord or ,sine of any ,arc of that ,radius4 ,this is done by first taking the extent of the given ,radius in your ,compasses1 and then opening the ,sector so as the distance cross-wise between the ends of the lines of ,sines or ,chords at ,s or ,c1 from ,leg to ,leg of the ,sector1 may be equal to that extent2 then1 without altering the ,sector1 take the ,sine or ,chord of the given ,arc with your ,compasses extended cross-wise from ,leg to ,leg of the ,sector in these lines4 ,but if the operator has not a ,sector1 he must construct these lines to such different lengths as he wants them in the projection4 ,and lest this ,treatise should fall into the hands of any person who would wish to project the ,figure of a solar or lunar ,eclipse1 and has not a ,sector to do it by1 we shall shew how he may make a line of ,sines or ,chords to any ,radius4 ,sidenote3 ,fig4 ,,ii4 ,how to make a line of ,chords4 ,pl4 ,,xii4 #cfi4 ,draw the right line ,,bca at pleasure2 and upon ,c as a ,center1 with the distance ,,ca or ,,cb as a ,radius1 describe the ,semi-circle ,,bda2 and from the ,center ,c draw ,,ac perpendicular to ,,bca4 ,then divide the ,quadrants ,,ad and ,,bd each into #ij equal parts or degrees1 and join the right line ,,ad for the ,chord of the ,quadrant ,,ad4 ,this done1 setting one foot of the ,compasses in ,a1 extend the other to the different divisions of the ,quadrant ,,ad2 and so transfer them to the right line ,,ad as in the ,figure1 and you have a line of ,chords ,,ad to the ,radius ,,ca4 ,n4 ,b4 #fj ,degrees on the ,line of ,chords is always equal to the ,radius of the ,circle it is made from2 as is evident by the ,figure1 where the ,arch ,e1 whose ,center is ,a1 drawn from #fj on the ,quadrant ,,ad1 cuts the ,chord line in #fj degrees1 and terminates in the ,center ,c4 ,sidenote3 ,and of ,sines4 ,then1 from the divisions or degrees of the ,quadrant ,,bd1 draw lines parallel to ,,cd1 which will fall perpendicularly on the ,radius ,,bc1 dividing it into a line of ,sines2 and it will be near enough for the present purpose1 to have them to every fifth ,degree1 as in the ,figure4 ,and thus the young ,tyro may supply himself with ,chords and ,sines1 if he has not a ,sector4 ,but as the ,sector greatly shortens the work1 we shall describe the projection as done by it1 so far as ,signs and ,chords are required4 ,sidenote3 ,fig4 ,,ii4 ,earth's ,semi-,disc4 #cgj4 ,make a ,scale of any convenient length 7six inches at least7 as ,,ac1 and divide it into as many equal parts as the semi-diameter of the ,earth's ,disc contains minutes1 which in this construction of the ,eclipse for ,london in ,april #agfd1 is #ed minutes and #eg seconds2 but as it wants only #c of #ee the ,scale may be divided into #ee equal parts1 as in the ,figure4 ,then1 with the whole length of the ,scale as a ,radius1 setting one foot of your ,compasses in ,c as a center1 describe the ,semi-circle ,,amb for the northern ,hemisphere or ,semi-disc of the ,earth1 as seen from the ,sun at that time4 ,had the ,place for which the ,construction is made been in ,south ,latitude1 this ,semi-circle would have been the ,southern ,hemisphere of the ,earth's ,disc4 ,sidenote3 ,axis of the ,ecliptic4 #cga4 ,upon the center ,c raise the straight line ,,ch for the ,axis of the ,ecliptic1 perpendicular to ,,acb4 ,sidenote3 ,north ,pole of the ,earth4 #cgb4 ,make a line of ,chords to the ,radius ,,ac1 and taking from thence the ,chord of #bc-a_/b ,degrees1 set it off from ,h to g and to h1 on the periphery of the ,semi-disc2 and draw the straight line g,nh1 in which the ,north ,pole of the ,disc is always found4 #cgc4 ,while the ,sun is in ,aries1 ,taurus1 ,gemini1 ,cancer1 ,leo1 and ,virgo1 the ,north ,pole of the ,disc is illuminated2 but while the ,sun is in ,libra1 ,scorpio1 ,sagittary1 ,capricorn1 and ,aquarius1 the ,north ,pole is hid in the obscure part behind the ,disc4 #cgd4 ,and1 whilst the ,sun is in ,capricorn1 ,aquarius1 ,pisces1 ,aries1 ,taurus1 and ,gemini1 the ,earth's ,axis ,,cp lies to the right hand of the ,axis of the ,ecliptic ,,ch as seen from the ,sun1 and to the left hand while the ,sun is in the other six ,signs4 ,sidenote3 ,earth's ,axis4 ,universal ,meridian4 #cge4 ,make a line of ,sines equal in length to ,ng or ,nh1 and take off with your ,compasses from it the ,sine of the ,sun's distance from the nearest ,solstice1 which in the present case is #gg #ea #cfg1 and set that distance to the right hand1 from ,n to ,p1 on the line g,nh1 because the ,sun being in ,aries #cei1 the ,earth's ,axis lies to the right hand of the ,axis of the ,ecliptic #cgd3 then draw the straight line ,c,,xii,p1 for the ,earth's ,axis and the ,universal ,meridian2 of both which ,p is the ,north ,pole4 ,sidenote3 ,path of a given ,place on the ,disc as seen from the ,sun4 #cgf4 ,to draw the parallel of ,latitude of any given ,place 7suppose ,london7 which parallel is the visible ,path of the ,place ,on the ,disc1 as seen from the ,sun1 from the time that the ,sun rises till it sets2 subtract the ,latitude of the ,place 7,london7 #ea-a_/b degrees from #ij degrees1 and there remains #ch-a_/b2 which take from the ,line of ,chords in your ,compasses1 and set it from h 7where the ,universal ,meridian ,,cp cuts the periphery of the ,semi-disc7 to ,,vi and ,,vi2 and draw the occult ,line ,,vi,l,,vi4 ,then1 on the left hand of the ,earth's ,axis1 set off the ,chord of the ,sun's ,declination #d #dh #e #cfg1 from ,,vi to ,d and to ,f2 set off the same on the right hand from ,,vi to ,e and to ,g2 and draw the occult ,lines ,ds,e and ,f,,xii,g parallel to ,,vi ,l ,,vi4 ,sidenote3 ,situation of the ,place on the ,disk from ,sun-rise to ,sun-set4 #cgg4 ,bisect s ,,xii in ,k1 and through the point ,k draw the black ,line ,,vi,k,v#a parallel to the occult or dotted ,line ,,vi,l,,vi4 ,then1 making ,,ac the ,radius or length of a ,line of ,lines1 set off the ,sine of #ch-a_/b degrees1 the ,co-,latitude of ,london1 from ,k to ,,vi and ,,vi2 and with that extent as a ,radius1 describe the ,semi-,circle ,,vi #g #h #i c4 and divide it into #ab equal parts1 beginning at ,,vi4 ,from these divisions1 draw the occult ,lines #gm1 #hl1 #ik1 c4 all to the ,line ,,vi,k,,vi1 and parallel to ,c,,xii,p4 ,then1 with ,k,,xii as a ,radius1 describe the ,circle abcdef1 round the ,center ,k1 and divide the ,quadrant a,,xii into six equal parts1 as ab1 bc1 cd1 de1 c4 ,then1 through these points of division b1 c1 d1 e1 and f1 draw the occult ,lines ,,viib,v1 ,,viiic,,iiii1 ,,ixd,,iii1 c4 intersecting the former ,lines #gm1 #hl1 #ik1 #aj;i1 c4 in the points ,,vii1 ,,viii1 ,,ix1 ,x1 ,,xi1 c4 which points mark the situation of ,london on the ,earth's ,disc as seen from the ,sun at these hours respectively1 from six in the morning till six at night3 and if the elliptic ,curve ,,vi1 ,,vii1 ,,viii1 c4 be drawn through these points1 it will represent the parallel of ,london1 or the path it seems to describe as viewed from the ,sun1 from ,sun-rise to ,sun-set4 ,n4,b4 ,when the ,sun's ,declination is ,north1 the said ,curve is the diurnal ,path of ,london2 and the opposite part ,,vis,,vi is it's nocturnal ,path behind the ,disc1 or in the obscure part thereof1 #cch1 #cci4 ,but if the ,sun's ,declination had been ,south1 the ,curve ,,vis,,vi would have been the diurnal path of ,london2 in which case the ,lines #gm1 #hl1 c4 must have been continued thro' the right ,line ,,vi,k,,vi1 and their lengths beyond that line determined by dividing the ,quadrant s a of the little ,circle abcd into six equal parts1 and drawing the parallels ,,viib1 ,,viiic c4 through that division1 in the same manner as done on the side ,k ,,xii2 and the ,curve ,,vii1 ,,viii1 ,,ix1 c4 would have been the nocturnal ,path4 ,it is requisite to divide the hours of the diurnal ,path into quarters1 as in the ,diagram2 and if possible into minutes also4 ,sidenote3 ,axis of the ,moon's ,orbit4 #cgh4 ,from the ,line of ,chords #cgb take the ,angle of the ,moon's visible ,path with the ,ecliptic1 viz4 #e #ch #cfg3 and note1 that when the ,moon's ,latitude is ,north ,ascending1 as in the present case1 the ,chord of this ,angle must be set off to the left hand of the ,axis of the ,ecliptic ,,ch1 as from ,h to ,m1 and the right line ,,cm drawn for the ,axis of the ,moon's ,orbit3 but when the ,moon's ,latitude is ,north ,descending1 this ,angle and ,axis must be set to the right hand1 or from ,h toward h4 ,when the ,moon's ,latitude ,south ,ascending1 the ,axis of her ,orbit lies the same way as when her ,latitude is ,north ,ascending2 and when ,south ,descending1 the same way as when ,north ,descending4 ,sidenote3 ,path of the ,penumbra's center over the ,earth4 #cgi4 ,take the ,moon's ,latitude1 #dj #i #cfg1 from the ,scale ,,ca1 and set it from ,c to ,t on the ,axis of the ,ecliptic2 and through ,t1 at right ,angles to the ,axis of the ,moon's ,orbit ,,cm1 draw the straight ,line ,,rts2 which is the ,moon's ,path1 or ,line that the center of her shadow and ,penumbra describes in going over the ,earth's ,disc4 ,the ,point ,t in the ,axis of the ,ecliptic is the ,place where the true ,conjunction of the ,sun and ,moon falls1 according to the ,tables2 and the ,point ,w1 in the ,axis of the ,moon's ,orbit1 is that where the center of the ,penumbra approaches nearest to the center of the ,earth's ,disc1 and consequently the middle of the general ,eclipse4 ,sidenote3 ,it's ,place on the ,earth's ,disc shewn for every minute of it's ,transit4 #chj4 ,take the ,moon's true ,horary ,motion from the ,sun #bg #ej #cfg1 from the ,scale ,,ca with your ,compasses 7every division of the ,scale being a minute of a ,degree7 and with that extent make marks in the ,line of the ,moon's ,path ,,rts3 then divide each of these equal spaces by dots into #fj equal parts or horary minutes1 and set the hours to every #fjth minute1 in such a manner that the dot2 signifying the precise minute of ,new ,moon by the ,tables1 may fall in the ,point ,t where the ,axis of the ,ecliptic cuts the ,line of the ,moon's ,path2 which1 in this ,eclipse1 is the #beth minute past ten in the ,forenoon3 and then the other marks will shew the places on the ,earth's ,disc where the center of the ,penumbra is1 at the hours and minutes denoted by them1 during its transit over the ,earth4 ,sidenote3 ,middle of the ,eclipse4 ,it's ,phases4 #cha4 ,apply one side of a ,square to the ,line of the ,moon's ,path1 and move the ,square backward or forward until the other side cuts the same hour and minute both in the ,path of the ,place 7,london1 in this ,construction7 and ,path of the ,moon2 and that minute1 cut at the same time in both ,paths1 will be the precise minute of visible ,conjunction of the ,sun and ,moon at ,london1 and therefore the time of greatest obscuration1 or middle of the ,eclipse at ,london2 which time1 in this ,projection1 falls at t1 #cd minutes past #aj in the ,moon's ,path2 and at u1 #cd minutes past #aj in the ,path of ,london4 ,then1 upon the ,point u as a center1 describe the ,circle z,yy whose ,radius uy is equal to the ,sun's semi-diameter #af #f #cfg1 taken from the ,scale ,,ca3 ,and upon the ,point t as a center1 describe the ,circle ,hy whose ,radius is equal to the ,moon's semi-diameter #ad #eh #cfg1 taken from the same ,scale4 ,the ,circle z,yy represents the ,disc of the ,sun as seen from the ,earth1 and the ,circle ,hy the ,disc of the ,moon4 ,the portion of the ,sun's ,disc cut off by the ,moon's shews the ,quantity of the ,eclipse at the time of greatest obscuration3 and if a right ,line as yz be drawn across the ,sun's ,disc through t and u1 the minute of greatest obscuration in both ,paths1 and divided into #ab equal parts1 it will shew what number of ,digits are then eclipsed4 ,if these two ,circles do not touch one another1 the ,eclipse will not be visible at the given ,place4 ,sidenote3 ,it's beginning and ending4 #chb4 ,lastly1 take the ,semi-diameter of the ,penumbra #ca #d #cfg1 from the ,scale ,,ca with your ,compasses2 and setting one foot in the ,moon's ,path1 to the left hand of the ,axis of the ,ecliptic1 direct the other toward the ,path of ,london2 and carry this extent backwards or forwards until both ,points of the ,compasses fall into the same instants of time in both ,paths3 which will denote the time of the beginning of the ,eclipse3 then1 do the same on the right hand of the ,axis of the ,ecliptic1 and where both ,points mark the same instants in both ,paths1 they will shew at what time the ,eclipse ends4 ,these trials give the ,points ,r in the ,moon's ,path and r in the ,path of ,london1 namely #i minutes past #i in the ,morning for the beginning of the ,eclipse at ,london1 ,april #a1 #agfd3 t and u for the middle or greatest obscuration1 at #ce minutes past #aj2 when the ,eclipse will be barely annular on the ,sun's lower-most edge1 and only two thirds of a ,digit left free on his upper-most edge3 and for the end of the ,eclipse1 ,s in the ,moon's ,path and x in the ,path of ,london1 at #d minutes past #ab at ,noon4 ,in this ,construction it is supposed that the ,equator1 ,tropics1 ,parallel of ,london1 and ,meridians through every #aeth degree of ,longitude are projected in visible ,lines on the ,earth's ,disc1 as seen from the ,sun at almost an infinite distance2 that the ,angle under which the ,moon's diameter is seen1 during the time of the ,eclipse1 continues invariably the same2 that the ,moon's motion is uniform1 and her ,path rectilineal1 for that time4 ,but all these suppositions do not exactly agree with the truth2 and therefore1 supposing the ,elements #cfg1 given by the ,tables to be perfectly accurate1 yet the time and phases of the ,eclipse deduced from it's ,construction will not answer exactly to what passeth in the ,heavens2 but may be two or three minutes wrong though done with the utmost care4 ,moreover1 the ,paths of all ,places of considerable ,latitude go nearer the center of the ,disc as seen from the ,moon than these ,constructions make them2 because the ,earth's ,disc is projected as if the ,earth were a perfect sphere1 although it is known to be a spheroid4 ,consequently1 the ,moon's shadow will go farther ,north in places of northern ,latitude1 and farther ,south in places of southern ,latitude than these projections answer to4 ,hence we may venture to predict that this ,eclipse will be more annular at ,london 7that is1 the annulus will be somewhat broader on the southern ,limb of the ,sun7 than the ,diagram shews it4 #chc4 ,having shewn how to compute the times and project the phases of a ,solar ,eclipse1 we now proceed to those of the ,lunar4 ,and it has been already mentioned #cag1 that when the ,full ,moon is within #ab degrees of either of her ,nodes1 she must be eclipsed4 ,we shall now enquire whether or no the ,moon will be eclipsed ,may #ah1 #agfa1 ,n4 ,s4 at #cb minutes past #aj at ,night4 ,see page #aic4 ,sidenote3 ,table ,,iv4 ,table ,,vi4 s ,sun from ,node at ,full ,moon in ,march #agfa #i #be #bg ,add his distance for two ,lunations1 to bring it into ,may #b #a #bj --------- ,and his distance at ,full ,moon in that month is #aa #bf #dg ,subtract this from a ,circle1 or #ab ,signs1 and there will remain #c #ac2 which is all that the ,sun wants of coming round to the ,ascending ,node2 and the ,moon being then opposite to the ,sun1 must be just as near the ,descending ,node3 consequently1 far within the limit of an ,eclipse4 #chd4 ,knowing then that the ,moon will be eclipsed in ,may #agfa1 we must find her true distance from the ,node at that time1 by applying the proper ,equations as taught #cfc1 and then find her true ,latitude as taught in that article4 ,sidenote3 ,table ,,iv4 ,table ,,xiii4 ,table ,,xii4 s ,sun's mean distance from the ,node at ,f4 ,moon in ,may #agfa #aa #bf #dg ,add the ,equation of the ,node1 for the ,sun's ,anomaly #ajs #ah #aehe #f -------- ,sun's mean distance from the ,node corrected #aa #bf #ec ,add the ,equation of the ,sun's mean ,place #a #ae -------- ,sun's true distance from the ,ascending ,node #aa #bh #h ,to which add #f ,signs1 ,see #cfc #f -------- ,the sum is the ,moon's true distance from the same ,node #e #bh #h ,sidenote3 ,pl4 ,,xii4 ,or the ,argument of her ,latitude2 which in ,table ,,xiv1 gives the ,moon's true ,latitude1 viz4 #i #ef ,north ,descending4 #che4 ,having by the foregoing precepts #cee found the true time of ,opposition of the ,sun and ,moon in a lunar ,eclipse1 with the ,moon's ,anomaly enter ,table ,,xv and take out her horizontal ,parallax1 also her true horary ,motion and ,semi-diameter3 and likewise those of the ,sun by his ,anomaly1 as already taught #cfd seq4 ,then add the ,sun's horizontal ,parallax1 which is always #aj ,seconds1 to the ,moon's horizontal ,parallax1 and from their sum subtract the ,sun's ,semi-diameter2 the remainder will be the ,semi-diameter of that part of the ,earth's shadow which the ,moon goes through4 #chf4 ,from the ,sum of the ,semi-diameters of the ,moon and ,earth's ,shadow1 subtract the ,moon's ,latitude2 the remainder is the parts deficient4 ,then1 as the ,semi-diameter of the ,moon is to #f ,digits1 so are the parts deficient to the ,digits eclipsed4 #chg4 ,if the parts deficient be more than the ,moon's ,diameter1 the ,eclipse will be total with continuance2 if less1 it will not be total2 if equal1 it will be total1 but without continuance4 #chh4 ,now collect the ,elements for projecting this ,eclipse4 ,moon's horizontal ,parallax #ee #cb ,sun's horizontal ,parallax 7always7 #aj ,the ,sum of both ,parallaxes #ee #db ,from which subtract the ,sun's ,semi-diameter #ae #ed ,remains the ,semi-diameter of the ,earth's ,shadow #ci #dh ,semidiameter of the ,moon #ae #b ,sum of the two last #ed #ej ,moon's ,latitude subtract #i #ef ,remains the parts deficient #de #j ,moon's horary motion #cj #df ,sun's horary motion subtract #b #bd ,remains the ,moon's horary motion from the ,sun #bh #bb ,sidenote3 ,to project a lunar ,eclipse4 ,fig4 ,,iii4 #chi4 ,this done1 make a ,scale of any convenient length as ,w1 whereof each division is a minute of a degree2 and take from it in your ,compasses #ed ,minutes #ej ,seconds1 the ,sum of ,semi-diameters of the ,moon and ,earth's shadow2 and with that extent as a ,radius1 describe that ,circle ,,ovlg round ,c as a ,center4 ,from the same ,scale take #ci ,minutes #dh ,seconds1 the ,semi-diameter of the ,earth's shadow1 and therewith as a ,radius1 describe the ,circle ,,uuuu for the ,earth's shadow1 round ,c as a ,center4 ,subtract the ,moon's ,semi-diameter from the ,semi-diameter of the ,shadow1 and with the difference #bd ,minutes #df seconds as a ,radius1 taken from the ,scale ,w1 describe the ,circle ,,yz round the ,center ,c4 ,draw the right line ,,ab through the ,center ,c for the ,ecliptic1 and cross it at right ,angles with the line ,,eg for the ,axis of the ,ecliptic4 ,because the ,moon's ,latitude in this ,eclipse is ,north ,descending1 #chd1 set off the ,angle of her visible ,path with the ,ecliptic #e ,degrees #ch ,minutes 7,page #bjb47 from ,e to ,v2 and draw ,v,cv for the ,axis of the ,moon's ,orbit4 ,had the ,moon's ,latitude been ,north ,ascending1 this ,angle must have been set off from ,e to f4 ,n4 ,b4 ,when the ,moon's ,latitude is ,south ,ascending1 the ,axis of her ,orbit lies the same way as when she has ,north ,ascending ,latitude2 and when her ,latitude is ,north ,descending1 the ,axis of her ,orbit lies the same way as when her ,latitude is ,south ,descending4 ,take the ,moon's true ,latitude #i #ef in your ,compasses from the ,scale ,w1 and set it off from ,c to ,f on the ,axis of the ,ecliptic because the ,moon is north of the ,ecliptic2 7had she been to the ,south of it1 her ,latitude must have been set off the contrary way1 as from ,c towards v37 and through ,f1 at right ,angles to the ,axis of the ,moon's ,orbit ,v,cv1 draw the right line ,,lmhno for the ,moon's ,orbit1 or her ,path through the ,earth's shadow4 ,n4 ,b4 ,when the ,moon's ,latitude is ,north ,ascending1 or ,north ,descending1 she is above the ,ecliptic3 but when her ,latitude is ,south ,ascending1 or ,south ,descending1 she is below it4 ,take the ,moon's true horary motion from the ,sun1 viz4 #bh ,minutes #bb ,seconds1 from the ,scale ,w in your ,compasses2 and with that extent make marks in the line of the ,moon's ,path ,,lmhno3 then divide each of these equal spaces into #fj equal parts or minutes of time3 and set the hours to them as in the ,figure1 in such a manner that the precise time of ,full ,moon1 as shewn by the ,tables1 may fall in the ,axis of the ,ecliptic at ,f1 where the line of the ,moon ,path cuts it4 ,lastly1 ,take the ,moon's ,semi-diameter #ae ,minutes #b ,seconds from the ,scale ,w in your ,compasses1 and therewith as a ,radius describe the ,circles ,p1 ,q1 ,r1 ,s1 and ,t on the ,centers ,l1 ,m1 ,h1 ,n1 and ,o2 the ,circles ,p and ,t just touching the ,earth's ,shadow ,,uu1 but no part of them within it2 the ,circles ,q and ,s all within it1 but touching at its edges2 and the ,circle ,r in the middle of the ,moon's ,path through the shadow4 ,so the ,circle ,p shall be the ,moon touching the shadow at the moment the ,eclipse begins2 the ,circle ,q the ,moon just immersed into the shadow at the moment she is totally eclipsed2 the ,circle ,r the ,moon at the greatest obscuration1 in the middle of the ,eclipse2 the ,circle ,s the ,moon just beginning to be enlightened on her western limb at the end of total darkness2 and the ,circle ,t the ,moon quite clear of the ,earth's shadow at the moment the ,eclipse ends4 ,the moments of time marked at the points ,l1 ,m1 ,h1 ,n and ,o answer to these ,phenomena3 and according to this small projection are as follow4 ,the beginning of the ,eclipse at #h ,hours #cf ,minutes ,p4 ,m4 ,the total immersion at #i ,hours #db ,minutes4 ,the middle of the ,eclipse at #aj ,hours #bf ,minutes4 ,the end of total darkness at #aa ,hours #ab ,minutes4 ,and the end of the ,eclipse at #ab ,hours #ah ,minutes2 but the ,figure is too small to admit of precision4 ,sidenote3 ,the examination of antient ,eclipses4 #cij4 ,by computing the times of ,new and ,full ,moons1 together with the distance of the ,sun and ,moon from the ,nodes2 and knowing that when the ,sun is within #ag ,degrees of either ,node at ,new ,moon he must be eclipsed2 and when the ,moon is within #ab ,degrees of either ,node at ,full she cannot escape an ,eclipse2 and that there can be no ,eclipses without these limits2 'tis easy to examine whether the accounts of antient ,eclipses recorded in history be true4 ,i shall take the liberty to examine two of those mentioned in the foregoing catalogue1 namely1 that of the ,moon at ,babylon on the #aith of ,march in the #gbast year before ,,christ2 and that of the ,sun at ,athens1 on the #bjth of ,march1 in the #dbdth year before ,,christ4 ,the time of ,full ,moon for the former of these ,eclipses is already calculated1 ,page #aih1 and the time of ,new ,moon for the latter1 ,page #aif1 both to the ,old ,style2 so that we have nothing now to do but find the ,sun's distance from the ,nodes the same way as we did the ,anomalies2 and if the ,full ,moon in ,march #gba years before ,,christ was within #ab degrees of either ,node1 she was then eclipsed2 and if the ,sun1 at the time of ,new ,moon in ,march #dbd years before ,,christ was within #ag degrees of either ,node1 he must have been eclipsed at that time4 ,,example ,i4 ,to find the distance of the ,sun and ,moon from the ,nodes1 at the time of ,full ,moon in ,march1 the year before ,,christ #gba1 ,o4 ,s4 ,the years #gbj added to #aghj make #bejj1 or #be ,centuries4 ,sun from ,node s ,to the mean time of ,full ,moon in ,march #aghj1 ,table ,,iii4 #aj #c #a ,add the distance for #a ,lunation ,see ,n4 ,b4 ,page #aie1 and ,example ,,iii1 ,page #aih #a #j #dj -------- ,sum #aa #c #da ,from which subtract the ,sun's distance from the ,node for #bejj years1 ,table ,v #e #d #aa -------- ,remains the ,sun's distance from the ,node1 ,march #ai1 #gba years before ,,christ #e #bi #cj ,to which add #f ,signs for the ,moon's distance1 because she was then in opposition to the ,sun #f #j #j -------- ,the ,sum is the ,moon's dist4 from the ,ascend4 ,node #aa #bi #cj ,that is1 she was within half a degree of coming round to it again2 and therefore1 being so near1 she must have been totally1 and almost centrally eclipsed4 ,,example ,,ii ,to find the ,suns distance from the ,node at the ,time of ,new ,moon in ,march1 the year before ,,christ #dbd1 ,o4 ,s4 ,the years #dbc added to #aggg make #bbjj1 or #bb ,centuries4 ,sun from ,node s ,at the mean time of ,new ,moon in ,march #aggg1 ,tab4 ,i4 #h #bc #cc ,from which subtract the ,sun's distance from the ,node for #bbjj years1 ,table ,v #c #f #j -------- ,remains the ,sun's distance from the ,ascending ,node1 ,march #ba1 #dbd years before ,,christ #e #ag #cc ,which1 taken from #f ,signs1 the distance of the ,nodes from each other #f #j #j -------- ,leaves the ,sun's distance at that time from the ,descending ,node1 ,descending viz4 #j #ab #bg ,which being less than #ag degrees1 shews that the ,sun was then eclipsed4 ,and as from these short ,calculations we find those two antient ,eclipses taken at a venture1 to be truly recorded2 it is natural to imagine that so are all the rest in the catalogue4 ,here follow ,,astronomical ,,tables1 for calculating the ,times of ,,new and ,,full ,,moons and ,,eclipses4 ---------------------------------------- --------------------------------- ,,table ,i4 ,the mean time of ,new ,moon in ,march1 the mean ,anomaly of the ,sun and ,moon1 the ,sun's mean ,distance from the ,ascending ,node2 with the mean ,longitude of the ,sun and ,node from the beginning of the ,sign ,aries1 at the times of all the ,new ,moons in ,march for #ajj years1 ,old ,style4 ---------------------------------------- --------------------------- ,years ,mean time ,the ,sun's ,the ,moon's,the ,sun's ,the ,sun's ,the ,node's of of ,new mean mean distance ,longitude ,longitude ,,christ4,moon in ,anomaly4 ,anomaly4 from the from from ,march4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agja #bg #ac #de #i #h #bc #j #bh #e #g #bc #ae #j #af #c #d #bb #dh #agjb #af #bb #cd #h #bg #ci #aa #g #ec #h #a #ag #j #e #bj #d #d #c #agjc #f #g #bc #h #af #ee #i #ag #da #h #i #bj #aa #bd #cg #c #ae #ag #agjd #bd #d #ee #i #d #cj #h #bc #ah #i #ah #c #j #ac #j #b #bd #eg #agje #ac #ac #dd #h #bc #ed #g #c #f #i #bf #f #j #b #ag #b #f #aa ---------------------------------------- --------------------------- #agjf #b #bb #cb #h #ac #dh #e #ab #ed #aj #d #i #aa #ba #cd #a #ag #be #agjg #ba #bj #e #i #b #ag #d #ah #ca #aa #ab #eb #j #i #eg #j #bg #e #agjh #aj #d #ed #h #ba #aj #b #bh #ai #aa #bj #ee #aa #bi #ad #j #h #ai #agji #bi #b #bf #i #i #dh #b #c #ef #j #bi #ch #j #ag #cg #aa #ag #ei #agaj #ah #aa #af #h #bh #cb #j #ac #dd #a #g #dj #j #f #ed #aj #bi #ad ---------------------------------------- --------------------------- #agaa #g #bj #e #h #ag #bg #aj #bc #cc #a #ae #dc #aa #bf #aa #aj #aj #bh #agab #be #ag #cf #i #e #h #i #bi #aj #b #bd #bf #j #ad #cd #i #bj #h #agac #ae #b #be #h #be #dh #h #h #eh #c #b #bi #j #c #ej #i #a #ba #agad #d #aa #ad #h #ad #eb #f #af #df #c #aj #cb #aa #bc #g #h #ab #ce #agae #bc #h #df #i #c #cg #e #bd #bb #d #ai #ae #j #aa #cj #g #bb #ae ---------------------------------------- --------------------------- #agaf #aa #ag #ce #h #ba #bf #d #d #aa #d #bg #ah #j #j #dg #g #c #bi #agag #a #b #bc #h #aa #eh #b #ac #ei #e #e #bj #aa #bj #d #f #ad #dd #agah #ai #bc #ef #i #j #ca #a #ai #cf #f #ad #c #j #h #bg #e #bd #bd #agai #i #h #de #h #ai #dg #aa #bi #bd #f #bb #f #aa #bg #dc #e #e #cg #agbj #bg #f #ag #i #h #i #aa #e #a #h #j #di #j #af #f #d #ae #ag ---------------------------------------- --------------------------- #agba #af #ae #f #h #bg #be #i #ad #di #h #h #eb #j #e #bc #c #bf #ca #agbb #e #bc #ee #h #af #da #g #bd #ch #h #af #ee #aa #bd #dj #c #g #de #agbc #bd #ba #bg #i #e #c #g #j #ae #i #be #ch #j #ac #d #b #ag #bf #agbd #ac #f #af #h #bd #ai #e #aj #c #aj #c #da #j #b #bb #a #bh #da #agbe #b #ae #d #h #ac #de #c #ai #ea #aj #aa #dc #aa #ba #ci #a #i #ef ---------------------------------------- --------------------------- #agbf #ba #ab #cg #i #a #eg #b #be #bh #aa #bj #bf #j #aj #c #j #ai #cg #agbg #aj #ba #bf #h #ba #ac #a #e #af #aa #bh #bi #aa #bi #bj #j #j #ea #agbh #bh #ah #eh #i #i #ce #j #aj #ec #a #g #ac #j #ag #dc #aa #aj #cj #agbi #ah #c #dg #h #bh #ea #aj #bj #da #a #ae #ae #j #g #j #aj #ba #de #agcj #g #ab #cf #h #ah #g #i #j #bi #a #bc #ah #aa #bf #ag #aj #b #ei ---------------------------------------- --------------------------- #agca #bf #aj #h #i #f #bi #h #f #f #c #b #a #j #ad #dj #i #ab #ci #agcb #ad #ah #eg #h #be #de #f #ae #ed #c #aj #c #j #c #eg #h #bc #ed #agcc #d #c #de #h #ad #di #d #be #dc #c #ah #f #aa #bc #ad #h #e #g #agcd #bc #a #ah #i #c #be #d #a #bj #d #bf #di #j #aa #cg #g #ad #dh #agce #ab #aj #g #h #bb #ci #b #aa #h #e #d #eb #j #j #ed #f #bf #a ---------------------------------------- --------------------------- #agcf #cj #g #ci #j #aa #a #a #af #de #f #ac #ce #j #ai #ag #f #e #db #agcg #ai #af #bh #i #j #a #aa #bf #cc #f #ba #ch #j #h #cd #e #af #ef #agch #i #a #ag #h #ai #cc #aj #f #ba #f #bi #db #aa #bg #ea #d #bh #i #agci #bg #bb #di #i #g #ee #i #aa #eh #h #h #bd #j #af #ad #d #g #ej #agdj #af #g #ch #h #bg #aa #g #ba #df #h #af #bg #j #e #cj #c #ai #c ---------------------------------------- --------------------------- #agda #e #af #bf #h #af #bg #f #a #cd #h #bd #cj #aa #bd #dg #c #j #af #agdb #bd #ac #ei #i #d #di #e #g #aa #aj #c #ab #j #ac #aj #b #i #eh #agdc #ac #bb #dh #h #bd #e #c #af #ei #aj #aa #ae #j #b #bg #a #ba #ab #agdd #b #g #cf #h #ac #ba #a #bf #dh #aj #ai #ah #aa #ba #dd #a #b #be #agde #ba #e #i #i #a #dc #a #b #be #aa #bh #j #j #aj #g #j #ab #g ---------------------------------------- --------------------------- #agdf #aj #ac #eh #h #bj #ei #aa #ab #ac #j #f #c #aa #bi #dd #aa #bc #bj #agdg #bi #aa #cj #i #i #ba #aj #ag #ej #a #ad #de #j #ag #dg #aa #c #b #agdh #ag #bj #ai #h #bh #cg #h #bg #ch #a #bb #di #j #g #d #aj #ad #ae #agdi #g #e #h #h #ag #ec #g #g #bf #b #j #ec #aa #bf #ba #i #be #bh #agej #bf #b #dj #i #f #ae #f #ac #c #c #i #ce #j #ad #dd #i #e #i ---------------------------------------- --------------------------- #agea #ae #aa #bi #h #be #cb #d #bb #ea #c #ag #ch #j #d #a #h #af #bc #ageb #c #bj #ag #h #ad #dg #c #b #ci #c #be #da #aa #bc #ah #g #bg #cg #agec #bb #ag #ej #i #c #aj #b #h #af #e #d #bd #j #aa #da #g #g #ag #aged #ab #b #ci #h #bb #bf #j #ah #d #e #ab #bg #j #j #ei #f #ah #cb #agee #a #aa #bg #h #aa #da #aj #bg #eb #e #bj #cj #aa #bj #af #e #bi #de ---------------------------------------- --------------------------- #agef #ai #i #j #i #j #d #aj #c #cj #f #bi #ac #j #h #ci #e #i #bg #ageg #h #ag #di #h #ai #bj #h #ac #ah #g #aj #ae #aa #bg #ef #d #bj #da #ageh #bg #ae #ba #i #g #db #g #ah #ee #h #ae #eh #j #af #ai #d #j #ba #agei #ag #j #aj #h #bf #eh #e #bh #dc #h #bd #a #j #e #cf #c #aa #cf #agfj #e #h #eh #h #af #ac #d #h #ca #i #b #d #aa #bd #ec #b #bb #di ---------------------------------------- --------------------------- #agfa #bd #f #ca #i #d #ce #c #ad #h #aj #aj #dg #j #ac #af #b #b #bi #agfb #ac #ae #ai #h #bc #eb #a #bc #ef #aj #ah #ea #j #b #cc #a #ac #dd #agfc #c #j #h #h #ac #g #j #c #dd #aj #bf #ec #aa #ba #ej #j #bd #eg #agfd #bj #ba #da #i #a #bi #aa #i #ba #j #e #cf #j #aj #ac #j #d #cg #agfe #aj #f #cj #h #bj #df #i #ai #i #j #ac #ch #aa #bi #cj #aa #ae #eb ---------------------------------------- --------------------------- #agff #bi #d #b #i #i #h #h #bd #df #a #bb #ba #j #ag #ec #aj #be #cb #agfg #ah #ab #ea #h #bh #bd #g #d #ce #b #j #bd #j #g #aj #aj #f #dg #agfh #f #ba #ci #h #ag #ci #e #ad #bc #b #h #bg #aa #bf #bg #i #ah #a #agfi #be #ai #ab #i #f #b #d #bj #j #c #ag #j #j #ad #ej #h #bg #da #aggj #ae #d #a #h #be #ag #b #bi #dh #c #be #ab #j #d #g #h #h #ef ---------------------------------------- --------------------------- #agga #d #ab #di #h #ad #cc #a #i #cf #d #c #af #aa #bc #bd #g #bj #h #aggb #bb #aj #bb #i #b #ef #j #ae #ac #e #aa #di #j #aa #dg #f #bi #dh #aggc #aa #ai #aj #h #bb #aa #aj #be #a #e #bj #a #j #a #d #f #aa #c #aggd #a #c #ei #h #aa #bg #i #d #di #e #bh #d #aa #bj #ba #e #bb #ag #agge #bj #a #cb #h #bi #ej #h #aj #bf #g #f #d #j #h #dd #e #a #eg ---------------------------------------- --------------------------- #aggf #h #aj #bj #h #ai #e #f #bj #ad #g #ad #ej #aa #bh #a #d #ac #ab #aggg #bg #g #ec #i #g #bg #e #be #ea #h #bc #bc #j #af #bd #c #bb #eb #aggh #af #af #db #h #bf #dc #d #e #dj #i #a #cf #j #e #da #c #d #f #aggi #f #a #cj #h #ae #ei #b #ae #bh #i #i #ci #aa #bd #eh #b #ae #ai #aghj #bc #bc #c #i #d #ba #a #ba #e #aj #ah #bb #j #ac #ba #a #bd #ei ---------------------------------------- -------------------------- #agha #ac #g #eb #h #bc #cg #j #j #ec #aj #bf #bd #j #b #ch #a #f #ad #aghb #b #af #dj #h #ab #ec #aj #aj #da #aa #d #bg #aa #ba #ed #j #ag #bg #aghc #ba #ad #ac #i #a #ae #i #af #ah #j #ac #aj #j #aj #ag #aa #bg #g #aghd #i #bc #b #h #bj #cb #g #bf #f #j #ba #ac #aa #bi #cd #aa #h #bb #aghe #bh #bj #ce #i #h #ed #g #a #dc #a #bi #ef #j #ag #eg #aj #ah #b ---------------------------------------- -------------------------- #aghf #ah #e #bc #h #bh #i #e #aa #ca #b #g #ei #j #g #ad #i #bi #af #aghg #g #ad #aa #h #ag #be #c #ba #ai #b #af #b #aa #bf #ca #i #aj #bi #aghh #be #aa #dd #i #e #dg #b #bf #ef #c #bd #de #j #ad #ed #h #bj #i #aghi #ad #bj #cc #h #be #c #a #f #de #d #b #dg #j #d #aa #h #a #be #agij #d #e #ba #h #ad #ai #aa #af #cc #d #aj #ej #aa #bc #bh #g #ab #ch ---------------------------------------- -------------------------- #agia #bc #b #ed #i #b #da #aj #bb #aj #e #ai #cc #j #aa #ea #f #bb #ah #agib #aa #aa #dc #h #ba #eg #i #a #eh #e #bg #ef #j #a #g #f #c #cb #agic #j #bj #ca #h #aa #ab #g #aa #de #f #e #ci #aa #bj #bd #e #ad #de #agid #ai #ah #d #h #bi #ce #f #ag #bc #g #ad #bb #j #h #dh #d #bd #bg #agie #i #b #eb #h #ah #ea #d #bg #aa #g #bb #be #aa #bh #f #d #e #da ---------------------------------------- -------------------------- #agif #bg #j #be #i #g #ac #d #b #dh #i #a #h #j #af #bi #c #ae #ba #agig #af #i #ad #h #bf #bi #b #ab #cf #i #i #aj #j #e #df #b #bf #cf #agih #e #ah #b #h #ae #dd #j #bb #bd #i #ag #ac #aa #be #c #b #g #ej #agii #bd #ae #ce #i #d #f #aa #bh #a #aj #be #ef #j #ac #bf #a #ag #cj #ahjj #ac #j #bd #h #bc #bc #aj #g #di #aa #c #ei #j #b #dc #j #bh #dd ---------------------------------------- -------------------------- ---------------------------------------- --------------------------------- ,,table ,,ii4 ,the mean ,new ,moons1 c4 in ,march to the ,new ,style4 ---------------------------------------- --------------------------- ,years ,mean time ,the ,sun's ,the ,moon's,the ,sun's ,the ,sun's ,the ,node's of of ,new mean mean distance ,longitude ,longitude ,,christ4,moon in ,anomaly4 ,anomaly4 from the from from ,march4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agec #d #e #f #g #d #b #a #ab #bg #d #c #dd #aa #ab #ce #g #h #ej #aged #bc #b #ci #h #bb #bf #j #ah #d #e #ab #bg #j #j #ei #f #ah #cb #agee #ab #aa #bg #h #aa #da #aj #bg #eb #e #bj #bi #aa #bj #af #e #bi #de ---------------------------------------- --------------------------- #agef #cj #i #j #i #j #c #aj #c #bi #f #bi #ab #j #h #ci #e #i #bg #ageg #ai #ag #di #h #ai #ai #h #ac #ag #g #g #ae #aa #bg #ef #d #bj #da #ageh #i #b #cg #h #h #ce #f #bc #e #g #ae #ah #aa #ag #ac #d #a #ed #agei #bh #j #i #h #bf #eh #e #bh #dc #h #bd #a #j #e #cf #c #aa #cf #agfj #af #h #eh #h #af #ad #d #h #ca #i #b #d #aa #bd #ec #b #bb #di ---------------------------------------- --------------------------- #agfa #e #g #dg #h #e #bi #b #ah #ai #i #aj #i #aa #ad #aj #b #d #a #agfb #bd #ae #ai #h #bc #eb #a #bc #ef #aj #ah #ea #j #b #cc #a #ac #dd #agfc #ad #j #h #h #ac #g #j #c #dd #aj #bf #ec #aa #ba #ej #j #bd #eg #agfd #b #h #eg #h #b #bc #aj #ac #cb #aa #d #eg #aa #aa #g #j #f #aj #agfe #ba #f #cj #h #bj #df #i #ai #i #j #ac #ch #aa #bi #cj #aa #ae #eb ---------------------------------------- --------------------------- #agff #aj #ae #ah #h #aj #a #g #bh #eh #j #ba #da #aa #ah #dg #aj #bg #e #agfg #bi #ab #ea #h #bh #bc #g #d #ce #b #j #bc #j #g #aj #aj #f #dg #agfh #ag #ba #ci #h #ag #ci #e #ad #bc #b #h #bf #aa #bf #bg #i #ah #a #agfi #g #f #bh #h #f #ee #c #bd #aa #b #af #bi #aa #ae #dd #h #bi #ae #aggj #bf #d #a #h #be #ah #b #bi #dh #c #be #aa #j #d #g #h #h #ef ---------------------------------------- --------------------------- #agga #ae #ab #di #h #ad #cc #a #i #cf #d #c #af #aa #bc #bd #g #bj #h #aggb #c #ba #ch #h #c #di #aa #ai #bd #d #aa #ai #aa #ab #da #g #a #bb #aggc #bb #ai #aj #h #bb #aa #aj #be #a #e #bj #a #j #a #d #f #aa #c #aggd #ab #c #ei #h #aa #bg #i #d #di #e #bh #d #aa #bj #ba #e #bb #ag #agge #a #ab #dh #h #j #dc #g #ad #cg #f #f #g #aa #i #ch #e #c #cj ---------------------------------------- --------------------------- #aggf #ai #aj #bj #h #ai #e #f #bj #ad #g #ad #ej #aa #bh #a #d #ac #ab #aggg #h #ai #i #h #h #ba #e #j #b #g #bb #ec #aa #ag #ah #c #bd #be #aggh #bg #af #db #h #bf #dc #d #e #dj #i #a #cf #j #e #da #c #d #f #aggi #ag #a #cj #h #ae #ei #b #ae #bh #i #i #ci #aa #bd #eh #b #ae #ai #aghj #e #aj #ai #h #e #ae #j #be #af #i #ag #db #aa #ad #ae #a #bf #cb ---------------------------------------- --------------------------- #agha #bd #g #eb #h #bc #cg #j #j #ec #aj #bf #bd #j #b #ch #a #f #ad #aghb #ac #af #dj #h #ab #ec #aj #aj #da #aa #d #bg #aa #ba #ed #j #ag #bg #aghc #c #a #bi #h #b #h #h #bj #bi #aa #ab #cj #aa #aa #aa #aa #bh #dj #aghd #bj #bc #b #h #bj #cb #g #bf #f #j #ba #ac #aa #bi #cd #aa #h #bb #aghe #aj #g #ej #h #i #dg #f #e #ed #j #bi #af #aa #ah #ea #aj #ai #ce ---------------------------------------- --------------------------- #aghf #bi #e #bc #h #bh #i #e #aa #ca #b #g #ei #j #g #ad #i #bi #af #aghg #ah #ad #aa #h #ag #be #c #ba #ai #b #af #b #aa #bf #ca #i #aj #bi #aghh #f #bc #j #h #f #da #b #a #g #b #bd #e #aa #ae #dh #h #ba #dc #aghi #be #bj #cc #h #be #c #a #f #de #d #b #dg #j #d #aa #h #a #be #agij #ae #e #ba #h #ad #ai #aa #af #cc #d #aj #ej #aa #bc #bh #g #ab #ch ---------------------------------------- --------------------------- #agia #d #ad #aj #h #c #cd #i #bf #ba #d #ah #ec #aa #ab #dd #f #bc #ea #agib #bb #aa #dc #h #ba #eg #i #a #eh #e #bg #cf #j #a #g #f #c #cb #agic #aa #bj #ca #h #aa #ab #g #aa #de #f #e #ci #aa #bj #bd #e #ad #de #agid #a #f #bj #h #j #bi #e #ba #cd #f #ac #db #aa #i #bb #d #g #ae #agie #bj #b #eb #h #ah #ea #d #bg #aa #g #bb #be #aa #bh #f #d #e #da ---------------------------------------- --------------------------- #agif #h #aa #da #h #h #f #c #f #ei #h #j #bh #aa #ag #bc #c #af #ed #agig #bg #i #ad #h #bf #bi #b #ab #cf #i #i #aj #j #e #df #b #bf #cf #agih #af #ah #b #h #ae #dd #j #bb #bd #i #ag #ac #aa #be #c #b #g #ej #agii #f #b #ea #h #e #j #aa #b #ab #i #be #af #aa #ad #bj #a #ai #c #ahjj #be #j #bd #h #bc #bc #aj #g #di #aa #c #ei #j #b #dc #j #bh #dd ---------------------------------------- --------------------------- ---------------------------------------- --------------------------------- ,,table ,,iii4 ,the mean time of ,full ,moon in ,march1 the mean ,anomaly of the ,sun and ,moon1 the ,sun's mean ,distance from the ,ascending ,node2 with the mean ,longitude of the ,sun and ,node from the beginning of the ,sign ,aries1 at the time of all the ,full ,moons in ,march for #ajj years1 ,old ,style4 ---------------------------------------- --------------------------- ,years ,mean time ,the ,sun's ,the ,moon's,the ,sun's ,the ,sun's ,the ,node's of of ,full mean mean distance ,longitude ,longitude ,,christ4,moon in ,anomaly4 ,anomaly4 from the from from ,march4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agja #ab #ai #bc #h #bc #ef #f #ae #aa #g #g #ee #j #a #cj #d #bc #ce #agjb #b #d #ab #h #ac #f #d #bd #ei #g #ae #eg #aa #bj #dg #d #d #dh #agjc #ba #a #de #i #a #bh #d #j #ce #h #bd #dj #j #i #aj #c #ad #cj #agjd #i #aj #cc #h #ai #eg #b #aj #bd #i #b #dc #aa #bh #bg #b #be #dc #agje #bh #h #f #i #h #bg #a #af #j #aj #aa #bf #j #af #ej #b #e #be ---------------------------------------- --------------------------- #agjf #ag #af #ed #h #bh #aa #aa #be #dh #aj #ai #bi #j #f #g #a #af #ch #agjg #g #a #dc #h #ag #dd #aj #e #cg #aj #bg #cb #aa #be #bd #j #bg #ea #agjh #bd #bc #af #i #e #dc #i #aa #ad #j #f #ae #j #ac #dg #j #g #cc #agji #ad #h #d #h #be #ae #g #ba #b #j #ad #ah #j #c #d #aa #ah #df #agaj #c #af #ed #h #ac #ei #f #j #ej #j #bb #ba #aa #bb #ba #aa #j #j ---------------------------------------- --------------------------- #agaa #bb #ad #bg #i #b #j #e #f #bg #b #a #c #j #aj #dd #aj #i #db #agab #aj #bc #ad #h #bj #ce #c #af #af #b #i #f #j #j #a #i #bj #ee #agac #bi #bj #dg #i #aj #ba #b #ba #eb #c #ag #dh #j #ah #bc #i #j #ce #agad #ai #e #cf #h #bi #be #a #a #dj #c #be #ec #j #g #dj #h #aa #dh #agae #h #ad #bd #h #ai #d #aa #aa #bh #d #c #ef #aa #bf #eg #g #bc #a ---------------------------------------- --------------------------- #agaf #bf #aa #eg #i #e #ei #j #ag #e #e #ab #ch #j #ae #bj #g #b #dc #agag #ae #bj #de #h #bf #ca #ah #bf #ec #e #bj #da #j #d #cg #f #ac #ef #agah #e #e #cd #h #ae #eh #g #f #db #e #bh #dd #aa #bc #ed #e #be #aj #agai #bd #c #g #i #d #bj #f #ab #ah #g #g #bf #j #ab #ag #e #d #eb #agbj #ab #aa #ee #h #bc #cf #d #bb #g #g #ae #bi #j #a #cd #d #af #e ---------------------------------------- --------------------------- #agba #a #bj #dd #h #ab #eb #c #a #ee #g #bc #cb #aa #bj #ea #c #bg #ah #agbb #bj #ah #ag #i #a #ad #b #g #cb #i #b #ae #j #i #ad #c #f #ei #agbc #aj #c #e #h #bj #cj #j #ag #ba #i #aj #ah #aa #bh #ca #b #ah #ab #agbd #bh #j #ch #i #h #eb #aa #bb #eg #aj #ai #j #j #af #ee #a #bg #ee #agbe #ag #i #bf #h #bh #ah #aj #b #de #aj #bg #c #j #f #ab #a #i #i ---------------------------------------- --------------------------- #agbf #f #ah #ae #h #ag #bd #h #ab #cd #aa #e #f #aa #be #cj #j #bj #bc #agbg #be #ae #dh #i #e #df #g #ah #aj #j #ac #di #j #ac #ec #j #j #e #agbh #ad #j #cf #h #be #b #e #bg #ei #j #ba #eb #j #c #aj #aa #aa #ah #agbi #c #i #be #h #ad #ah #d #g #dg #j #bi #ee #aa #bb #bg #aj #bb #cb #agcj #bb #f #eh #i #b #dj #c #ac #bc #b #h #ch #j #aj #ej #aj #b #ac ---------------------------------------- --------------------------- #agca #aa #ae #df #h #ba #ef #a #bc #ab #b #af #da #j #j #g #i #ac #bf #agcb #bi #ac #ai #i #aj #ah #j #bh #dh #c #be #bc #j #ah #cj #h #bc #h #agcc #ah #bb #g #h #bi #bb #aa #h #cg #d #c #bf #j #g #dg #h #d #ba #agcd #h #f #ef #h #ah #ej #i #ah #bf #d #aa #bi #aa #bg #d #g #ae #cd #agce #bg #d #bi #i #g #ab #h #bd #b #e #bj #ab #j #ae #bg #f #be #ae ---------------------------------------- --------------------------- #agcf #ae #ac #ag #h #bf #bi #g #c #ea #e #bh #ae #j #d #dd #f #f #bi #agcg #d #bb #f #h #ae #dd #e #ac #ci #f #f #ah #aa #bd #a #e #ag #db #agch #bc #ai #ci #i #d #f #d #ai #ae #g #ae #a #j #ab #bd #d #bg #bd #agci #ac #d #bg #h #bc #bb #b #bi #d #g #bc #d #j #a #da #d #h #cg #agdj #a #ac #af #h #ab #ch #a #h #eb #h #a #g #aa #bj #eg #c #ai #ej ---------------------------------------- --------------------------- #agda #bj #aj #dh #i #a #j #j #ad #bh #i #i #di #j #i #bj #b #bi #cj #agdb #i #ai #cg #h #bj #af #aj #bd #ag #i #ag #eb #aa #bh #cg #b #aj #dd #agdc #bh #ag #aj #i #h #ch #i #bi #ec #aj #bf #ce #j #ag #j #a #bj #bf #agdd #ag #a #eh #h #bg #ed #h #i #db #aa #d #ch #j #f #ag #a #a #ci #agde #f #aj #dg #h #ag #aj #f #ai #ca #aa #ab #da #aa #be #cd #j #ab #eb ---------------------------------------- --------------------------- #agdf #be #h #ai #i #e #cb #e #be #g #j #ba #bd #j #ac #eg #aa #bb #cd #agdg #ad #ag #h #h #bd #dh #d #d #ef #j #bi #bg #j #c #ad #aa #c #dg #agdh #c #a #eg #h #ad #d #b #ad #dd #a #g #cj #aa #bb #ca #aj #ae #j #agdi #ba #bc #cj #i #b #bf #a #bj #bj #b #af #ab #j #aj #ed #i #bd #db #agej #aa #h #ah #h #ba #db #j #j #i #b #bd #ae #j #j #aa #i #e #ei ---------------------------------------- --------------------------- #agea #cj #e #ea #i #aj #e #aa #e #de #d #b #eh #j #ah #cd #h #ae #cg #ageb #ah #ad #ci #h #bi #bj #i #ae #cc #d #aa #a #j #g #ea #g #bf #ej #agec #g #bc #ah #g #ah #ce #g #be #ba #d #ai #d #aa #bg #h #g #h #d #aged #bf #ba #a #i #f #ei #g #j #eh #g #bg #dg #j #ae #cb #f #ag #de #agee #af #e #di #h #bf #ad #e #aj #df #f #e #di #j #d #di #e #bi #j ---------------------------------------- --------------------------- #agef #d #ad #ch #h #ae #cj #c #bj #ce #f #ac #eb #aa #bd #f #e #aj #ad #ageg #bc #ab #aa #i #c #ec #b #bf #ab #g #be #ce #j #ab #bi #d #ai #ed #ageh #ab #bj #ei #h #bc #h #a #e #ei #h #j #ch #j #a #df #d #a #i #agei #b #e #dg #h #ab #be #aa #ae #dh #h #h #da #aa #ba #c #c #ab #bb #agfj #bj #c #bj #i #j #df #aj #ba #be #i #ag #bd #j #i #bf #b #bb #b ---------------------------------------- --------------------------- #agfa #i #ab #i #h #bj #b #i #a #ac #i #be #bg #aa #bh #dc #b #c #af #agfb #bh #i #da #i #h #be #h #f #ej #aa #d #aa #j #ag #f #a #ab #eg #agfc #ag #ah #cj #h #bg #dj #f #af #ch #aa #ab #ac #j #f #bc #j #bd #aa #agfd #f #c #ai #h #af #ef #d #bf #bf #aa #bj #af #aa #be #dj #j #e #bd #agfe #be #j #eb #i #e #ai #d #b #c #j #bh #eh #j #ad #c #aa #ae #e ---------------------------------------- --------------------------- #agff #ad #i #dj #h #bd #cd #b #aa #eb #a #g #a #j #c #bj #aj #bf #bj #agfg #g #ah #bi #h #ac #ej #j #ba #da #a #ae #d #aa #bb #cg #aj #g #cd #agfh #ba #af #a #i #b #ab #aa #bg #ag #b #bc #dg #j #aa #j #i #ag #ad #agfi #aa #j #ej #h #ba #bh #aj #g #i #c #a #di #j #j #ag #h #bh #bh #aggj #j #i #ci #h #aj #dd #h #af #eg #c #i #eb #aa #ai #ed #h #i #db ---------------------------------------- --------------------------- #agga #ai #g #aa #h #bi #f #g #bb #cj #d #ah #cf #j #g #eg #g #ai #ba #aggb #g #af #j #h #ah #bb #f #b #ah #d #bf #ci #aa #bg #ad #g #j #ce #aggc #bf #ac #cb #i #f #dd #e #g #ee #f #e #ba #j #ae #cg #f #aj #af #aggd #ae #bb #ba #h #bf #j #c #ag #dc #f #ac #bd #j #d #ed #e #ba #ca #agge #e #g #aj #h #ae #af #a #bg #ca #f #ba #bg #aa #bd #aa #e #b #dd ---------------------------------------- --------------------------- #aggf #bc #d #db #i #c #ch #a #c #h #h #j #aj #j #ab #cd #d #ab #be #aggg #ab #ac #ca #h #bb #ed #aa #ab #ef #h #h #ac #j #a #ea #h #bc #cj #aggh #a #bb #bj #h #ab #aj #i #bb #de #h #af #af #aa #ba #h #c #d #eb #aggi #bj #ai #eb #i #j #cb #h #bh #bb #i #bd #ei #j #i #ca #b #ad #cb #aghj #i #d #da #h #ai #dh #g #h #aj #aj #c #a #aa #bh #dh #a #be #dg ---------------------------------------- --------------------------- #agha #bh #b #ad #i #h #i #f #ac #dg #aa #aa #dd #j #ag #aa #a #e #bg #aghb #ai #aa #b #h #bg #bh #d #bc #cd #aa #ai #dg #j #f #bg #j #f #da #aghc #f #ai #ea #h #af #dd #c #c #bc #aa #bg #ej #aa #be #dd #aa #bg #ed #aghd #bd #ag #bd #i #e #d #b #i #j #a #f #ce #j #ad #g #aa #g #ce #aghe #ad #b #ab #h #bd #bj #j #ah #dh #a #ad #cf #j #c #bd #aj #ah #dh ---------------------------------------- --------------------------- #aghf #c #aa #a #h #ac #cf #aj #bh #cg #a #bb #ci #aa #bb #da #aj #j #b #aghg #bb #h #cc #i #a #eg #aj #d #ac #c #a #bb #j #aa #d #i #i #db #aghh #aj #ag #bb #h #ba #ad #h #ad #b #c #i #be #j #j #ba #h #bj #eg #aghi #bi #ad #ee #i #i #cf #g #ai #ci #d #ah #g #j #ah #dd #h #j #ch #agij #ah #bc #dc #h #bh #eb #e #bi #bg #d #bf #aj #j #h #a #g #aa #ea ---------------------------------------- --------------------------- #agia #h #h #cb #h #ah #h #d #i #ae #e #d #ac #aa #bg #ag #f #bc #d #agib #bf #f #e #i #f #bj #c #ad #eb #f #ab #ef #j #ae #dj #f #b #de #agic #ae #ad #ec #h #be #df #a #bd #dj #f #bj #ei #j #d #eh #e #ac #ei #agid #d #bc #db #h #ae #b #j #d #bi #f #bi #b #aa #bd #ae #d #be #ac #agie #bc #ba #ad #i #c #ad #aa #aj #e #h #g #de #j #ab #ci #d #d #ed ---------------------------------------- --------------------------- #agif #ab #f #c #h #bb #ci #i #ai #ec #h #ae #dh #j #a #ef #c #af #h #agig #a #ad #eb #h #aa #ee #g #bi #db #h #bc #ej #aa #ba #ac #b #bg #bc #agih #bj #ab #bd #i #j #g #g #e #ah #aj #b #cc #j #i #cf #b #g #c #agii #i #ba #ac #h #ai #cc #e #ae #f #aj #aj #cf #aa #bh #ec #a #ah #ah #ahjj #bg #ah #df #i #g #df #d #bj #dc #aa #ai #ai #j #ag #af #j #bg #eg ---------------------------------------- --------------------------- ---------------------------------------- --------------------------------- ,,table ,,iv4 ,the mean ,full ,moons1 c4 in ,march to the ,new ,style4 ---------------------------------------- --------------------------- ,years ,mean time ,the ,sun's ,the ,moon's,the ,sun's ,the ,sun's ,the ,node's of of ,full mean mean distance ,longitude ,longitude ,,christ4,moon in ,anomaly4 ,anomaly4 from the from from ,march4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- --------------------------- #agec #ah #bc #ah #g #ah #ce #g #be #ba #d #ai #d #aa #bg #h #g #h #d #aged #h #h #ag #g #g #ec #f #e #aj #d #bg #g #aa #af #bf #f #ai #ah #agee #bg #e #di #h #bf #ad #e #aj #df #f #e #di #j #d #di #e #bi #j ---------------------------------------- --------------------------- #agef #ae #ad #ch #h #ae #cj #c #bj #ce #f #ac #eb #aa #bd #f #e #aj #ad #ageg #d #bc #bg #h #d #cf #b #j #bc #f #ba #ee #aa #ac #bc #d #ba #bg #ageh #bc #bj #ei #h #bc #h #a #e #ei #h #j #ch #j #a #df #d #a #i #agei #ac #e #dg #h #ab #be #aa #ae #dh #h #h #da #aa #ba #c #c #ab #bb #agfj #a #ad #cf #h #a #da #i #be #cg #h #af #dd #aa #aj #bj #b #bc #ce ---------------------------------------- --------------------------- #agfa #bj #ab #i #h #bj #b #i #a #ac #i #be #bg #aa #bh #dc #b #c #af #agfb #i #bj #eg #h #i #ai #g #aa #b #aj #c #ca #aa #ah #j #a #ad #bi #agfc #bh #ah #cj #h #bg #dj #f #af #ch #aa #ab #ac #j #f #bc #j #bd #aa #agfd #ag #c #ai #h #af #ef #d #bf #bf #aa #bj #af #aa #be #dj #j #e #bd #agfe #f #ab #h #h #f #ac #c #f #ae #aa #bh #ai #aa #ad #eg #aa #af #ch ---------------------------------------- --------------------------- #agff #be #i #dj #h #bd #cd #b #aa #eb #a #g #a #j #c #bj #aj #bf #bj #agfg #ah #ah #bi #h #ac #ej #j #ba #da #a #ae #d #aa #bb #cg #aj #g #cc #agfh #c #c #ag #h #c #f #aa #a #bi #a #bc #g #aa #aa #ed #i #ah #df #agfi #bb #j #ej #h #ba #bh #aj #g #e #c #a #di #j #j #ag #h #bh #bh #aggj #aa #i #ci #h #ae #de #h #af #ed #c #i #eb #aa #ai #cd #h #i #db ---------------------------------------- --------------------------- #agga #cj #g #aa #h #bi #f #g #bb #cj #d #ah #cf #j #g #eg #g #ai #ba #aggb #ah #af #j #h #ah #bb #f #b #ah #d #bf #ci #aa #bg #ad #g #j #ce #aggc #h #j #dh #h #g #ch #d #ab #g #e #d #db #aa #af #ca #f #aa #di #aggd #bf #bb #ba #h #bf #j #c #ag #dc #f #ac #bd #j #d #ed #e #ba #ca #agge #af #g #aj #h #ae #af #a #bg #ca #f #ba #bg #aa #bd #aa #e #b #dd ---------------------------------------- --------------------------- #aggf #d #ae #eh #h #d #cb #j #g #bj #f #bi #cj #aa #ac #bh #d #ac #eh #aggg #bc #ac #ca #h #bb #ed #aa #ab #ef #h #h #ac #j #a #ea #c #bc #ci #aggh #ab #bb #bj #h #ab #aj #i #bb #de #h #af #af #aa #ba #h #c #d #eb #aggi #b #g #h #h #a #bf #h #b #cd #h #bd #ai #aa #aj #be #b #af #e #aghj #bj #d #da #h #ai #dh #g #h #aj #aj #c #a #aa #bh #dh #a #be #dg ---------------------------------------- --------------------------- #agha #i #ac #cj #h #i #d #e #ag #ei #aj #aa #d #aa #ah #e #a #g #j #aghb #bh #aa #b #h #bg #bh #d #bc #cd #aa #ai #dg #j #f #bg #j #af #da #aghc #ag #ai #ea #h #af #dd #c #c #bc #aa #bg #ej #aa #be #dd #aa #bg #ed #aghd #f #d #dj #h #e #ei #a #ac #ab #j #e #ec #aa #ae #a #aa #i #g #aghe #be #b #ab #h #bd #bj #j #ah #dh #a #ad #cf #j #c #bd #aj #ah #dh ---------------------------------------- --------------------------- #aghf #ad #aa #a #h #ac #cf #aj #bh #cg #a #bb #ci #aa #bb #da #aj #j #b #aghg #c #ai #di #h #b #eb #i #h #be #b #j #db #aa #aa #eh #i #aa #ae #aghh #ba #ag #bb #h #ba #ad #h #ad #b #c #i #be #j #j #ba #h #bj #eg #aghi #aa #b #aa #h #aj #cj #f #bc #ea #c #ag #bh #aa #ai #ch #h #b #aj #agij #bi #bc #dc #h #bh #eb #e #bi #bg #d #bf #aj #j #h #a #g #aa #ea ---------------------------------------- --------------------------- #agia #ai #h #cb #h #ah #h #d #i #ae #e #d #ac #aa #bg #ag #f #bc #d #agib #g #ag #ba #h #g #bd #b #ai #d #e #ab #af #aa #af #cd #f #d #ag #agic #bf #ad #ec #h #be #df #a #bd #dj #f #bj #ei #j #d #eh #e #ac #ei #agid #ae #bc #db #h #ae #b #j #d #bi #f #bi #b #aa #bd #ae #d #be #ac #agie #e #h #cj #h #d #ah #aj #ad #ag #g #g #e #j #ac #cb #d #f #bf ---------------------------------------- --------------------------- #agif #bc #f #c #h #bb #ci #i #ai #ec #h #ae #dh #j #a #ef #c #af #h #agig #ab #ad #eb #h #aa #ee #g #bi #db #h #bc #ej #aa #ba #ac #b #bg #bc #agih #a #bc #dj #h #a #aa #f #i #cj #i #a #ec #aa #aj #cj #b #h #cf #agii #bj #ba #ac #h #ai #cc #e #ae #f #aj #aj #cf #aa #bh #ec #a #ah #ah #ahjj #aj #f #b #h #h #ej #c #bd #ee #aj #ah #ci #aa #ah #aj #j #bi #ca ---------------------------------------- --------------------------- ---------------------------------------- ------------------------------------ ,,tab4 ,v4 ,the first mean ,conjunction of the ,sun and ,moon after a compleat ,century1 beginning with ,march1 for #ejjj years #aj days #g hours #ef minutes 7in which time there are just #fahdc mean ,lunations7 with the mean ,anomaly of the ,sun and ,moon1 the ,sun's mean distance from the ,ascending ,node1 and the mean ,long4 of the ,sun and ,node from the beginning of the sign ,aries1 at the times of all those mean ,conjunctions4 ---------------------------------------- ------------------------------ ,centuries ,first ,the ,sun's ,the ,moon's,the ,sun's ,the ,sun's ,the ,node's of ,conjunction mean mean distance ,longitude ,longitude ,julian after a ,anomaly4 ,anomaly4 from the from from ,years4 ,century4 ,node4 ,aries4 ,aries4 ---------------------------------------- --------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- ------------------------------ #ajj #d #h #aa #j #c #ba #h #ae #bb #d #ai #bg #j #e #b #d #ad #be #bjj #h #af #bb #j #f #db #e #j #dd #i #h #ee #j #aj #d #h #bh #ea #cjj #ac #j #cc #j #aj #c #a #af #f #a #bh #bb #j #ae #f #a #ac #af #djj #ag #h #dc #j #ac #bd #aj #a #bh #f #ag #di #j #bj #h #e #bg #da #ejj #ba #af #ed #j #af #df #f #af #ej #aa #g #af #j #be #aj #aj #ab #f ---------------------------------------- ------------------------------ #fjj #bf #a #e #j #bj #g #c #b #ab #c #bf #dd #a #j #ab #b #bf #cb #gjj #j #bj #cb #aa #bd #bb #aj #ba #de #g #ae #ca #j #f #g #g #i #bd #hjj #e #d #dc #aa #bg #dc #g #g #g #j #d #eh #j #aa #i #aa #bc #di #ijj #i #ab #ed #j #a #d #c #bb #bi #d #bd #be #j #af #ab #d #h #ac #ajjj #ac #ba #e #j #d #be #j #g #ea #i #ac #ec #j #ba #ad #h #bb #ci ---------------------------------------- ------------------------------ #aajj #ah #e #af #j #g #df #h #bc #ac #b #c #bj #j #bf #af #a #g #d #abjj #bb #ac #bf #j #aa #g #e #h #ce #f #bb #dg #a #a #ah #e #ba #bi #acjj #bf #ba #cg #j #ad #bh #a #bc #eg #aa #ab #ae #a #f #bj #aj #e #ee #adjj #a #ag #d #aa #ah #dc #i #ac #cj #c #a #b #j #ab #ae #b #ah #dg #aejj #f #a #ae #aa #bb #d #e #bh #eb #g #bj #bi #j #ag #ag #g #c #ab ---------------------------------------- ------------------------------ #afjj #aj #i #bf #aa #be #be #b #ad #ad #j #i #ef #j #bb #ai #aa #ag #cg #agjj #ad #ag #cg #aa #bh #df #aj #bi #cf #d #bi #bc #j #bg #bb #d #b #b #ahjj #ai #a #dh #j #b #h #g #ad #eh #i #ah #ea #a #b #bd #h #af #bg #aijj #bc #i #eh #j #e #bi #d #j #bj #b #h #ah #a #g #bf #a #j #eb #bjjj #bg #ah #i #j #h #ej #j #ae #db #f #bg #de #a #ab #bh #e #ae #ag ---------------------------------------- ------------------------------ #bajj #b #ac #cf #aa #ac #e #h #e #ae #aj #af #cb #j #ah #bd #i #bh #h #bbjj #f #ba #dg #aa #af #bf #d #bj #cg #c #f #j #j #bc #bf #b #ab #cd #bcjj #aa #e #eh #aa #ai #dg #a #e #ei #g #be #bg #j #bh #bh #f #bf #ei #bdjj #ae #ad #i #aa #bc #h #i #ba #ba #j #ad #ed #a #c #cj #aa #aa #bd #bejj #ai #bb #bj #aa #bf #bi #f #f #dc #e #d #aa #a #h #cb #c #be #di ---------------------------------------- ------------------------------ #bfjj #bd #f #ca #aa #bi #ej #b #bb #d #i #bc #di #a #ac #ce #h #aj #ad #bgjj #bh #ad #da #j #c #aa #aa #ag #bf #b #ac #af #a #ah #cg #j #bd #ci #bhjj #c #aj #h #aa #g #bf #f #bf #ei #f #b #c #j #bd #ca #e #g #cc #bijj #g #ah #ai #aa #aj #dg #c #ab #ba #aj #ba #cj #j #bi #cc #i #ba #eh #cjjj #ab #b #cj #aa #ad #h #aa #bg #dc #c #aj #eh #a #d #ce #b #f #bc ---------------------------------------- ------------------------------ #cajj #af #aj #da #aa #ag #cj #h #ac #e #h #aj #be #a #i #cg #f #bj #dh #cbjj #bj #ah #eb #aa #bj #ea #d #bh #bg #j #ai #eb #a #ad #ci #aa #e #ac #ccjj #be #c #c #aa #bd #aa #a #ac #di #e #i #bj #a #ai #da #c #ai #ci #cdjj #bi #aa #ad #aa #bg #cb #i #bi #aa #i #bh #dg #a #bd #dc #h #d #d #cejj #d #f #da #aa #a #dg #e #ah #dd #a #ag #cd #a #j #da #j #af #ec ---------------------------------------- ------------------------------ #cfjj #h #ad #eb #aa #d #eh #b #d #f #f #g #a #a #e #db #e #a #ai #cgjj #ab #bc #c #aa #h #i #aj #ai #bh #aj #bf #bh #a #aj #dc #i #ae #de #chjj #ag #g #ad #aa #aa #bj #g #d #ej #c #ae #ee #a #ae #de #b #j #aj #cijj #ba #ae #be #aa #ad #ca #d #bj #ab #h #e #bb #a #bj #dg #f #ad #ce #djjj #be #bc #cf #aa #ag #db #a #e #cd #j #bd #di #a #be #di #aj #bi #j ---------------------------------------- ------------------------------ #dajj #j #ai #c #aj #bb #ef #h #be #g #d #ac #cf #a #j #de #c #ab #ea #dbjj #e #c #ad #aj #bf #ag #e #aj #bi #i #c #c #a #f #dg #g #f #af #dcjj #i #aa #be #aj #bi #cg #a #be #ea #a #ab #cj #a #aa #dh #aa #be #ci #ddjj #ac #ai #cf #aa #b #eh #aj #aa #ac #f #a #eg #a #af #ea #d #aj #d #dejj #ah #c #df #aa #f #ah #f #bf #ce #aj #ba #bd #a #ba #ec #h #bi #ca ---------------------------------------- ------------------------------ #dfjj #bb #aa #eg #aa #i #ci #c #aa #ae #c #aj #ea #a #bf #ee #a #ac #ef #dgjj #bf #bj #g #aa #ab #ei #aa #bg #ai #h #j #af #b #a #eg #e #bh #ai #dhjj #a #ae #cd #aj #ag #ad #g #af #eb #aa #ai #d #a #g #ec #aj #aa #aa #dijj #e #bc #de #aj #bj #ce #d #b #ad #d #h #cj #a #ab #ee #b #be #ce #ejjj #aj #g #ef #aj #bc #ef #j #ag #cf #h #bg #eg #a #ag #eg #g #aj #j ---------------------------------------- ------------------------------ ---------------------------------------- ------------------------------------- ,,table ,,vi4 ,the mean ,anomaly of the ,sun and ,moon1 the ,sun's mean distance from the ,ascending ,node1 with the mean ,longitude of the ,sun and ,node from the beginning of the ,sign ,aries1 for #ac mean ,lunations4 ---------------------------------------- ------------------------------- ,the ,sun's ,the ,moon's,the ,sun's ,the ,sun's ,the ,node's ,lunations4 ,mean mean mean motion mean retrograde ,lunations4 ,anomaly4 ,anomaly4 from ,motion4 ,motion4 the ,node4 ---------------------------------------- --------------------- ,d4 ,h4 ,m4 s s s s s ---------------------------------------- ------------------------------- #a #bi #ab #dd #j #bi #f #j #be #di #a #j #dj #j #bi #f #j #a #cd #b #ei #a #bh #a #bh #ac #a #ba #ch #b #a #bj #a #bh #ac #j #c #h #c #hh #ad #ab #b #bg #ai #b #ag #bg #c #b #a #b #bg #ai #j #d #da #d #aah #b #ef #c #bf #bf #c #ac #af #d #b #da #c #bf #bf #j #f #ae #e #adg #ae #d #d #be #cb #d #i #e #e #c #ba #d #be #cb #j #g #di ---------------------------------------- ------------------------------- #f #agg #d #bd #e #bd #ch #e #d #ed #f #d #a #e #bd #ch #j #i #bc #g #bjf #ag #h #f #bc #dd #f #j #dc #g #d #db #f #bc #de #j #aj #eg #h #bcf #e #eb #g #bb #ej #f #bf #cb #h #e #bb #g #bb #ea #j #ab #ca #i #bfe #ah #cf #h #ba #eg #g #bb #ba #i #f #b #h #ba #eh #j #ad #d #aj #bie #g #ba #i #ba #c #h #ah #aj #aj #f #db #i #ba #d #j #ae #ch ---------------------------------------- ------------------------------- #aa #cbd #bj #e #aj #bj #i #i #ac #ei #aa #g #bb #aj #bj #aj #j #ag #ab #ab #ced #h #di #aa #ai #af #aj #i #dh #j #h #c #aa #ai #ag #j #ah #df #ac #chc #ba #cc #j #ah #bb #aa #e #cg #a #h #dc #j #ah #bc #j #bj #bj ---------------------------------------- ------------------------------- ,the first1 second1 third1 and fourth ,tables may be continued1 by means of the sixth1 to any length of time3 for1 by adding #ab ,lunations to the mean time of the ,new or ,full ,moon which happens next after the #aath day of ,march1 and then1 casting out #cfe days in common years1 and #cff days in leap-years1 we have the mean time of ,new or ,full ,moon in ,march the following year4 ,but when the mean ,new or ,full ,moon happens on or before the #aath of ,march1 there must be #ac ,lunations added to carry it to ,march again4 ,the ,anomalies1 ,sun's distance from the ,node1 and ,longitude of the ,sun1 are found the same way1 by adding them for #ab or #ac ,lunations4 ,but the retrograde ,motion of the ,node for these ,lunations must be subtracted from it's longitude from ,aries in ,march1 to have it's ,longitude or ,place in the ,march following4 ---------------------------------------- ------------ ,,table ,,vii4 ,the number of ,days1 reckoned from the beginning of ,march1 answering to the ,days of all the mean ,new and ,full ,moons4 ---------------------------------------- ,days,mar,apr,may,jun,jul,aug,sep,oct,no v,dec,jan,feb ---------------------------------------- #a #a #cb #fb #icabcaedahebaebdfbgfcjgcch #b #b #cc #fc #idabdaeeahfbafbdgbggcjhcci #c #c #cd #fd #ieabeaefahgbagbdhbghcjicdj #d #d #ce #fe #ifabfaegahhbahbdibgicajcda #e #e #cf #ff #igabgaehahibaibejbhjcaacdb ---------------------------------------- #f #f #cg #fg #ihabhaeiaijbbjbeabhacabcdc #g #g #ch #fh #iiabiafjaiabbabebbhbcaccdd #h #h #ci #fiajjacjafaaibbbbbecbhccadcde #i #i #dj #gjajaacaafbaicbbcbedbhdcaecdf #aj #aj #da #gaajbacbafcaidbbdbeebhecafcdg ---------------------------------------- #aa #aa #db #gbajcaccafdaiebbebefbhfcagcdh #ab #ab #dc #gcajdacdafeaifbbfbegbhgcahcdi #ac #ac #dd #gdajeaceaffaigbbgbehbhhcaicej #ad #ad #de #geajfacfafgaihbbhbeibhicbjcea #ae #ae #df #gfajgacgafhaiibbibfjbijcbaceb ---------------------------------------- #af #af #dg #ggajhachafibjjbcjbfabiacbbcec #ag #ag #dh #ghajiaciagjbjabcabfbbibcbcced #ah #ah #di #giaajadjagabjbbcbbfcbiccbdcee #ai #ai #ej #hjaaaadaagbbjcbccbfdbidcbecef #bj #bj #ea #haaabadbagcbjdbcdbfebiecbfceg ---------------------------------------- #ba #ba #eb #hbaacadcagdbjebcebffbifcbgceh #bb #bb #ec #hcaadaddagebjfbcfbfgbigcbhcei #bc #bc #ed #hdaaeadeagfbjgbcgbfhbihcbicfj #bd #bd #ee #heaafadfaggbjhbchbfibiiccjcfa #be #be #ef #hfaagadgaghbjibcibgjcjjccacfb ---------------------------------------- #bf #bf #eg #hgaahadhagibajbdjbgacjaccbcfc #bg #bg #eh #hhaaiadiahjbaabdabgbcjbccccfd #bh #bh #ei #hiabjaejahababbdbbgccjcccdcfe #bi #bi #fj #ijabaaeaahbbacbdcbgdcjdccecff #cj #cj #fa #iaabbaebahcbadbddbgecjeccf--- #ca #ca -- #ib---aecahd---bde---cjfccg--- ---------------------------------------- ---------------------------------------- - ,,table ,,viii4 ,the ,moon's annual ,equation4 --------------------------------------- ,sun's ,subtract ,sun's ,ano4 ------------------------,ano4 #j #a #b #c #d #e ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ---------------------------------- ,d4 ,m4 ,m4 ,m4 ,m4 ,m4 ,m4 ,d4 ---------------------------------- #j #j #aa #ah #bb #ai #aa #cj #a #j #aa #ai #bb #ai #aa #bi #b #a #aa #ai #bb #ah #aj #bh #c #a #aa #ai #bb #ah #aj #bg #d #a #ab #ai #bb #ah #aj #bf #e #b #ab #ai #bb #ah #i #be #f #b #ab #ai #ba #ah #i #bd #g #c #ac #bj #ba #ag #i #bc #h #c #ac #bj #ba #ag #h #bb #i #c #ac #bj #ba #ag #h #ba #aj #d #ad #bj #ba #ag #h #bj #aa #d #ad #bj #ba #af #g #ai #ab #d #ad #bj #ba #af #g #ah #ac #e #ad #bj #ba #af #f #ag #ad #e #ae #bj #ba #af #f #af #ae #e #ae #ba #ba #ae #f #ae #af #f #ae #ba #ba #ae #e #ad #ag #f #ae #ba #ba #ae #e #ac #ah #f #af #ba #ba #ae #e #ab #ai #g #af #ba #bj #ad #d #aa #bj #g #af #ba #bj #ad #d #aj #ba #g #af #ba #bj #ad #c #i #bb #h #ag #ba #bj #ac #c #h #bc #h #ag #ba #bj #ac #c #g #bd #i #ag #ba #bj #ac #b #f #be #i #ag #ba #bj #ac #b #e #bf #i #ah #ba #bj #ab #b #d #bg #aj #ah #ba #ai #ab #a #c #bh #aj #ah #ba #ai #ab #a #b #bi #aj #ah #bb #ai #aa #j #a #cj #aa #ah #bb #ai #aa #j #j ---------------------------------- ,sun's #aa #aj #i #h #g #f ,sun's ,ano4 ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ,ano4 ------------------------ ,add --------------------------------------- ---------------------------------------- - ,,table ,,ix4 ,equation of the ,moon's mean ,anomaly4 --------------------------------------- ,sun's ,sun's ,anom4 ,add ,anom4 ---------------------------------- #j #a #b #c #d #e ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ---------------------------------- ---------------------------------- #j #j #aj #ag #bj #ag #aj #cj #a #j #aj #ag #bj #ag #aj #bi #b #a #aa #ag #bj #ag #i #bh #c #a #aa #ah #bj #ag #i #bg #d #a #aa #ah #bj #ag #i #bf #e #b #ab #ah #bj #ag #i #be #f #b #ab #ah #bj #af #h #bd #g #b #ab #ah #bj #af #h #bc #h #c #ab #ah #bj #af #h #bb #i #c #ab #ai #bj #af #g #ba #aj #c #ac #ai #bj #af #g #bj #aa #d #ac #ai #bj #ae #g #ai #ab #d #ac #ai #bj #ae #f #ah #ac #d #ac #ai #ai #ae #f #ag #ad #e #ad #ai #ai #ae #f #af #ae #e #ad #ai #ai #ad #e #ae #af #e #ad #ai #ai #ad #e #ad #ag #f #ad #ai #ai #ad #e #ac #ah #f #ae #ai #ai #ad #d #ab #ai #f #ae #bj #ai #ac #d #aa #bj #g #ae #bj #ai #ac #d #aj #ba #g #ae #bj #ai #ac #c #i #bb #g #af #bj #ai #ac #c #h #bc #h #af #bj #ai #ab #c #g #bd #h #af #bj #ah #ab #b #f #be #h #af #bj #ah #ab #b #e #bf #i #af #bj #ah #aa #a #d #bg #i #ag #bj #ah #aa #a #c #bh #i #ag #bj #ah #aa #a #b #bi #aj #ag #bj #ah #aj #j #a #cj #aj #ag #bj #ag #aj #j #j ---------------------------------- #aa #aj #i #h #g #f ,sun's ,s4 ,s4 ,s4 ,s4 ,s4 ,s4,sun's ,anom4------------------------,anom4 ,subtract --------------------------------------- ---------------------------------------- --------------------- ,,table ,x4 ,the ,moon's elliptic ,equation4 ---------------------------------------- ------------------- ,moon's ,add ,moon's ---------------------------------------- -- ,ano4 #j #a #b #c #d #e ,ano4 ,signs ,signs ,signs ,signs ,signs ,signs ---------------------------------------- -------------- ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ---------------------------------------- -------------- #j #j #j #d #di #h #h #i #b #g #cb #d #ad #cj #a #j #aj #d #eg #h #ab #i #a #g #bg #d #f #bi #b #j #bj #e #e #h #af #i #j #g #bb #c #eh #bh #c #j #cj #e #ac #h #bj #h #ei #g #ag #c #ej #bg #d #j #dj #e #ba #h #bd #h #eh #g #ab #c #db #bf #e #j #ej #e #bi #h #bh #h #eg #g #f #c #cd #be #f #a #j #e #cg #h #ca #h #ee #g #j #c #bf #bd #g #a #aj #e #de #h #cd #h #ec #f #ed #c #ah #bc #h #a #bj #e #ec #h #cg #h #ea #f #dh #c #aj #bb #i #a #cj #f #a #h #dj #h #di #f #db #c #b #ba #aj #a #dj #f #i #h #dc #h #dg #f #cf #b #ec #bj #aa #a #ej #f #af #h #de #h #dd #f #cj #b #de #ai #ab #b #j #f #bc #h #dg #h #da #f #bd #b #cg #ah #ac #b #aj #f #cj #h #di #h #ch #f #ah #b #bi #ag #ad #b #bj #f #cg #h #ea #h #ce #f #aa #b #ba #af #ae #b #cj #f #dd #h #ec #h #cb #f #d #b #ab #ae #af #b #dj #f #ea #h #ee #h #bi #e #eg #b #c #ad #ag #b #ej #f #eh #h #eg #h #bf #e #ej #a #ed #ac #ah #c #j #g #d #h #ei #h #bc #e #dc #a #de #ab #ai #c #aj #g #aj #i #j #h #bj #e #cf #a #cf #aa #bj #c #ai #g #af #i #a #h #af #e #bi #a #bg #aj #ba #c #bh #g #bb #i #b #h #ab #e #bb #a #ai #i #bb #c #cg #g #bh #i #b #h #h #e #ae #a #aa #h #bc #c #df #g #cc #i #c #h #d #e #h #a #c #g #bd #c #ee #g #ch #i #c #h #j #e #a #j #ed #f #be #d #d #g #dc #i #d #g #ef #d #ed #j #de #e #bf #d #ac #g #dh #i #d #g #eb #d #df #j #cf #d #bg #d #bb #g #ec #i #d #g #dg #d #ch #j #bg #c #bh #d #ca #g #eh #i #c #g #db #d #cj #j #ah #b #bi #d #dj #h #c #i #c #g #cg #d #bb #j #i #a #cj #d #di #h #h #i #b #g #cb #d #ad #j #j #j ---------------------------------------- -------------- #aa #aj #i #h #g #f ,moon's ,signs ,signs ,signs ,signs ,signs ,signs ,moon's ---------------------------------------- -- ,ano4 ,subtract ,ano4 ---------------------------------------- ------------------- ---------------------------------------- ----------------------- ,,table ,,xi4 ,the ,sun's ,equation at the time of ,new and ,full ,moon4 ---------------------------------------- --------------------- ,subtract ,sun's ---------------------------------------- -- ,sun's ,anom4 #j #a #b #c #d #e ,anom4 ,signs ,signs ,signs ,signs ,signs ,signs ---------------------------------------- ---------------- ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ,h4 ,m4 ---------------------------------------- ---------------- #j #j #j #a #dd #c #b #c #cb #c #e #a #dh #cj #a #j #d #a #dg #c #c #c #cb #c #c #a #de #bi #b #j #g #a #ej #c #e #c #cb #c #b #a #db #bh #c #j #aa #a #ec #c #g #c #cb #c #j #a #ch #bg #d #j #ad #a #eg #c #i #c #cb #b #eh #a #ce #bf #e #j #ah #b #j #c #aj #c #ca #b #ef #a #ca #be #f #j #bb #b #c #c #ab #c #ca #b #ed #a #bh #bd #g #j #be #b #f #c #ad #c #ca #b #eb #a #bd #bc #h #j #bi #b #h #c #af #c #cj #b #ej #a #ba #bb #i #j #cb #b #aa #c #ag #d #cj #b #dh #a #ag #ba #aj #j #cf #b #ad #c #ah #c #cj #b #de #a #ad #bj #aa #j #dj #b #ag #c #ai #c #bi #b #dc #a #aa #ai #ab #j #dc #b #bj #c #bj #c #bi #b #dj #a #g #ah #ac #j #dg #b #bb #c #ba #c #bh #b #cg #a #d #ag #ad #j #ej #b #be #c #bb #c #bg #b #ce #a #j #af #ae #j #ed #b #bh #c #bc #c #bf #b #cb #j #ef #ae #af #j #eg #b #cj #c #bd #c #be #b #bi #j #eb #ad #ag #a #j #b #cb #c #be #c #bd #b #bf #j #di #ac #ah #a #d #b #ce #c #bf #c #bc #b #bc #j #de #ab #ai #a #g #b #ch #c #bg #c #bb #b #ba #j #da #aa #bj #a #aa #b #dj #c #bh #c #ba #b #ah #j #ch #aj #ba #a #ad #b #dc #c #bh #c #bj #b #ae #j #cd #i #bb #a #ag #b #de #c #bi #c #ai #b #ab #j #cj #h #bc #a #ba #b #dg #c #bi #c #ah #b #aj #j #bf #g #bd #a #bd #b #di #c #cj #c #ag #b #g #j #bc #f #be #a #bh #b #ea #c #cj #c #ae #b #d #j #ai #e #bf #a #ca #b #ed #c #ca #c #ac #b #a #j #ae #d #bg #a #cd #b #eg #c #ca #c #aa #a #eh #j #aa #c #bh #a #ch #b #ei #c #ca #c #i #a #ee #j #g #b #bi #a #da #c #a #c #cb #c #g #a #eb #j #d #a #cj #a #dd #c #b #c #cb #c #e #a #dh #j #j #j ---------------------------------------- ---------------- #aa #aj #i #h #g #f ,sun's ,signs ,signs ,signs ,signs ,signs ,signs ,sun's ,anom4 ---------------------------------------- -- ,anom4 ,add ---------------------------------------- --------------------- ---------------------------------------- ----------------------- ,,table ,,xii4 ,equation of the ,sun's mean ,place4 ---------------------------------------- --------------------- ,subtract ,sun's ---------------------------------------- -- ,sun's ,anom4 #j #a #b #c #d #e ,anom4 ,signs ,signs ,signs ,signs ,signs ,signs ---------------------------------------- ---------------- ---------------------------------------- ---------------- #j #j #j #j #eg #a #dj #a #ef #a #db #j #ei #cj #a #j #b #j #ei #a #da #a #ef #a #da #j #eg #bi #b #j #d #a #j #a #db #a #ef #a #dj #j #ef #bh #c #j #f #a #a #a #dc #a #ef #a #ci #j #ed #bg #d #j #h #a #b #a #dd #a #ef #a #ch #j #eb #bf #e #j #aj #a #d #a #de #a #ef #a #cf #j #ej #be #f #j #ab #a #f #a #de #a #ef #a #ce #j #dh #bd #g #j #ad #a #g #a #df #a #ee #a #cd #j #df #bc #h #j #af #a #i #a #dg #a #ee #a #cc #j #dd #bb #i #j #ah #a #aj #a #dh #a #ee #a #cb #j #db #ba #aj #j #bj #a #ab #a #dh #a #ed #a #cj #j #da #bj #aa #j #bb #a #ad #a #di #a #ed #a #bi #j #ci #ai #ab #j #bd #a #ae #a #ej #a #ed #a #bh #j #cg #ah #ac #j #bf #a #ag #a #ea #a #ec #a #bf #j #ce #ag #ad #j #bh #a #ah #a #ea #a #ec #a #be #j #cc #af #ae #j #cj #a #bj #a #eb #a #eb #a #bc #j #ca #ae #af #j #ca #a #ba #a #eb #a #eb #a #bb #j #bi #ad #ag #j #cc #a #bb #a #ec #a #ea #a #ba #j #bg #ac #ah #j #ce #a #bd #a #ec #a #ea #a #ai #j #be #ab #ai #j #cg #a #be #a #ed #a #ej #a #ah #j #bc #aa #bj #j #ci #a #bg #a #ed #a #di #a #af #j #ba #aj #ba #j #da #a #bh #a #ee #a #di #a #ad #j #ai #i #bb #j #dc #a #bi #a #ee #a #dh #a #ac #j #ag #h #bc #j #de #a #cj #a #ee #a #dg #a #aa #j #ad #g #bd #j #df #a #cb #a #ef #a #df #a #aj #j #ab #f #be #j #dh #a #cc #a #ef #a #df #a #h #j #aj #e #bf #j #ej #a #cd #a #ef #a #de #a #f #j #h #d #bg #j #eb #a #ce #a #ef #a #de #a #e #j #f #c #bh #j #ed #a #cf #a #ef #a #dd #a #c #j #d #b #bi #j #ee #a #ch #a #ef #a #dc #a #a #j #b #a #cj #j #eg #a #dj #a #ef #a #db #j #ei #j #j #j ---------------------------------------- ---------------- #aa #aj #i #h #g #f ,sun's ,signs ,signs ,signs ,signs ,signs ,signs ,sun's ,anom4 ---------------------------------------- -- ,anom4 ,add ---------------------------------------- --------------------- ---------------------------------------- - ,,table ,,xiii4 ,equation of the ,moon's ,nodes4 --------------------------------------- ,subtract ,sun's------------------------,sun's ,ano4 #j #a #b #c #d #e ,ano4 ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ---------------------------------- ---------------------------------- #j #j #e #h #aj #h #e #cj #a #j #e #h #aj #h #e #bi #b #j #e #h #aj #h #e #bh #c #j #e #h #aj #h #d #bg #d #a #e #h #aj #h #d #bf #e #a #e #h #aj #h #d #be #f #a #f #i #aj #h #d #bd #g #a #f #i #i #h #d #bc #h #a #f #i #i #h #d #bb #i #a #f #i #i #g #c #ba #aj #b #f #i #i #g #c #bj #aa #b #f #i #i #g #c #ai #ab #b #f #i #i #g #c #ah #ac #b #f #i #i #g #c #ag #ad #b #g #i #i #g #c #af #ae #b #g #i #i #g #c #ae #af #b #g #i #i #g #b #ad #ag #c #g #i #i #g #b #ac #ah #c #g #i #i #f #b #ab #ai #c #g #i #i #f #b #aa #bj #c #g #i #i #f #b #aj #ba #c #g #i #i #f #b #i #bb #d #g #i #i #f #a #h #bc #d #h #i #i #f #a #g #bd #d #h #i #i #f #a #f #be #d #h #i #i #f #a #e #bf #d #h #aj #i #e #a #d #bg #d #h #aj #i #e #a #c #bh #d #h #aj #h #e #j #b #bi #e #h #aj #h #e #j #a #cj #e #h #aj #h #e #j #j ---------------------------------- #aa #aj #i #h #g #f ,sun's ,s4 ,s4 ,s4 ,s4 ,s4 ,s4 ,sun's ,ano4 ------------------------,ano4 ,add ---------------------------------------- ,the above titles1 ,add and ,subtract1 are right when the ,equation is applied to the ,sun's mean distance from the ,node2 but when it is applied to the mean place of the ,node1 the titles must be changed4 ---------------------------------------- - ------------------------ ,,tab4 ,,xiv4 ,the ,moon's latitude in ,eclipses4 ------------------------ ,argument of ,latit4 ----------------------- ,moon fr4 ,sig4 #j ,n4 ,a4 the ,sig4 #f ,s4 ,d4 ,node4 ---------------------- ---------------------- #j #j #j #j #cj #a #j #e #ae #bi #b #j #aj #cj #bh #c #j #ae #dd #bg #d #j #bj #ei #bf #e #j #bf #ac #be #f #j #ca #bf #bd #g #j #cf #ci #bc #h #j #da #ea #bb #i #j #dg #b #ba #aj #j #eb #ac #bj #aa #j #eg #bc #ai #ab #a #b #ca #ah #ac #a #g #ch #ag #ad #a #ab #dd #af #ae #a #ag #di #ae #af #a #bb #eb #ad #ag #a #bg #ec #ac #ah #a #cb #ed #ab ---------------------- ,moon ,n4 ,d4 ,sig4 #e fr4 ,s4 ,a4 ,sig4 #aa the ,node4 ----------------------- ,argument of ,latit4 ------------------------ ,this ,table extends no farther than the limits of ,eclipses4 ,n4 ,a4 signifies ,north ,ascending ,lat4 ,s4 ,a4 ,south ,ascending2 ,n4 ,d4 ,north ,descending2 and ,s4 ,d4 ,south ,descending4 ------------------------ ---------------------------------------- ---------------- ,,table ,,xv4 ,the ,moons ,horizontal ,parallax2 the ,semidiameters and true ,horary motions of the ,sun and ,moon4 ---------------------------------------- ---------------- ,anomaly of the ,sun and ,moon4 ---------------------------------------- -------- ,moon's ,horizontal ,parallax4 ---------------------------------------- ,sun's ,semidiameter4 -------------------------------- ,moon's ,semidiamet4 ------------------------ ,moon's horary ,mot4 ---------------- ,sun's horary ,mot4 --------- ,anomaly of the ,sun and ,moon4 ---------------------------------------- ---------- s s ---------------------------------------- ---------- #j #j #ed #ei #ae #ej #ad #ed #cj #aj #b #bc #ab #j #f #ed #ei #ae #ej #ad #ee #cj #ab #b #bc #bd #ab #ee #j #ae #ej #ad #ef #cj #ae #b #bc #ah #ah #ee #d #ae #ea #ad #eg #cj #ah #b #bc #ab #bd #ee #aa #ae #ea #ad #eh #cj #bf #b #bc #f #a #j #ee #bj #ae #eb #ad #ei #cj #cd #b #bc #aa #j #f #ee #cj #ae #ec #ae #a #cj #dd #b #bd #bd #ab #ee #dj #ac #ed #ae #d #cj #ee #b #bd #ah #ah #ee #ea #ae #ee #ae #h #ca #i #b #bd #ab #bd #ef #j #ae #ef #ae #ab #ca #bc #b #be #f #b #j #ef #aa #ae #eh #ae #ag #ca #dj #b #be #aj #j #f #ef #bd #ae #ei #ae #bb #ca #eh #b #bf #bd #ab #ef #da #af #a #ae #bf #cb #ag #b #bg #ah #ah #eg #ab #af #b #ae #cj #cb #ci #b #bg #ab #bd #eg #cj #af #d #ae #cf #cc #aa #b #bh #f #c #j #eg #di #af #f #ae #da #cc #bc #b #bh #i #j #f #eh #aj #af #h #ae #df #cc #dg #b #bi #bd #ab #eh #ca #af #i #ae #eb #cd #aa #b #bi #ah #ah #eh #eb #af #aa #ae #eh #cd #cd #b #bi #ab #bd #ei #aa #af #ac #af #c #cd #eh #b #cj #f #d #j #ei #cj #af #ad #af #i #ce #bb #b #cj #h #j #f #ei #eb #af #ae #af #ad #ce #de #b #ca #bd #ab #fj #i #af #ag #af #ai #cf #j #b #ca #ah #ah #fj #bf #af #ai #af #bd #cf #bj #b #cb #ab #bd #fj #dj #af #bj #af #bh #cf #dj #b #cb #f #e #j #fj #ed #af #ba #af #ca #cg #j #b #cb #g #j #f #fa #d #af #ba #af #cd #cg #aj #b #cc #bd #ab #fa #aa #af #bb #af #cg #cg #ai #b #cc #ah #ah #fa #af #af #bb #af #ch #cg #bh #b #cc #ab #bd #fa #bj #af #bc #af #ci #cg #cf #b #cc #f #f #j #fa #bd #af #bc #af #ci #cg #dj #b #cc #f #j ---------------------------------------- ---------- ,the gradual increase or decrease of the above numbers being so small1 it is sufficient to have them to every sixth degree2 the proportions for the intermediate degrees being easily made by sight4 ---------------------------------------- ---------------- ---------------------------------- ,,table ,,xvi4 ,the ,sun's mean ,motion and ,anomaly4 -------------------------------- ,sun's mean ,sun's ,years of ,longitude mean ,christ from ,aries4 ,anomaly4 beginning----------------------- s s -------------------------------- ,o4,s4 #a #i #g #ec #aj #f #bi #ed #acja #i #ag #db #cj #f #af #eh #adja #i #ah #bg #ej #f #ae #ei #aeja #i #ai #ac #aj #f #ad #ei #afja #i #ai #eh #cj #f #ac #ei #agja #i #bj #dc #ej #f #ab #ei ,n4,s4 #agec #i #aj #af #eb #f #a #ch #ahja #i #i #ci #ci #f #j #aj ,old ,style -------------------------------- to the ,sun's mean ,sun's beginning ,years of ,motion4 mean of ,a4 ,d4 ,christ ,anomaly4 #agec2 compleat ----------------------- then s s ,new ,style -------------------------------- #a #aa #bi #de #dj #aa #bi #de #b #aa #bi #ca #bj #aa #bi #bi #c #aa #bi #ag #j #aa #bi #ad #d #j #j #a #di #aa #bi #eh #e #aa #bi #dg #bi #aa #bi #db #f #aa #bi #cc #i #aa #bi #bg #g #aa #bi #ah #di #aa #bi #aa #h #j #j #c #ch #aa #bi #ee #i #aa #bi #di #ah #aa #bi #dj #aj #aa #bi #cd #eh #aa #bi #bd #aa #aa #bi #bj #ch #aa #bi #i #ab #j #j #e #bf #aa #bi #ec #ac #aa #bi #ea #g #aa #bi #cg #ad #aa #bi #cf #dg #aa #bi #bb #ae #aa #bi #bb #bg #aa #bi #g #af #j #j #g #ae #aa #bi #ej #ag #aa #bi #eb #ee #aa #bi #ce #ah #aa #bi #ch #ce #aa #bi #bj #ai #aa #bi #bd #af #aa #bi #d #bj #j #j #i #d #aa #bi #dh #dj #j #j #ah #h #aa #bi #cf #fj #j #j #bg #ab #aa #bi #bd #hj #j #j #cf #af #aa #bi #ab #ajj #j #j #de #bj #aa #bi #j #bjj #j #a #cj #dj #aa #bh #a #cjj #j #b #af #j #aa #bg #a #djj #j #c #a #bj #aa #bf #a #ejj #j #c #df #dj #aa #be #b #fjj #j #d #cb #j #aa #bd #b #gjj #j #e #ag #bj #aa #bc #b #hjj #j #f #b #dj #aa #bb #c #ijj #j #f #dh #j #aa #ba #c #ajjj #j #g #cc #bj #aa #bj #c #bjjj #j #ae #f #dj #aa #aj #g #cjjj #j #bb #dj #j #aa #j #aj #djjj #a #j #ac #bj #aj #bj #ac #ejjj #a #g #df #dj #aj #aj #af #fjjj #a #ae #bj #j #aj #j #ai -------------------------------- ,sun's mean ,sun's ,motion4 mean ,anomaly4 ,months ----------------------- s s -------------------------------- ,jan4 #j #j #j #j #j #j #j ,feb4 #a #j #cc #ah #a #j #cc ,mar4 #a #bh #i #aa #a #bh #i ,apr4 #b #bh #db #cj #b #bh #db ,may4 #c #bh #af #dj #c #bh #ag ,june #d #bh #di #eh #d #bh #ej ,july #e #bh #bd #h #e #bh #bd ,aug4 #f #bh #eg #bf #f #bh #eg ,sep4 #g #bi #cj #dd #g #bi #cj ,oct4 #h #bi #d #ed #h #bi #d ,nov4 #i #bi #ch #ab #i #bi #cg ,dec4 #aj #bi #ab #bb #aj #bi #aa -------------------------------- ------------------ ,sun's mean ,motion and ,anomaly4 ,days4------------- s ------------------ #a #j #j #ei #h #b #j #a #eh #ag #c #j #b #eg #be #d #j #c #ef #cc #e #j #d #ee #db #f #j #e #ed #ej #g #j #e #ec #eh #h #j #g #ec #g #i #j #h #eb #ae #aj #j #i #ea #bc #aa #j #aj #ej #cb #ab #j #aa #di #dj #ac #j #ab #dh #dh #ad #j #ac #dg #eg #ae #j #ad #dg #e #af #j #ae #df #ac #ag #j #af #de #bb #ah #j #ag #dd #cj #ai #j #ah #dc #ch #bj #j #ai #db #dg #ba #j #bj #da #ee #bb #j #ba #da #c #bc #j #bb #dj #ab #bd #j #bc #ci #bj #be #j #bd #ch #bh #bf #j #be #cg #cg #bg #j #bf #cf #de #bh #j #bg #ce #ec #bi #j #bh #ce #b #cj #j #bi #cd #aj #ca #a #j #cc #ah ------------------ ,in ,leap-years1 after ,february1 add one ,day and one ,day's motion4 ------------------- ---------------------- ,sun's mean ,motion and ,anomaly4 --------------------- ,hours4 ,mot4 ,ano4 --------------- --------------------- #a #j #b #bh #b #j #d #ef #c #j #g #bd #d #j #i #ea #e #j #ab #ai #f #j #ad #dg #g #j #ag #ae #h #j #ai #dc #i #j #bb #aa #aj #j #bd #ch #aa #j #bg #f #ab #j #bi #cd #ac #j #cb #b #ad #j #cd #cj #ae #j #cf #eh #af #j #ci #bf #ag #j #da #ec #ah #j #dd #ba #ai #j #df #di #bj #j #di #ag #ba #j #ea #de #bb #j #ed #ac #bc #j #ef #dj #bd #j #ei #h #be #a #a #cf #bf #a #d #d #bg #a #f #cb #bh #a #i #j #bi #a #aa #bh #cj #a #ac #ee #ca #a #af #bc #cb #a #ah #ea #cc #a #ba #ai #cd #a #bc #dg #ce #a #bf #ae #cf #a #bh #db #cg #a #ca #aj #ch #a #cc #ch #ci #a #cf #f #dj #a #ch #cd #da #a #da #b #db #a #dc #cj #dc #a #de #eg #dd #a #dh #be #de #a #ej #ec #df #a #ec #ba #dg #a #ee #di #dh #a #eh #ag #di #b #j #dd #ej #b #c #ab #ea #b #e #dj #eb #b #h #h #ec #b #aj #cf #ed #b #ac #d #ee #b #ae #cb #ef #b #ag #ei #eg #b #bj #bg #eh #b #bb #ee #ei #b #be #bc #fj #b #bg #ea --------------------- ,in ,leap-years1 after ,february1 add one ,day and one ,day's motion4 ---------------------- ---------------------------------------- ------ ,,table ,,xvii4 ,the ,sun's ,declination in every ,degree of the ,ecliptic4 ---------------------------------------- -- ,signs #j #f #a #g #b #h ,nor4 ,sou4 ,nor4 ,sou4 ,nor4 ,sou4 ---------------------------------------- -- ---------------------------------------- -- #j #j #j #j #aa #bi #cc #bj #aa #af #cj #a #j #bc #ed #aa #ej #ce #bj #bc #di #bi #b #j #dg #dh #ab #aa #bf #bj #cf #j #bh #c #a #aa #db #ab #cb #e #bj #dg #dh #bg #d #a #ce #cd #ab #eb #ca #bj #ei #ac #bf #e #a #ei #be #ac #ab #dd #ba #aj #ae #be #f #b #bc #ad #ac #cb #ed #ba #bj #ec #bd #g #b #dg #a #ac #eb #cb #ba #ca #g #bc #h #c #aj #de #ad #ab #e #ba #dj #eh #bb #i #c #cd #bf #ad #ca #bd #ba #ej #bd #ba #aj #c #eh #d #ad #ej #bh #ba #ei #be #bj #aa #d #ba #ch #ae #i #ag #bb #h #b #ai #ab #d #de #h #ae #bg #ea #bb #af #ad #ah #ac #e #h #cd #ae #df #i #bb #bd #j #ag #ad #e #ca #ee #af #d #aa #bb #ca #ba #af #ae #e #ee #aa #af #ba #eg #bb #ch #af #ae #af #f #ah #ba #af #ci #bf #bb #dd #de #ad #ag #f #da #be #af #ef #cg #bb #ej #di #ac #ah #g #d #bc #ag #ac #ca #bb #ef #bf #ab #ai #g #bg #ae #ag #cj #g #bc #a #cf #aa #bj #g #ej #j #ag #df #ae #bc #f #bj #aj #ba #h #ab #cf #ah #b #bd #bc #aj #ch #i #bb #h #ce #e #ah #ah #c #bc #ad #bi #h #bc #h #eg #bf #ah #cc #bd #bc #ag #eb #g #bd #i #ai #ci #ah #dh #be #bc #bj #di #f #be #i #da #dc #ai #c #e #bc #bc #ai #e #bf #aj #c #cg #ai #ag #bf #bc #be #bb #d #bg #aj #be #ba #ai #ca #be #bc #bf #eg #c #bh #aj #df #ef #ai #de #c #bc #bh #e #b #bi #aa #h #bj #ai #eh #bj #bc #bh #df #a #cj #aa #bi #cc #bj #aa #af #bc #bi #j #j ---------------------------------------- -- ,signs #a #e #aj #d #i #c ,sou4 ,nor4 ,sou4 ,nor4 ,sou4 ,nor4 ---------------------------------------- -- ,if the ,sun's place be taken from the ,tables on pag4 #aad and #aae1 his declination may be had thereby1 near enough for common use1 from this ,table1 by entering it with the signs at the head and degrees at the left hand2 or with the signs at the foot and degrees at the right hand4 ,thus1 ,march the #eth1 the ,sun's place is #ad #ec 7call it #ae1 being so near7 to which answers #e #ee #aa of the south declination4 ---------------------------------------- ----- --------------------------------- ,,table ,,xviii4 ,lunations from #a to #ajjjjj4 ----------------------------- ,lunat4 ,days4 ,h4 ,m4 ,s4 ----------------------------- ,contain #a #bi #ab #dd #c #b #ei #a #bh #f #c #hh #ad #ab #i #d #aah #b #ef #ac #e #adg #ae #dj #af ----------------------------- #f #agg #d #bd #ai #g #bjf #ag #h #bb #h #bcf #e #eb #be #i #bfe #ah #cf #bh #aj #bie #g #bj #ca ----------------------------- #bj #eij #ad #da #c #cj #hhe #bb #a #cd #dj #aaha #e #bb #f #ej #adgf #ab #db #cg #fj #agga #bj #c #i ----------------------------- #gj #bjfg #c #bc #dj #hj #bcfb #aj #dd #ab #ij #bfeg #ah #d #dc #ajj #biec #a #be #ae #bjj #eijf #b #ej #cj ----------------------------- #cjj #hhei #d #ae #de #djj #aahab #e #da #j #ejj #adgfe #g #f #ae #fjj #aggah #h #ca #cj #gjj #bjfga #i #ef #de ----------------------------- #hjj #bcfbd #aa #bb #j #ijj #bfegg #ab #dg #ae #ajjj #biecj #ad #ab #cj #bjjj #eijfa #d #be #j #cjjj #hheia #ah #cg #cj ----------------------------- #djjj #aahabb #h #ej #j #ejjj #adgfeb #bc #b #cj #fjjj #aggahc #ac #ae #j #gjjj #bjfgad #c #bg #cj #hjjj #bcfbdd #ag #dj #j ----------------------------- #ijjj #bfegge #g #eb #cj #ajjjj #biecje #bb #e #bjjjj #eijfaa #bj #aj #cjjjj #hheiag #ah #ae #djjjj #aahabbc #af #bj ----------------------------- #ejjjj #adgfebi #ad #be #fjjjj #aggahce #ab #cj #gjjjj #bjfgada #aj #ce #hjjjj #bcfbddg #h #dj #ijjjj #bfeggec #f #de #ajjjjj #biecjei #d #ej ----------------------------- ,by comparing this ,table with the ,table on page #aac1 it is easy to find how many ,lunations are contained in any given number of ,sidereal1 ,julian1 and ,solar years1 from #a to #hjjj4 --------------------------------- ,,chap4 ,,xx4 ,of the fixed ,stars4 ,sidenote3 ,why the fixed ,stars appear bigger when viewed by the bare eye than when seen through a telescope4 #cia4 ,the ,stars are said to be fixed1 because they have been generally observed to keep at the same distance from each other3 their apparent diurnal revolutions being caused solely by the ,earth's turning on its ,axis4 ,they appear of a sensible magnitude to the bare eye1 because the retina is affected not only by the rays of light which are emitted directly from them1 but by many thousands more1 which falling upon our eye-lids1 and upon the aerial particles about us1 are reflected into our eyes so strongly as to excite vibrations not only in those points of the retina where the real images of the ,stars are formed1 but also in other points at some distance round about4 ,this makes us imagine the ,stars to be much bigger than they would appear1 if we saw them only by the few rays which come directly from them1 so as to enter our eyes without being intermixed with others4 ,any one may be sensible of this1 by looking at a ,star of the first ,magnitude through a long narrow tube2 which1 though it takes in as much of the sky as would hold a thousand such ,stars1 yet scarce renders that one visible4 ,sidenote3 ,a proof that they shine by their own light4 ,the more a telescope magnifies1 the less is the aperture through which the ,star is seen2 and consequently the fewer rays it admits into the eye4 ,now since the ,stars appear less in a telescope which magnifies #bjj times than they do to the bare eye1 insomuch that they seem to be only indivisible points1 it proves at once both that the ,stars are at immense distances from us1 and that they shine by their own proper light4 ,if they shone by borrowed light they would be as invisible without telescopes as the ,satellites of ,jupiter are3 for these ,satellites appear bigger when viewed with a good telescope than the largest fixed ,stars do4 ,sidenote3 ,their number much less than is generally imagined4 #cib4 ,the number of ,stars discoverable1 in either ,hemisphere1 by the naked eye1 is not above a thousand4 ,this at first may appear incredible1 because they seem to be without number3 ,but the deception arises from our looking confusedly upon them1 without reducing them into any order4 ,for look but stedfastly upon a pretty large portion of the sky1 and count the number of ,stars in it1 you will be surprised to find them so few4 ,or1 if one considers how seldom the ,moon meets with any ,stars in her way1 although there are as many about her ,path as in other parts of the ,heavens 7the ,milky way excepted7 he will soon be convinced that the ,stars are much thinner sown than he was aware of4 ,the ,british catalogue1 which1 besides the ,stars visible to the bare eye1 includes a great number which cannot be seen without the assistance of a telescope1 contains no more than #cjjj1 in both ,hemispheres4 ,sidenote3 ,the absurdity of supposing the ,stars were made only to enlighten our nights4 #cic4 ,as we have incomparably more light from the ,moon than from all the ,stars together1 it were the greatest absurdity to imagine that the ,stars were made for no other purpose than to cast a faint light upon the ,earth3 especially since many more require the assistance of a good telescope to find them out1 than are visible without that ,instrument4 ,our ,sun is surrounded by a system of ,planets and ,comets2 all which would be invisible from the nearest fixed ,star4 ,and from what we already know of the immense distance of the ,stars1 the nearest may be computed at #cb1jjj1jjj1jjj1jjj of miles from us which is more than a cannon bullet would fly in #g1jjj1jjj of years4 ,hence 'tis easy to prove1 that the ,sun seen from such a distance1 would appear no bigger than a ,star of the first magnitude4 ,from all this it is highly probable that each ,star is a ,sun to a system of worlds moving round it though unseen by us2 especially1 as the doctrine of a plurality of worlds is rational1 and greatly manifests the ,power1 ,wisdom1 and ,goodness of the great ,creator4 ,sidenote3 ,their different ,magnitudes4 #cid4 ,the ,stars1 on account of their apparently various magnitudes1 have been distributed into several classes or orders4 ,those which appear largest are called ,stars of the first magnitude2 the next to them in lustre1 ,stars of the second magnitude1 and so on to the sixth1 which are the smallest that are visible to the bare eye4 ,this distribution having been made long before the invention of telescopes1 the ,stars which cannot be seen without the assistance of these instruments are distinguished by the name of ,telescopic ,stars4 ,sidenote3 ,and division into ,constellations4 #cie4 ,the antients divided the starry ,sphere into particular ,constellations1 or ,systems of ,stars1 according as they lay near one another1 so as to occupy those spaces which the figures of different sorts of animals or things would take up1 if they were there delineated4 ,and those ,stars which could not be brought into any particular ,constellation were called unformed ,stars4 ,sidenote3 ,the use of this division4 #cif4 ,this division of the ,stars into different ,constellations or ,asterisms1 serves to distinguish them from one another1 so that any particular ,star may be readily found in the ,heavens by means of a ,celestial ,globe2 on which the ,constellations are so delineated as to put the most remarkable ,stars into such parts of the figures as are most easily distinguished4 ,the number of the antient ,constellations is #dh1 and upon our present ,globes about #gj4 ,on ,senex's ,globes are inserted ,bayer's ,letters2 the first in the ,greek ,alphabet being put to the biggest ,star in each ,constellation1 the second to the next1 and so on3 by which means1 every ,star is as easily found as if a name were given to it4 ,thus1 if the ,star in the ,constellation of the ,ram be mentioned1 every ,astronomer knows as well what ,star is meant as if it were pointed out to him in the ,heavens4 ,sidenote3 ,the ,zodiac4 #cig4 ,there is also a division of the ,heavens into three parts4 #a4 ,the ,zodiac1 77 from ,zodion an ,animal1 because most of the ,constellations in it1 which are twelve in number1 are the figures of ,animals3 as ,aries the ,ram1 ,taurus the ,bull1 ,gemini the ,twins1 ,cancer the ,crab1 ,leo the ,lion1 ,virgo the ,virgin1 ,libra the ,balance1 ,scorpio the ,scorpion1 ,sagittarius the ,archer1 ,capricornus the ,goat1 ,aquarius the ,water-bearer1 and ,pisces the ,fishes4 ,the ,zodiac goes quite round the ,heavens3 it is about #af degrees broad1 so that it takes in the ,orbits of all the ,planets1 and likewise the ,orbit of the ,moon4 ,along the middle of this ,zone or ,belt is the ,ecliptic1 or ,circle which the ,earth describes annually as seen from the ,sun2 and which the ,sun appears to describe as seen from the ,earth4 #b4 ,all that ,region of the ,heavens1 which is on the north side of the ,zodiac1 containing #ba ,constellations4 ,and #c4 that on the south side1 containing #ae4 ,sidenote3 ,the manner of dividing it by the antients4 #cih4 ,the antients divided the ,zodiac into the above #ab ,constellations or ,signs in the following manner4 ,they took a vessel with a small hole in the bottom1 and having filled it with water1 suffered the same to distil drop by drop into another ,vessel set beneath to receive it2 beginning at the moment when some ,star rose1 and continuing until it rose the next following night4 ,the water fallen down into the receiver they divided into twelve equal parts2 and having two other small vessels in readiness1 each of them fit to contain one part1 they again poured all the water into the upper vessel1 and strictly observing the rising of some ,star in the ,zodiac1 they at the same time suffered the water to drop into one of the small vessels2 and as soon as it was full1 they shifted it and set an empty one in it's place4 ,by this means1 when each vessel was full1 they observed what ,star of the ,zodiac rose2 and though not possible in one night1 yet in many1 they observed the rising of twelve ,stars1 by which they divided the ,zodiac into twelve parts4 #cii4 ,the names of the ,constellations1 and the number of ,stars observed in each of them by different ,astronomers1 are as follows4 ,key to table ,p ,ptolemy4 ,t ,tycho4 ,h ,hevelius4 ,f ,flamsteed4 ,the antient ,constellations4 ,p ,t ,h ,f ,ursa minor ,the ,little ,bear #h #g #ab #bd ,ursa major ,the ,great ,bear #ce #bi #gc #hg ,draco ,the ,dragon #ca #cb #dj #hj ,cepheus ,cepheus #ac #d #ea #ce ,bootes1 ,arctophilax #bc #ah #eb #ed ,corona ,borealis ,the northern ,crown #h #h #h #ba ,hercules1 ,engonasin ,hercules kneeling #bi #bh #de #aac ,lyra ,the ,harp #aj #aa #ag #ba ,cygnus1 ,gallina ,the ,swan #ai #ah #dg #ha ,cassiopea ,the ,lady in her ,chair #ac #bf #cg #ee ,perseus ,perseus #bi #bi #df #ei ,auriga ,the ,waggoner #ad #i #dj #ff ,serpentarius1 ,ophiuchus ,serpentarius #bi #ae #dj #gd ,serpens ,the ,serpent #ah #ac #bb #fd ,sagitta ,the ,arrow #e #e #e #ah ,aquila1 ,vultur ,the ,eagle #ab #bc #ae #ga ,antinous ,antinous #c #ai ,delphinus ,the ,dolphin #aj #aj #ad #ah ,equulus1 ,equi sectio ,the ,horse's ,head #d #d #f #aj ,pegasus1 ,equus ,the ,flying ,horse #bj #ai #ch #hi ,andromeda ,andromeda #bc #bc #dg #ff ,triangulum ,the ,triangle #d #d #ab #af ,aries ,the ,ram #ah #ba #bg #ff ,taurus ,the ,bull #dd #dc #ea #ada ,gemini ,the ,twins #be #be #ch #he ,cancer ,the ,crab #bc #ae #bi #hc ,leo ,the ,lion #cj #di #ie #ce ,coma ,berenices ,berenice's ,hair #ad #ba #dc ,virgo ,the ,virgin #cb #cc #ej #aaj ,libra1 ,chel ,the ,scales #ag #aj #bj #ea ,scorpius ,the ,scorpion #bd #aj #bj #dd ,sagittarius ,the ,archer #ca #ad #bb #fi ,capricornus ,the ,goat #bh #bh #bi #ea ,aquarius ,the ,water-bearer #de #da #dg #ajh ,pisces ,the ,fishes #ch #cf #ci #aac ,cetus ,the ,whale #bb #ba #de #ig ,orion ,orion #ch #db #fb #gh ,eridanus1 ,fluvius ,eridanus1 the ,river #cd #aj #bg #hd ,lepus ,the ,hare #ab #ac #af #ai ,canis major ,the ,great ,dog #bi #ac #ba #ca ,canis minor ,the ,little ,dog #b #b #ac #ad ,argo ,navis ,the ,ship #de #c #d #fd ,hydra ,the ,hydra #bg #ai #ca #fj ,crater ,the ,cup #g #c #aj #ca ,corvus ,the ,crow #g #d #i ,centaurus ,the ,centaur #cg #ce ,lupus ,the ,wolf #ai #bd ,ara ,the ,altar #g #i ,corona ,australis ,the southern ,crown #ac #ab ,pisces ,australis ,the southern ,fish #ah #bd ,the ,new ,southern ,constellations4 ,columba ,noachi ,noah's ,dove #aj ,robur ,carolinum ,the ,royal ,oak #ab ,grus ,the ,crane #ac ,phnix ,the ,phenix #ac ,indus ,the ,indian #ab ,pavo ,the ,peacock #ad ,apus1 ,avis ,indica ,the ,bird of ,paradise #aa ,apis1 ,musca ,the ,bee or ,fly #d ,chamleon ,the ,chameleon #aj ,triangulum ,australis ,the ,south ,triangle #e ,piscis volans1 ,passer ,the ,flying ,fish #h ,dorado1 ,xiphias ,the ,sword ,fish #f ,toucan ,the ,american ,goose #i ,hydrus ,the ,water ,snake #aj ,hevelius's ,constellations made out of the unformed ,stars4 ,hevelius4 ,flamsteed4 ,lynx ,the ,lynx #ai #dd ,leo minor ,the ,little ,lion #ec ,asterion ,chara ,the ,greyhounds #bc #be ,cerberus ,cerberus #d ,vulpecula ,anser ,the ,fox and ,goose #bg #ce ,scutum ,sobieski ,sobieski's ,shield #g ,lacerta ,the ,lizard #aj #af ,camelopardalus ,the ,camelopard #cb #eh ,monoceros ,the ,unicorn #ai #ca ,sextans ,the ,sextant #aa #da ,sidenote3 ,the ,milky ,way4 #djj4 ,there is a remarkable track round the ,heavens1 called the ,milky ,way from its peculiar whiteness1 which is owing to a great number of ,stars scattered therein2 none of which can be distinctly seen without telescopes4 ,this track appears single in some parts1 in others double4 ,sidenote3 ,lucid ,spots4 #dja4 ,there are several little whitish spots in the ,heavens1 which appear magnified1 and more luminous when seen through telescopes2 yet without any ,stars in them4 ,one of these is in ,andromeda's girdle1 first observed ,a4 ,d4 #afab1 by ,simon ,marius2 and which has some whitish rays near its middle3 it is liable to several changes1 and is sometimes invisible4 ,another is near the ,ecliptic1 between the head and bow of ,sagittarius3 it is small1 but very luminous4 ,a third is on the back of the ,centaur1 which is too far ,south to be seen in ,britain4 ,a fourth1 of a smaller size1 is before ,antinous's right foot2 having a ,star in it1 which makes it appear more bright4 ,a fifth is in the ,constellation of ,hercules1 between the ,stars and 1 which spot1 though but small1 is visible to the bare eye if the sky be clear and the ,moon absent4 ,sidenote3 ,cloudy ,stars4 ,magellanic ,clouds4 #djb4 ,cloudy ,stars are so called from their misty appearance4 ,they look like dim ,stars to the naked eye2 but through a telescope they appear broad illuminated parts of the sky2 in some of which is one ,star1 in others more4 ,five of these are mentioned by ,ptolemy4 #a4 ,one at the extremity of the right hand of ,perseus4 #b4 ,one in the middle of the ,crab4 #c4 ,one unformed1 near the ,sting of the ,scorpion4 #d4 ,the eye of ,sagittarius4 #e4 ,one in the head of ,orion4 ,in the first of these appear more ,stars through the telescope than in any of the rest1 although #ba have been counted in the head of ,orion1 and above #dj in that of the ,crab4 ,two are visible in the eye of ,sagittarius without a telescope1 and several more with it4 ,flamsteed observed a cloudy ,star in the bow of ,sagittarius1 containing many small ,stars3 and the ,star d above ,sagittary's right shoulder is encompassed with several more4 ,both ,cassini and ,flamsteed discovered one between the ,great and ,little ,dog1 which is very full of ,stars visible only by the telescope4 ,the two whitish spots near the ,south ,pole1 called the ,magellanic ,clouds by ,sailors1 which to the bare eye resemble part of the ,milky-,way1 appear through telescopes to be a mixture of small ,clouds and ,stars4 ,but the most remarkable of all the cloudy ,stars is that in the middle of ,orion's ,sword1 where seven ,stars 7of which three are very close together7 seem to shine through a cloud1 very lucid near the middle1 but faint and ill defined about the edges4 ,it looks like a gap in the sky1 through which one may see 7as it were7 part of a much brighter region4 ,although most of these spaces are but a few minutes of a degree in breadth1 yet1 since they are among the fixed ,stars1 they must be spaces larger than what is occupied by our solar ,system2 and in which there seems to be a perpetual uninterrupted day among numberless ,worlds which no human art ever can discover4 ,sidenote3 ,changes in the ,heavens4 #djc4 ,several ,stars are mentioned by antient ,astronomers1 which are not now to be found2 and others are now visible to the bare eye which are not recorded in the antient catalogues4 ,hipparchus observed a new ,star about #abj years before ,,christ2 but he has not mentioned in what part of the ,heavens it was seen1 although it occasioned his making a catalogue of the ,stars2 which is the most antient that we have4 ,sidenote3 ,new ,stars4 ,the first ,new ,star that we have any good account of1 was discovered by ,cornelius ,gemma on the #hth of ,november ,a4 ,d4 #aegb1 in the ,chair of ,cassiopea4 ,it surpassed ,sirius in brightness and magnitude2 and was seen for #af months successively4 ,at first it appeared bigger than ,jupiter to some eyes1 by which it was seen even at mid-day3 afterwards it decayed gradually both in magnitude and lustre1 until ,march #aegc1 when it became invisible4 ,on the #acth of ,august #aeif1 ,david ,fabricius observed the ,stella ,mira1 or wonderful ,star1 in the ,neck of the ,whale2 which has been since found to appear and disappear periodically1 seven times in six years1 continuing in its greatest lustre for #ae days together2 and is never quite extinguished4 ,in the year #afjj1 ,william ,jansenius discovered a changeable ,star in the ,neck of the ,swan2 which1 in time became so small as to be thought to disappear entirely1 till the years #afeg1 #afeh1 and #afei1 when it recovered its former lustre and magnitude2 but soon decayed1 and is now of the smallest size4 ,in the year #afjd ,kepler and several of his friends saw a new ,star near the heel of the right foot of ,serpentarius1 so bright and sparkling that it exceeded any thing they had ever seen before2 and took notice that it was every moment changing into some of the colours of the rainbow1 except when it was near the horizon1 at which time it was generally white4 ,it surpassed ,jupiter in magnitude1 which was near it all the month of ,october1 but easily distinguished from it by a steady light4 ,it disappeared between ,october #afje and the ,february following1 and has not been seen since that time4 ,in the year #afgj1 ,july #ae1 ,hevelius discovered a new ,star1 which in ,october was so decayed as to be scarce perceptible4 ,in ,april following it regained its lustre1 but wholly disappeared in ,august4 ,in ,march #afgb it was seen again1 but very small2 and has not been visible since4 ,in the year #afhf a new ,star was discovered by ,kirch1 which returns periodically in #djd days4 ,in the year #afgb1 ,cassini saw a ,star in the ,neck of the ,bull1 which he thought was not visible in ,tycho's time2 nor when ,bayer made his ,figures4 ,sidenote3 ,cannot be ,comets4 #djd4 ,many ,stars1 besides those above-mentioned1 have been observed to change their magnitudes3 and as none of them could ever be perceived to have tails1 'tis plain they could not be ,comets2 especially as they had no parallax1 even when largest and brightest4 ,it would seem that the periodical ,stars have vast clusters of dark spots1 and very slow rotations on their ,axis2 by which means1 they must disappear when the side covered with spots is turned towards us4 ,and as for those which break out all of a sudden with such lustre1 'tis by no means improbable that they are ,suns whose ,fuel is almost spent1 and again supplied by some of their ,comets falling upon them1 and occasioning an uncommon blaze and splendor for some time3 which indeed appears to be the greatest use of the cometary part of any system#hf4 ,sidenote3 ,some ,stars change their ,places4 ,some of the ,stars1 particularly ,arcturus1 have been observed to change their places above a minute of a degree with respect to others4 ,but whether this be owing to any real motion in the ,stars themselves1 must require the observations of many ages to determine4 ,if our solar ,system changeth its ,place1 with regard to absolute space1 this must in process of time occasion an apparent change in the distances of the ,stars from each other3 and in such a case1 the places of the nearest ,stars to us being more affected than of those which are very remote1 their relative positions must seem to alter1 though the ,stars themselves were really immoveable4 ,on the other hand1 if our own system be at rest1 and any of the ,stars in real motion1 this must vary their positions2 and the more so1 the nearer they are to us1 or the swifter their motions are2 or the more proper the direction of their motion is1 for our perception4 ,sidenote3 ,the ,ecliptic less oblique now to the ,equator than formerly4 #dje4 ,the obliquity of the ,ecliptic to the ,equinoctial is found at present to be above a third part of a degree less than ,ptolemy found it4 ,and most of the observers after him found it to decrease gradually down to ,tycho's time4 ,if it be objected1 that we cannot depend on the observations of the antients1 because of the incorrectness of their ,instruments2 we have to answer1 that both ,tycho and ,flamsteed are allowed to have been very good observers3 and yet we find that ,flamsteed makes this obliquely #b-a_/b minutes of a degree less than ,tycho did1 about #ajj years before him3 and as ,ptolemy was #acbd years before ,tycho1 so the gradual decrease answers nearly to the difference of time between these three ,astronomers4 ,if we consider1 that the ,earth is not a perfect sphere1 but an oblate spheroid1 having its ,axis shorter than its ,equatoreal diameter2 and that the ,sun and ,moon are constantly acting obliquely upon the greater quantity of matter about the ,equator1 pulling it1 as it were1 towards a nearer and nearer co-incidence with the ,ecliptic2 it will not appear improbable that these actions should gradually diminish the ,angle between those ,planes4 ,nor is it less probable that the mutual attractions of all the ,planets should have a tendency to bring the planes of all their ,orbits to a co-incidence3 but this change is too small to become sensible in many ages4 ,,chap4 ,,xxi4 ,of the ,division of ,time4 ,a perpetual ,table of ,new ,moons4 ,the ,times of the ,birth and ,death of ,,christ4 ,a ,table of remarkable ras or ,events4 #djf4 ,the parts of time are ,seconds1 ,minutes1 ,hours1 ,days1 ,years1 ,cycles1 ,ages1 and ,periods4 ,sidenote3 ,a ,year4 #djg4 ,the original standard1 or integral measure of ,time1 is a year2 which is determined by the ,revolution of some ,celestial ,body in its ,orbit1 viz4 the ,sun or ,moon4 ,sidenote3 ,tropical ,year4 #djh4 ,the time measured by the ,sun's ,revolution in the ,ecliptic1 from any ,equinox or ,solstice to the same again1 is called the ,solar or ,tropical ,year1 which contains #cfe days #e hours #dh minutes #eg seconds2 and is the only proper or natural year1 because it always keeps the same seasons to the same months4 ,sidenote3 ,sidereal year4 #dji4 ,the quantity of time1 measured by the ,sun's ,revolution1 as from any fixed ,star to the same ,star again1 is called the ,sidereal ,year2 which contains #cfe days #f hours #i minutes #ad-a_/b seconds2 and is #bj minutes #ag-a_/b seconds longer than the true ,solar ,year4 ,sidenote3 ,lunar ,year4 #daj4 ,the time measured by twelve ,revolutions of the ,moon1 from the ,sun to the ,sun again1 is called the ,lunar ,year2 it contains #ced days #h hours #dh minutes #cg seconds2 and is therefore #aj days #ba hours #j minutes #bj seconds shorter than the ,solar ,year4 ,this is the foundation of the ,epact4 ,sidenote3 ,civil ,year4 #daa4 ,the ,civil ,year is that which is in common use among the different nations of the world2 of which1 some reckon by the ,lunar1 but most by the ,solar4 ,the ,civil ,solar ,year contains #cfe days1 for three years running1 which are called ,common ,years2 and then comes in what is called the ,bissextile or ,leap-,year1 which contains #cff days4 ,this is also called the ,julian ,year on account of ,julius ,csar1 who appointed the ,intercalary-day every fourth year1 thinking thereby to make the ,civil and ,solar ,year keep pace together4 ,and this day1 being added to the #bc;d of ,february1 which in the ,roman ,calendar1 was the sixth of the ,calends of ,march1 that sixth day was twice reckoned1 or the #bc;d and #bdth were reckoned as one day2 and was called ,bis sextus dies1 and thence came the name ,bissextile for that year4 ,but in our common ,almanacks this day is added at the end of ,february4 ,sidenote3 ,lunar ,year4 #dab4 ,the ,civil ,lunar ,year is also common or intercalary4 ,the common ,year consists of #ab ,lunations1 which contain #ced days2 at the end of which1 the year begins again4 ,the ,intercalary1 or ,embolimic ,year is that wherein a month was added1 to adjust the ,lunar ,year to the ,solar4 ,this method was used by the ,jews1 who kept their account by the ,lunar ,motions4 ,but by intercalating no more than a month of #cj days1 which they called ,ve-,adar1 every third year1 they fell #c-c_/d days short of the ,solar ,year in that time4 ,sidenote3 ,roman ,year4 #dac4 ,the ,romans also used the ,lunar ,embolimic ,year at first1 as it was settled by ,romulus their first ,king1 who made it to consist only of ten months or ,lunations2 which fell #fa days short of the ,solar ,year1 and so their year became quite vague and unfixed2 for which reason1 they were forced to have a ,table published by the ,high ,priest1 to inform them when the spring and other seasons began4 ,but ,julius ,csar1 as already mentioned1 #daa1 taking this troublesome affair into consideration1 reformed the ,calendar1 by making the year to consist of #cfe days #f hours4 ,sidenote3 ,the original of the ,gregorian1 or ,new ,style4 #dad4 ,the year thus settled1 is what we still make use of in ,britain3 but as it is somewhat more than #aa minutes longer than the ,solar ,tropical ,year1 the times of the ,equinoxes go backward1 and fall earlier by one day in about #acj years4 ,in the time of the ,nicene ,council 7,a4 ,d4 #cbe47 which was #adca years ago1 the vernal ,equinox fell on the #bast of ,march3 and1 if we divide #adca by #acj1 it will quote #aa1 which is the number of days the ,equinox has fallen back since the ,council of ,nice4 ,this causing great disturbances1 by unfixing the times of the celebration of ,easter1 and consequently of all the other moveable ,feasts1 ,pope ,gregory the #acth1 in the year #aehb ordered ten days to be at once struck out of that year2 and the next day after the fourth of ,october was called the fifteenth4 ,by this means the vernal ,equinox was restored to the #bast of ,march2 and it was endeavoured1 by the omission of three intercalary days in #djj years1 to make the civil or political year keep pace with the ,solar for time to come4 ,this new form of the year is called the ,gregorian ,account or ,new ,style2 which is received in all ,countries where the ,pope's ,authority is acknowledged1 and ought to be in all places where truth is regarded4 ,sidenote3 ,months4 #dae4 ,the principal division of the year is into ,months1 which are of two sorts1 namely ,astronomical and ,civil4 ,the ,astronomical month is the time in which the ,moon runs through the ,zodiac1 and is either ,periodical or ,synodical4 ,the ,periodical ,month is the time spent by the ,moon in making one compleat ,revolution from any point of the ,zodiac to the same again2 which is #bg;d #g;h #dcm4 ,the ,synodical ,month1 called a ,lunation1 is the time contained between the ,moon's parting with the ,sun at a ,conjunction1 and returning to him again2 which is in #bi;d #ab;h #ddm4 ,the ,civil ,months are those which are framed for the uses of ,civil life2 and are different as to their names1 number of days1 and times of beginning1 in several different ,countries4 ,the first month of the ,jewish ,year fell according to the ,moon in our ,august and ,september1 ,old ,style2 the second in ,september and ,october1 and so on4 ,the first month of the ,egyptian ,year began on the #bith of our ,august4 ,the first month of the ,arabic and ,turkish ,year began the #afth of ,july4 ,the first month of the ,grecian ,year fell according to the ,moon in ,june and ,july1 the second in ,july and ,august1 and so on1 as in the following ,table4 ---------------------------------------- ------------------------- ,no ,the ,jewish year4 ,days,no ,the ,egyptian year4 ,days ---------------------------------------- ------------------------- #a ,tisri ,aug4-,sept4 #cj #a ,thoth ,august #bi #cj #b ,marchesvan ,sept4-,oct4 #bi #b ,paophi ,septemb4 #bh #cj #c ,casleu ,oct4-,nov4 #cj #c ,athir ,october #bh #cj #d ,tebeth ,nov4-,dec4 #bi #d ,chojac ,novemb4 #bg #cj #e ,shebat ,dec4-,jan4 #cj #e ,tybi ,decemb4 #bg #cj #f ,adar ,jan4-,feb4 #bi #f ,mechir ,january #bf #cj #g ,nisan or ,abib ,feb4-,mar4 #cj #g ,phamenoth ,februar4 #be #cj #h ,jiar ,mar4-,apr4 #bi #h ,parmuthi ,march #bg #cj #i ,sivan ,april-,may #cj #i ,pachon ,april #bf #cj #aj ,tamuz ,may-,june #bi #aj ,payni ,may #bf #cj #aa ,ab ,june-,july #cj #aa ,epiphi ,june #be #cj #ab ,elul ,july-,aug4 #bi #ab ,mesori ,july #be #cj ---------------------------------------- ------------------------- ,days in the year #ced ,epagomen or days added #e ---------------------------------------- --------------------------- ,in the ,embolimic year after ,days in the year #cfe ,adar they added a month called ,ve-,adar of #cj days4 ---------------------------------------- --------------------------- ---------------------------------------- --------------------------- ,no,the ,arabic and ,days,no,the ancient ,grecian year4 ,days ,turkish year4 ---------------------------------------- --------------------------- #a ,muharram ,july #af #cj #a ,hecatombon ,june-,july #cj #b ,saphar ,august #ae #bi #b ,metagitnion ,july-,aug4 #bi #c ,rabia ,i4 ,septemb4 #ac #cj #c ,boedromion ,aug4-,sept4 #cj #d ,rabia ,,ii4 ,october #ac #bi #d ,pyanepsion ,sept4-,oct4 #bi #e ,jomada ,i4 ,novemb4 #aa #cj #e ,mmacterion ,oct4-,nov4 #cj #f ,jomada ,,ii4 ,decemb4 #aa #bi #f ,posideon ,nov4-,dec4 #bi #g ,rajab ,january #i #cj #g ,gamelion ,dec4-,jan4 #cj #h ,shasban ,february #h #bi #h ,anthesterion ,jan4-,feb4 #bi #i ,ramadan ,march #i #cj #i ,elapheloblion ,feb4-,mar4 #cj #aj ,shawal ,april #h #bi #aj ,munichion ,mar4-,apr4 #bi #aa ,dulhaadah ,may #g #cj #aa ,thargelion ,april-,may #cj #ab ,dulheggia ,june #e #bi #ab ,schirrophorion ,may-,june #bi ---------------------------------------- --------------------------- ,days in the year #ced ,days in the year #ced ---------------------------------------- ----------------------------- ,the ,arabians add #aa days at the end of every year1 which keep the same months to the same seasons4 ---------------------------------------- --------------------------------- ,sidenote3 ,weeks #daf4 ,a month is divided into four parts called ,weeks1 and a ,week into seven parts called ,days2 so that in a ,julian ,year there are #ac such ,months1 or #eb ,weeks1 and one ,day over4 ,the ,gentiles gave the names of the ,sun1 ,moon1 and ,planets to the ,days of the ,week4 ,to the first1 the ,name of the ,sun2 to the second1 of the ,moon2 to the third1 of ,mars2 to the fourth1 of ,mercury2 to the fifth1 of ,jupiter2 and to the sixth1 of ,saturn4 ,sidenote3 ,days #dag4 ,a ,day is either ,natural or ,artificial4 ,the ,natural ,day contains #bd hours2 the ,artificial the time from ,sun-rise to ,sun-set4 ,the ,natural ,day is either ,astronomical or ,civil4 ,the ,astronomical ,day begins at ,noon1 because the increase and decrease of ,days terminated by the ,horizon are very unequal among themselves2 which inequality is likewise augmented by the inconstancy of the horizontal ,refractions #ahc3 and therefore the ,astronomer takes the ,meridian for the limit of diurnal ,revolutions2 reckoning ,noon1 that is the instant when the ,sun's ,center is on the ,meridian1 for the beginning of the ,day4 ,the ,british1 ,french1 ,dutch1 ,germans1 ,spaniards1 ,portuguese1 and ,egyptians1 begin the ,civil ,day at mid-night3 the antient ,greeks1 ,jews1 ,bohemians1 ,silesians1 with the modern ,italians1 and ,chinese1 begin it at ,sun-setting3 ,and the antient ,babylonians1 ,persians1 ,syrians1 with the modern ,greeks1 at ,sun-rising4 ,sidenote3 ,hours #dah4 ,an ,hour is a certain determinate part of the ,day1 and is either equal or unequal4 ,an equal ,hour is the #bdth part of a mean natural ,day1 as shewn by well regulated ,clocks and ,watches2 but those ,hours are not quite equal as measured by the returns of the ,sun to the ,meridian1 because of the obliquity of the ,ecliptic and ,sun's unequal motion in it #bbd-bde4 ,unequal ,hours are those by which the ,artificial ,day is divided into twelve ,parts1 and the ,night into as many4 ,sidenote3 ,minutes1 ,seconds1 ,thirds1 and ,scruples4 #dai4 ,an ,hour is divided into #fj equal parts called ,minutes1 a minute into #fj equal parts called ,seconds1 and these again into #fj equal parts called ,thirds4 ,the ,jews1 ,chaldeans1 and ,arabians1 divide the ,hour into #ajhj equal parts called ,scruples2 which number contains #ah times #fj1 so that one minute contains #ah ,scruples4 ,sidenote3 ,cycles1 of the ,sun1 ,moon1 and ,indiction4 #dbj4 ,a ,cycle is a perpetual round1 or circulation of the same parts of time of any sort4 ,the ,cycle of the ,sun is a revolution of #bh years1 in which time1 the days of the months return again to the same days of the week2 the ,sun's ,place to the same ,signs and ,degrees of the ,ecliptic on the same months and days1 so as not to differ one degree in #ajj years2 and the leap-years begin the same course over again with respect to the days of the week on which the days of the months fall4 ,the ,cycle of the ,moon1 commonly called the ,golden ,number1 is a revolution of #ai years2 in which time1 the ,conjunctions1 ,oppositions1 and other ,aspects of the ,moon are within an hour and half of being the same as they were on the same days of the months #ai years before4 ,the ,indiction is a revolution of #ae years1 used only by the ,romans for indicating the times of certain payments made by the subjects to the republic3 ,it was established by ,constantine1 ,a4,d4 #cab4 ,sidenote3 ,to find the ,years of these ,cycles4 #dba4 ,the year of our ,,saviour's ,birth1 according to the vulgar ra1 was the #ith year of the ,solar ,cycle2 the first year of the ,lunar ,cycle2 and the #cabth year after his birth was the first year of the ,roman ,indiction4 ,therefore1 to find the year of the ,solar ,cycle1 add #i to any given year of ,,christ1 and divide the sum by #bh1 the ,quotient is the number of ,cycles elapsed since his birth1 and the remainder is the ,cycle for the given year3 if nothing remains1 the ,cycle is #bh4 ,to find the ,lunar ,cycle1 add #a to the given year of ,,christ1 and divide the sum by #ai2 the ,quotient is the number of ,cycles elapsed in the interval1 and the remainder is the ,cycle for the given year3 if nothing remains1 the ,cycle is #ai4 ,lastly1 subtract #cab from the given year of ,,christ1 and divide the remainder by #ae2 and what remains after this division is the ,indiction for the given year3 if nothing remains1 the ,indiction is #ae4 ,sidenote3 ,the deficiency of the ,lunar ,cycle1 and consequence thereof4 #dbb4 ,although the above deficiency in the ,lunar ,cycle of an hour and half every #ai years be but small1 yet in time it becomes so sensible as to make a whole ,natural ,day in #caj years4 ,so that1 although this ,cycle be of use1 when rightly placed against the days of the month in the ,calendar1 as in our ,common ,prayer ,books1 for finding the days of the mean ,conjunctions or ,oppositions of the ,sun and ,moon1 and consequently the time of ,easter2 it will only serve for #caj years ,old ,style4 ,for as the ,new and ,full ,moons anticipate a day in that time1 the ,golden ,numbers ought to be placed one day earlier in the ,calendar for the next #caj years to come4 ,these ,numbers were rightly placed against the days of ,new ,moon in the ,calendar1 by the ,council of ,nice1 ,a4 ,d4 #cbe2 but the anticipation which has been neglected ever since1 is now grown almost into #e days3 and therefore1 all the ,golden ,numbers ought now to be placed #e days higher in the ,calendar for the ,o4,s4 than they were at the time of the said ,council2 or six days lower for the ,new ,style1 because at present it differs #aa days from the ,old4 ---------------------------------------- ------------ ,days,jan4,feb4,mar4,apr4,may ,jun4,jul4,aug4,sep4,oct4,nov4,dec4 ---------------------------------------- ------------ #a #i #i #ag #ag #f #aa #ai #b #ag #f #ad #ad #c #aa #ai #c #ag #f #ag #f #c #aa #ai #h #h #d #f #f #ad #ad #c #ai #h #af #e #ad #c #aa #aa #ai #h #af ---------------------------------------- ------------ #f #ad #c #ad #c #ai #af #e #e #g #c #c #aa #aa #ai #h #af #ac #h #aa #ai #h #h #af #e #e #ac #i #aa #ai #aa #ai #ac #b #aj #ai #h #h #af #af #e #ac #b #aj ---------------------------------------- ------------ #aa #ai #h #e #ac #b #b #aj #ab #h #af #h #af #af #e #aj #ah #ac #e #ac #ac #b #aj #ah #g #ad #af #e #af #e #b #aj #ah #ah #g #ae #e #e #ac #ac #b #g #ae ---------------------------------------- ------------ #af #ac #b #aj #aj #ah #g #ae #ag #ac #b #ac #b #ah #g #ae #d #d #ah #b #b #aj #aj #ah #ae #ab #ai #aj #ah #g #g #ae #d #d #ab #bj #aj #ah #aj #ah #ae #ab #a #a ---------------------------------------- ------------ #ba #ah #g #g #ae #d #ab #i #bb #ah #g #ae #d #d #ab #a #a #i #bc #g #ae #g #ae #ab #i #ag #ag #bd #ae #d #d #ab #a #i #f #be #ae #d #ab #a #i #ag #ag #f ---------------------------------------- ------------ #bf #d #d #ab #a #f #ad #bg #ab #a #a #i #i #ag #f #ad #bh #ab #a #ab #i #ag #f #ad #ad #c #c #bi #a #a #i #ag #c #aa #cj #ag #f #f #ad #c #aa ---------------------------------------- ------------ #ca #i #i #ad #c #aa #ai ---------------------------------------- ------------ ,sidenote3 ,how to find the day of the ,new ,moon by the ,golden ,number4 #dbc4 ,in the annexed ,table1 the ,golden ,numbers under the months stand against the days of ,new ,moon in the left hand column1 for the ,new ,style2 adapted chiefly to the second year after leap-year as being the nearest mean for all the four2 and will serve till the year #aijj4 ,therefore1 to find the day of ,new ,moon in any month of a given year till that time1 look for the ,golden ,number of that year under the desired month1 and against it1 you have the day of ,new ,moon in the left hand column4 ,thus1 suppose it were required to find the day of ,new ,moon in ,september #ageg2 the ,golden ,number for that year is #aj1 which ,i look for under ,september and right against it in the left hand column ,i find #ac1 which is the day of ,new ,moon in that month4 ,n4 ,b4 ,if all the ,golden ,numbers1 except #ag and #f1 were set one day lower in the ,table1 it would serve from the beginning of the year #aijj till the end of the year #baii4 ,the first ,table after this chapter shews the ,golden ,number for #djjj years after the birth of ,,christ1 by looking for the even hundreds of any given year at the left hand1 and for the rest to make up that year at the head of the ,table2 and where the columns meet1 you have the ,golden ,number 7which is the same both in ,old and ,new ,style7 for the given year4 ,thus1 suppose the ,golden ,number was wanted for the year #ageg2 ,i look for #agjj at the left hand of the ,table1 and for #eg at the top of it2 then guiding my eye downward from #eg to over against #agjj1 ,i find #aj1 which is the ,golden ,number for that year4 ,sidenote3 ,a perpetual ,table of the time of ,new ,moon to the nearest hour1 for the ,old ,style4 #dbd4 ,but because the lunar ,cycle of #ai years sometimes includes five leap-years1 and at other times only four1 this ,table will sometimes vary a day from the truth in leap-years after ,february4 ,and it is impossible to have one more correct1 unless we extend it to four times #ai or #gf years2 in which there are #ai leap years without a remainder4 ,but even then to have it of perpetual use1 it must be adapted to the ,old ,style1 because in every centurial year not divisible by #d1 the regular course of leap-years is interrupted in the ,new2 as will be the case in the year #ahjj4 ,therefore1 upon the regular ,old ,style plan1 ,i have computed the following ,table of the mean times of all the ,new ,moons to the nearest hour for #gf years2 beginning with the year of ,,christ #agbd1 and ending with the year #ahjj4 ,this ,table may be made perpetual1 by deducting #f hours from the time of ,new ,moon in any given year and month from #agbd to #ahjj1 in order to have the mean time of ,new ,moon in any year and month #gf years afterward2 or deducting #ab hours for #aeb years1 #ah hours for #bbh years2 and #bd hours for #cjd years1 because in that time the changes of the ,moon anticipate almost a complete natural day4 ,and if the like number of hours be added for so many years past1 we shall have the mean time of any ,new ,moon already elapsed4 ,suppose1 for example1 the mean time of ,change was required for ,january #ahjb2 deduct #gf years and there remains #agbf1 against which in the following ,table under ,january ,i find the time of ,new ,moon was on the #bast day at #aa in the evening3 from which take #f hours and there remains the #bast day at #e in the evening for the mean time of ,change in ,january #ahjb4 ,or1 if the time be required for ,may1 ,a4 ,d4 #agja1 add #gf years and it makes #aggg1 which ,i look for in the ,table1 and against it under ,may ,i find the ,new ,moon in that year falls on the #beth day at #i in the evening2 to which add #f hours1 and it gives the #bfth day at #c in the ,morning for the time of ,new ,moon in ,may1 ,a4 ,d4 #agja4 ,by this addition for time past1 or subtraction for time to come1 the ,table will not vary #bd hours from the truth in less than #adeib years4 ,and if1 instead of #f hours for every #gf years1 we add or subtract only #e hours #eb minutes1 it will not vary a day in #aj millions of years4 ,although this ,table is calculated for #gf years only1 and according to the ,old ,style1 yet by means of two easy ,equations it may be made to answer as exactly to the ,new ,style1 for any time to come4 ,thus1 because the year #agbd in this ,table is the first year of the ,cycle for which it is made2 if from any year of ,,christ after #ahjj you subtract #agbc1 and divide the overplus by #gf1 the ,quotient will shew how many entire ,cycles of #gf years are elapsed since the beginning of the ,cycle here provided for2 and the remainder will shew the year of the current ,cycle answering to the given year of ,,christ4 ,hence1 if the remainder be #j1 you must instead thereof put #gf1 and lessen the ,quotient by unity4 ,then1 look in the left hand column of the ,table for the number in your remainder1 and against it you will find the times of all the mean ,new ,moons in that year of the present ,cycle4 ,and whereas in #gf ,julian ,years the ,moon anticipates #e hours #eb minutes1 if therefore these #e hours #eb minutes be multiplied by the above found ,quotient1 that is1 by the number of entire ,cycles past2 the product subtracted from the times in the ,table will leave the corrected times of the ,new ,moons to the ,old ,style2 which may be reduced to the ,new ,style thus3 ,divide the number of entire hundreds in the given year of ,,christ by #d1 multiply this ,quotient by #c1 to the product add the remainder1 and from their sum subtract #b3 this last remainder denotes the number of days to be added to the times above corrected1 in order to reduce them to the ,new ,style4 ,the reason of this is1 that every #djj years of the ,new ,style gains #c days upon the ,old ,style3 one of which it gains in each of the centurial years succeeding that which is exactly divisible by #d without remainder2 but then1 when you have found the days so gained1 #b must be subtracted from their number on account of the rectifications made in the ,calendar by the ,council of ,nice1 and since by ,pope ,gregory4 ,it must also be observed1 that the additional days found as above directed do not take place in the centurial ,years which are not multiples of #d till ,february #bith1 ,o4 ,s4 for on that day begins the difference between the ,styles2 till which day therefore1 those that were added in the preceding years must be used4 ,the following ,example will make this accommodation plain4 ,required the mean time of ,new ,moon in ,june1 ,a4,d4 #aiji1 ,n4,s4 ,from #aiji take #agbc ,years1 and there rem4 #ahf ,which divided by #gf1 gives the ,quotient #b and the remainder #cd ,then1 against #cd in the ,table is ,june #e;d #h;h #jm ,afternoon4 ,and #e;h #ebm multiplied by #b make to be subtr4 #aa #dd ------------- ,remains the mean time according to the ,old ,style1 ,june #e;d #i;h #afm ,morning4 ,entire hundred in #aiji are #ai1 which divided by #d1 quotes #d ,and leaves a remainder of #c ,which ,quotient multiplied by #c makes #ab1 and the remainder added makes #ae ,from which subtract #b1 and there remains #ac ,which number of days added to the above time ,old ,style1 gives ,june #ah;d #i;h #afm ,morn4,n4,s4 ,so the mean time of ,new ,moon in ,june #aiji ,new ,style is the #ahth day at #af minutes past #i in the ,morning4 ,if #aa days be added to the time of any ,new ,moon in this ,table1 it will give the time thereof according to the ,new ,style till the year #ahjj4 ,and if #ad days #ah hours #bb minutes be added to the mean time of ,new ,moon in either ,style1 it will give the mean time of the next ,full ,moon according to that ,style4 ---------------------------------------- ---------------------------------------- ------------- ,a ,,table shewing the times of all the mean ,changes of the ,moon1 to the nearest ,hour1 through four ,lunar ,periods1 or #gf years4 ,m signifies morning1 ,a afternoon4 ---------------------------------------- ---------------------------------------- ,yrs ,january ,march ,may ,july ,sept4 ,novemb4 of ,a4,d4 ,february ,april ,june ,august ,october ,decemb4 the ---------------------------------------- ------------------------------------ ,cyc4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ,d4 ,h4 ---------------------------------------- ---------------------------------------- #a #agbdad #e;,a#ac #e,m#ac #f;,a#ab #g,m#aa #h;,a#aj #h,m #i #i;,a #h #aj,m #f #aj;,a #f #aa,m #d #ab;,a #d #a;,a #a #d,m #b #agbe #c #b,m #a #b;,a #c #c,m #a #d;,a #bi #f,m#bh #g;,a#bg #h,m#be #h;,a#be #i,m#bc #aj;,a#bc #aa,m #cj #e;,a #c #agbfba #aa;,a#bj #aa,m#ba #ab;,a#bj #a;,a#bj #a,m#ah #b;,a#ah #c,m#af #d;,a#ae #e,m#ad #e;,a#ac #f,m#ab #g;,a #b #d,m #d #agbgaa #h,m #i #i;,a#aa #i,m #i #aj;,a #i #aa,m #g #ab;,a #g #j;,a #f #a,m #d #a;,a #d #b,m #b #c;,a #ca #e;,a #e #agbhcj #f,m#bh #g;,a#bi #g,m#bg #h;,a#bg #h,m#be #i;,a#be #aj,m#bc #aa;,a#bb #aa,m#ba #ab;,a#bj #a;,a#bj #b,m #f #agbiah #b;,a#ag #c,m#ah #d;,a#ag #d,m#af #e;,a#ae #f,m#ad #g;,a#ab #g,m#aa #h;,a#aa #i,m #i #j;,a #i #aa,m #b #e,m #g #agcj #g #aa;,a #f #j;,a #h #a,m #f #a;,a #f #b,m #d #c;,a #d #c,m #b #d;,a #cj #g,m#bh #h;,a#bh #i,m #cj #f;,a #h #agcabf #i;,a#be #aj,m#bf #aj;,a#be #aa,m#bd #aa;,a#bc #j;,a#bc #a,m#ba #b;,a#bj #b,m#ai #c;,a#ah #d,m#ag #e;,a #i #agcbaf #e,m#ad #f;,a#ae #g,m#ac #h;,a#ac #h,m#aa #i;,a#aa #aj,m #i #aa;,a #h #aa,m #g #ab;,a #f #a;,a #f #b,m #a #f,m #aj #agcc #d #b;,a #c #c,m #d #d;,a #c #d,m #b #e;,a #cj #h,m#bh #h;,a#bg #i,m#bf #aj;,a#be #aa,m#bd #aa;,a #cj #g;,a #aa #agcdbc #j;,a#bb #a,m#bc #a;,a#bb #b,m#ba #b;,a#bj #c,m#ai #d;,a#ah #e,m#af #e;,a#af #f,m#ad #g;,a#ad #h,m #ab #agceab #i;,a#aa #i,m#ab #aj;,a#aa #aa,m#aj #aa;,a #i #j;,a #i #a,m #g #b;,a #f #b,m #e #c;,a #d #d,m #c #e;,a #b #e,m #a #g,m #ac #agcf ---- #bi #i,m#bh #i;,a#bg #aj,m#bf #aa;,a#be #j;,a#bc #ab;,a#bc #a;,a#bb #b,m#ba #c;,a #ca #f;,a #cj #h;,a #ad #agcgbj #c,m#ah #d;,a#bj #d,m#ah #e;,a#ah #e,m#af #f;,a#af #g,m#ad #h;,a#ac #h,m#ab #i;,a#aa #aj,m#aj #aa;,a #b #f,m #ae #agch #i #aa,m #g #ab;,a #i #a;,a #h #a,m #g #b;,a #f #c,m #e #d;,a #d #e,m #b #e;,a #cj #h,m#bi #h;,a #ca #g;,a #af #agcibh #i,m#bf #aj;,a#bh #aa,m#bf #ab;,a#bf #j;,a#be #a,m#bd #b;,a#bc #c,m#ba #c;,a#ba #d,m#ai #e;,a#ai #f,m #ag #agdjag #f;,a#af #g,m#af #h;,a#ae #i,m#ad #i;,a#ac #aj,m#ab #aa;,a#aa #j;,a#i #ab;,a #i #a;,a #h #b,m #g #c;,a #b #g,m #ah #agda #f #c,m #d #d;,a #f #d,m #d #e;,a #d #e,m #b #f;,a #cj #h,m#bh #i;,a#bh #aj,m#bf #aa;,a#bf #aa,m #ca #g;,a #ai #agdbbd #ab;,a#bc #a;,a#be #b,m#bc #c;,a#bc #c,m#ba #d;,a#ba #e,m#ai #f;,a#ah #f,m#ag #g;,a#af #h,m#ae #i;,a #bj #agdcad #i,m#ab #aj;,a#ad #aa,m#ab #ab;,a#ab #j;,a#aa #a,m#aj #b;,a #i #c,m #g #c;,a #g #d,m #e #e;,a #e #f,m #a #i,m #ba #agdd #c #f;,a #b #g,m #b #h;,a #cj #aj,m#bh #aa;,a#bh #j;,a#bf #ab;,a#be #a;,a#be #b,m#bc #c;,a#bc #c,m #cj #i;,a #bb #agdeba #d;,a#bj #e,m#ba #e;,a#bj #f,m#ai #f;,a#ah #g,m#ag #h;,a#af #h,m#ad #i;,a#ad #aj,m#ab #aa;,a#ab #j;,a #a #i;,a #bc #agdfaj #ab;,a#i #a;,a#aa #b,m #i #c;,a #i #c,m #g #d;,a #g #e,m #e #f;,a #d #f,m #c #g;,a #b #h,m #ca #aj,m #bd #agdgbi #aj;,a#bh #aa,m#bi #aa;,a#bh #j;,a#bg #ab;,a#bf #a;,a#bf #b,m#bd #c;,a#bc #c,m#bb #d;,a#ba #e,m#bj #f;,a #be #agdhai #f,m#ag #g;,a#ah #h,m#af #i;,a#af #i,m#ad #aj;,a#ad #aa,m#ab #ab;,a#aa #j;,a#aa #a,m #i #b;,a #i #c,m #b #i,m #bf #agdi #g #c;,a #f #d,m #g #e;,a #f #f,m #e #f;,a #d #g,m #c #h;,a #cj #aj,m#bi #aa;,a#bh #j;,a#bg #ab;,a #ca #i;,a #bg #agejbf #a;,a#be #b,m#bf #c;,a#be #d,m#bd #d;,a#bc #e,m#bb #f;,a#ba #g,m#ai #g;,a#ai #h,m#ag #i;,a#ag #aj,m #bh #ageaae #aj;,a#ad #aa,m#ae #aa;,a#ad #j;,a#ac #ab;,a#ab #a;,a#ab #b,m#aj #c;,a #i #c,m #h #d;,a #g #e,m #f #f;,a #b #i,m #bi #ageb #e #f,m #c #g;,a #d #h,m #b #i;,a #cj #aa,m#bi #ab;,a#bh #j;,a#bg #a,m#bf #b;,a#be #c,m#bd #c;,a #ca #aj;,a #cj #agecbc #d,m#ba #e;,a#bc #f,m#ba #g;,a#ba #g,m#ai #h;,a#ai #i,m#ag #aj;,a#af #aj,m#ae #aa;,a#ad #j;,a#ad #a,m #ca #agedab #a;,a#aa #b,m#ab #c;,a#aa #d,m#aj #d;,a #i #e,m #h #f;,a #g #g,m #e #g;,a #e #h,m #c #i;,a #c #aj,m #a #aj;,a #a #aa;,a #cb #agee ---- #bi #ab;,a#bi #a;,a#bh #b,m#bg #c;,a#be #c,m#bd #d;,a#bd #e,m#bb #f;,a#bb #f,m #ca #aa,m #ca #j;,a #cc #agefbj #g;,a#ai #h,m#ai #i;,a#ah #i,m#ag #aj;,a#af #aa,m#ae #ab;,a#ad #a;,a#ac #a,m#ab #b;,a#aa #c,m#aj #d;,a #a #ad;,a #cd #ageg #i #d,m #g #e;,a #i #f,m #g #g;,a #g #g,m #e #h;,a #e #i,m #c #aj;,a #b #aj,m #cj #a,m#bi #a;,a #ca #j;,a #ce #agehbh #b,m#bf #c;,a#bh #c,m#bf #d;,a#bf #d,m#bd #e;,a#bd #f,m#bb #g;,a#ba #g,m#bj #h;,a#ai #i,m#ah #aj;,a #cf #ageiag #aj,m#ae #aa;,a#ag #j;,a#af #a,m#ae #a;,a#ad #b,m#ac #c;,a#ab #b,m#aj #d;,a#aj #e,m #h #f;,a #h #g,m #a #ab;,a #cg #agfj #f #g;,a #e #h,m #e #i;,a #d #aj,m #c #aj;,a #b #aa,m #cj #a,m#bh #b;,a#bh #c,m#bf #d;,a#bf #d,m #ca #a;,a #ch #agfabd #e;,a#bc #f,m#bd #g;,a#bc #h,m#bb #i;,a#ba #aj,m#bj #aj;,a#ai #aa,m#ag #aa;,a#ag #j;,a#af #a,m#ae #b;,a #ci #agfbad #b,m#ab #c;,a#ad #c,m#ab #d;,a#ab #d,m#aj #e;,a#aj #f,m#h #g;,a #g #g,m #f #h;,a #e #i,m #d #aj;,a ---------------------------------------- ---------------------------------------- #a #a;,a #dj #agfc #c #aa,m #a #ab;,a #c #j;,a #b #a,m #bi #c;,a#bi #d,m#bg #d,m#bf #e,m#be #f;,a#bd #g,m#bc #g;,a #ca #b,m #da #agfdbb #h,m#bj #i;,a#ba #aj,m#ai #aa;,a#ai #aa,m#ag #ab;,a#ag #a;,a#af #b,m#ad #b;,a#ad #c,m#ab #d;,a#ab #e,m #a #a;,a #db #agfeaj #e;,a #i #f,m#aj #f;,a #i #g,m #h #g;,a #g #h,m #f #i;,a #e #aj,m #c #aj;,a #c #aa,m #a #ab;,a #ca #a,m #dc #agffbi #b;,a#bh #c,m#bi #d;,a#bh #e,m#bg #e;,a#bf #f,m#be #g;,a#bd #h,m#bb #h;,a#bb #i,m#bj #aj;,a#bj #aa,m #dd #agfgah #aa;,a#ag #j;,a#ai #a,m#ag #b;,a#ag #b,m#ae #c;,a#ae #d,m#ac #e;,a#ab #f,m#aa #f;,a#aj #g,m #i #h;,a #b #b,m #de #agfh #h #h,m #f #i;,a #g #aj,m #e #aa;,a #e #aa,m #c #ab;,a #c #a;,a #cj #c,m#bi #d;,a#bh #e,m#bg #e;,a #ca #b;,a #df #agfibf #f,m#bd #g;,a#bf #g,m#bd #h;,a#bd #h,m#bb #i;,a#bb #aj,m#bj #aa;,a#ai #aa,m#ah #ab;,a#ag #a;,a#ag #b,m #dg #aggjae #b;,a#ad #c,m#ae #d;,a#ad #e,m#ac #e;,a#ab #d,m#aa #g;,a#aj #h,m #h #h;,a #h #i,m #f #aj;,a #f #aa,m #a #d,m #dh #agga #d #aa,m #c #j;,a #e #a,m #c #b;,a #c #b,m #a #c;,a #bi #e,m#bg #f;,a#bg #g,m#be #h;,a#be #i,m #cj #e;,a #di #aggbbc #i;,a#bb #aj,m#bb #aj;,a#ba #aa,m#bj #aa;,a#ai #j;,a#ai #a,m#ag #b;,a#af #b,m#ae #c;,a#ad #d,m#ac #e;,a #ej #aggcab #e,m#aj #f;,a#ab #g,m#aj #h;,a#aj #h,m #h #i;,a #h #i,m #f #aj;,a #e #aa,m #d #ab;,a #c #a;,a #c #b,m #a #b;,a #a #d;,a #ea #aggd ---- #bi #e;,a#bi #f,m#bg #g;,a#bg #h,m#be #h;,a#bd #i,m#bc #aj;,a#bb #aa,m#ba #aa;,a #ca #c,m #ca #e,m #eb #aggebj #j;,a#ai #a,m#bj #b;,a#ai #c,m#ah #c;,a#ag #d,m#af #e;,a#ae #f,m#ac #f;,a#ac #g,m#aa #h;,a#aa #i,m #a #c;,a #ec #aggf #i #i;,a #h #aj,m #h #aj;,a #g #aa,m #f #ab;,a #e #j;,a #e #a,m #c #b;,a #b #b,m #bi #e;,a#bi #e,m #ca #d,m #ed #agggbg #f;,a#bf #g,m#bg #h;,a#bf #i,m#be #i;,a#bd #aj,m#bc #aa;,a#bb #j;,a#bj #ab;,a#bj #a;,a#ai #b,m#ah #c;,a #ee #agghag #c,m#ae #d;,a#ag #e,m#ae #f;,a#ae #f,m#ac #g;,a#ac #h,m#aa #i;,a#aj #i,m #i #aj;,a #h #aa,m #g #ab;,a #a #f,m #ef #aggi #f #j;,a #e #a,m #f #b;,a #e #c,m #d #c;,a #c #d,m #b #e;,a #bi #g,m#bh #h;,a#bg #i,m#bf #i;,a #cj #f;,a #eg #aghjbe #aj,m#bc #aa;,a#bd #aa,m#bb #ab;,a#bb #j;,a#ba #a,m#bj #b;,a#ai #c,m#ag #c;,a#ag #d,m#ae #e;,a#ae #f,m #eh #aghaac #f;,a#ab #g,m#ac #h;,a#ab #i,m#aa #i;,a#aj #aj,m #i #aa;,a #h #j;,a #f #ab;,a #f #a;,a #e #b,m #d #c;,a #a #f,m #ei #aghb #c #c,m #a #d;,a #c #e,m #a #f;,a #bi #h,m#bh #i;,a#bg #i,m#be #aj;,a#be #aa,m#bc #ab;,a#bc #j;,a #cj #g;,a #fj #aghcbb #a,m#bj #b;,a#bb #b,m#bj #c;,a#bj #c,m#ah #d;,a#ah #e,m#af #f;,a#ae #f,m#ad #g;,a#ac #h,m#ab #i;,a #a #f,m #fa #aghdaa #i,m #i #aj;,a#aj #aa,m #h #ab;,a #h #j;,a #g #a,m #f #b;,a #e #c,m #c #c;,a #c #d,m #a #e;,a #cj #f;,a #fb #aghebi #g,m#bg #h;,a#bi #i,m#bg #aj;,a#bg #aj,m#be #aa;,a#be #j;,a#bd #a,m#bb #a;,a#bb #b,m#bj #c;,a#bj #c,m #fc #aghfah #d;,a#ag #e,m#ah #e;,a#ag #f,m#af #f;,a#ae #g,m#ad #h;,a#ac #i,m#aa #i;,a#aa #aj,m #i #aa;,a #i #j;,a #a #f,m #fd #aghg #g #ab;,a #f #a;,a #h #b,m #f #c;,a #f #c,m #d #d;,a #d #e,m #b #f;,a #cj #h,m#bh #i;,a#bh #i,m #cj #g;,a #fe #aghhbf #aj;,a#be #aa,m#be #ab;,a#bd #a;,a#bd #a,m#bb #b;,a#bb #c,m#bj #d,m#ai #d,m#ah #e;,a#ag #f,m#af #g;,a #ff #aghiae #g,m#ac #h;,a#ae #i,m#ac #aj;,a#ac #aj,m#aa #aa;,a#aa #j;,a#aj #a,m #h #a;,a #h #b,m #f #c;,a #f #d,m #a #g,m #fg #agij #d #d;,a #c #e,m #d #e;,a #c #f,m #b #f;,a #cj #i,m#bh #i;,a#bg #aj,m#bf #aa;,a#be #j;,a#bd #ab;,a #cj #h;,a #fh #agiabc #a;,a#bb #b,m#bc #c;,a#bb #d,m#ba #d;,a#bj #e,m#ai #f;,a#ah #g,m#af #g;,a#af #h,m#ad #i;,a#ad #aj,m #fi #agibab #aj;,a#aa #aa,m#aa #ab;,a#aj #a;,a#aj #a,m #h #b;,a #h #c,m #f #d;,a #e #d;,a #d #e;,a #c #f,m #b #g;,a #a #g,m #a #i,m #gj #agic ---- #bi #aj,m#bh #aa;,a#bg #j;,a#bg #a,m#be #a;,a#bd #b,m#bc #c;,a#bb #d,m#ba #d;,a #cj #h;,a #cj #aj;,a #ga #agidbj #e,m#ah #f;,a#bj #f,m#ah #g;,a#ah #g,m#af #h;,a#af #i,m#ad #aj;,a#ac #aj,m#ab #aa;,a#aa #j;,a#aa #a,m #b #h,m #gb #agie #i #a;,a #h #b,m #i #c;,a #h #d,m #g #d;,a #f #e,m #e #f;,a #d #g,m #b #g;,a #cj #aj,m#bi #aj;,a #ca #i;,a #gc #agifbh #aa,m#bf #ab;,a#bg #j;,a#bf #a,m#be #a;,a#bd #b,m#bc #c;,a#bb #d,m#bj #d;,a#bj #e,m#ah #f;,a#ah #g,m #gd #agigaf #g;,a#ae #h,m#af #i;,a#ae #aj,m#ad #aj;,a#ac #aa,m#ab #ab;,a#aa #a;,a#aj #a,m #i #b;,a #h #c,m #g #d;,a #b #i,m #ge #agih #f #d,m #d #e;,a #f #f,m #d #g;,a #d #g,m #b #h;,a #cj #aj,m#bh #aa;,a#bh #j;,a#bg #a,m#bf #a;,a #ca #aj;,a #gf #agii #be #b,m#bc #c;,a#be #d,m#bc #e;,a#bc #e,m#ba #f;,a#ba #f,m#ai #h;,a#ah #h,m#ag #i;,a#af #aj,m#ae #aa;,a #a #ahjjad #aa;,a#ab #ab;,a#ac #j;,a#ab #a,m#aa #a;,a#aj #b,m #i #c;,a #h #d,m #f #d;,a #f #e,m #d #f;,a #d #g,m ---------------------------------------- ---------------------------------------- ,the year #ahjj begins a new ,cycle4 ,sidenote3 ,easter ,cycle1 deficient4 #dbe4 ,the ,cycle of ,easter1 also called the ,dionysian ,period1 is a revolution of #ecb years1 found by multiplying the ,solar ,cycle #bh by the ,lunar ,cycle #ai4 ,if the ,new ,moons did not anticipate upon this ,cycle1 ,easter-,day would always be the ,sunday next after the first ,full ,moon which succeeds the #bast of ,march4 ,but1 on account of the above anticipation #dbb1 to which no proper regard was had before the late alteration of the ,style1 the ,ecclesiastic ,easter has several times been a week different from the true ,easter within this last ,century3 which inconvenience is now remedied by making the ,table which used to find ,easter for ever1 in the ,common ,prayer ,book1 of no longer use than the ,lunar difference from the ,new ,style will admit of4 ,sidenote3 ,number of ,direction4 ,to find the true ,easter4 #dbf4 ,the earliest ,easter possible is the #bb;d of ,march1 the latest the #beth of ,april4 ,within these limits are #ce days1 and the number belonging to each of them is called the ,number of ,direction2 because thereby the time of ,easter is found for any given year4 ,to find the ,number of ,direction1 according to the ,new ,style1 enter ,table ,v following this ,chapter1 with the compleat hundreds of any given year at the top1 and the years thereof 7if any7 below an hundred at the left hand2 and where the columns meet is the ,dominical ,letter for the given year4 ,then1 enter ,table ,i1 with the compleat hundreds of the same year at the left hand1 and the years below an hundred at the top2 and where the columns meet is the ,golden ,number for the same year4 ,lastly1 enter ,table ,,ii with the ,dominical ,letter at the left hand and ,golden ,number at the top2 and where the columns meet is the ,number of ,direction for that year2 which number1 added to the #bast day of ,march shews on what day either of ,march or ,april ,easter ,sunday falls in that year4 ,thus1 the ,dominical ,letter ,new ,style for the year #ageg is ,b 7,table ,v7 and the ,golden ,number is #aj1 7,table ,i7 by which in ,table ,,ii1 the ,number of ,direction is found to be #bj2 which1 reckoned from the #bast of ,march1 ends on the #ajth of ,april1 and that is ,easter ,sunday in the year #ageg4 ,n4 ,b4 ,there are always two ,dominical ,letters to the leap-year1 the first of which takes place to the #bdth of ,february1 the last for the following part of the year4 ,sidenote3 ,dominical ,letter4 #dbg4 ,the first seven ,letters of the ,alphabet are commonly placed in the annual ,almanacks to shew on what days of the week the days of the months fall throughout the year4 ,and because one of those seven ,letters must necessarily stand against ,sunday it is printed in a capital form1 and called the ,dominical ,letter3 the other six being inserted in small characters to denote the other six days of the week4 ,now1 since a common ,julian ,year contains #cfe ,days1 if this number be divided by #g 7the number of days in a week7 there will remain one day4 ,if there had been no remainder1 'tis plain the year would constantly begin on the same day of the week4 ,but since one remains1 'tis as plain that the year must begin and end on the same day of the week2 and therefore the next year will begin on the day following4 ,hence1 when ,january begins on ,sunday1 ,a is the ,dominical or ,sunday ,letter for that year3 then1 because the next year begins on ,monday1 the ,sunday will fall on the seventh day1 to which is annexed the seventh ,letter ,g1 which therefore will be the ,dominical ,letter for all that year3 and as the third year will begin on ,tuesday1 the ,sunday will fall on the sixth day2 therefore ,f will be the ,sunday ,letter for that year4 ,whence 'tis evident that the ,sunday ,letters will go annually in a retrograde order thus1 ,g1 ,f1 ,e1 ,d1 ,c1 ,b1 ,a4 ,and in the course of seven years1 if they were all common ones1 the same days of the week and ,dominical ,letters would return to the same days of the months4 ,but because there are #cff days in a leap-year1 if this number be divided by #g1 there will remain two days over and above the #eb weeks of which the year consists4 ,and therefore1 if the leap-year begins on ,sunday1 it will end on ,monday2 and the next year will begin on ,tuesday1 the first ,sunday whereof must fall on the sixth of ,january1 to which is annexed the ,letter ,f1 and not ,g as in common years4 ,by this means1 the leap-year returning every fourth year1 the order of the ,dominical ,letters is interrupted2 and the ,series does not return to its first state till after four times seven1 or #bh years3 and then the same days of the month return in order to the same days of the week4 ,sidenote3 ,to find the ,dominical ,letter4 #dbh4 ,to find the ,dominical ,letter for any year either before or after the ,christian ra#hg3 ,in ,table ,,iii or ,,iv for ,old ,style1 or ,v for ,new ,style1 look for the hundreds of years at the head of the ,table1 and for the years below an hundred 7to make up the given year7 at the left hand3 and where the columns meet you have the ,dominical ,letter for the year desired4 ,thus1 suppose the ,dominical ,letter be required for the year of ,,christ #ageh1 ,new ,style1 ,i look for #agjj at the head of ,table ,v1 and for #eh at the left hand of the same ,table2 and in the angle of meeting1 ,i find ,a1 which is the ,dominical ,letter for that year4 ,if it was wanted for the same year ,old ,style1 it would be found by ,table ,,iv to be ,d4 ,but to find the ,dominical ,letter for any given year before ,,christ1 subtract one from that year and then proceed in all respects as just now taught1 to find it by ,table ,,iii ,thus1 suppose the ,dominical ,letter be required for the #eheth year before the first year of ,,christ1 look for #ejj at the head of ,table ,,iii1 and for #hd at the left hand2 in the meeting of these columns is ,,fe1 which were the ,dominical ,letters for that year1 and shews that it was a leap-year2 because1 leap-year has always two ,dominical ,letters4 ,sidenote3 ,to find the ,days of the ,months4 #dbi4 ,to find the day of the month answering to any day of the week1 or the day of the week answering to any day of the month2 for any year past or to come3 ,having found the ,dominical ,letter for the given year1 enter ,table ,,vi1 with the ,dominical ,letter at the head2 and under it1 all the days in that column to the right hand are ,sundays1 in the divisions of the months2 the next column to the right are ,mondays2 the next1 ,tuesdays2 and so on to the last column under ,g1 from which go back to the column under ,a1 and thence proceed towards the right hand as before4 ,thus1 in the year #ageg1 the ,dominical ,letter ,new ,style is ,b1 in ,table ,v1 then in ,table ,,vi all the days under ,b are ,sundays in that year1 viz4 the #b;d1 #ith1 #afth1 #bc;d1 and #cjth of ,january and ,october2 the #fth1 #acth1 #bjth1 and #bgth of ,february1 ,march and ,november2 the #c;d1 #ajth1 and #agth1 of ,april and ,july1 together with the #cast of ,july3 and so on to the foot of the column4 ,then1 of course1 all the days under ,c on ,mondays1 namely the #c;d1 #ajth1 c4 of ,january and ,october2 and so of all the rest in that column4 ,if the day of the week answering to any day of the month be required1 it is easily had from the same ,table by the ,letter that stands at the top of the column in which the given day of the month is found4 ,thus1 the ,letter that stands over the #bhth of ,may is ,a2 and in the year #ehe before ,,christ the ,dominical ,letter was found to be ,,fe #dbh2 which being a leap-year1 and ,e taking place from the #bdth of ,february to the end of that year1 shews by the ,table that the #beth of ,may was on a ,sunday2 and therefore the #bhth must have been on a ,wednesday3 for when ,e stands for ,sunday1 ,f must stand for ,monday1 ,g for ,tuesday1 ,a for ,wednesday1 ,b for ,thursday1 ,c for ,friday1 and ,d for ,saturday4 ,hence1 as it appears that the famous ,eclipse of the ,sun foretold by ,,thales1 by which a peace was brought about between the ,medes and ,lydians1 happened on the #bhth of ,may1 in the #eheth year before ,,christ1 it certainly fell on a ,wednesday4 ,sidenote3 ,julian ,period4 #dcj4 ,from the multiplication of the ,solar ,cycle of #bh years into the ,lunar ,cycle of #ai years1 arises the great ,julian ,period consisting of #gihj years2 which had its beginning #gfd years before the supposed year of the creation 7when all the three ,cycles began together7 and is not yet compleated1 and therefore it comprehends all other ,cycles1 ,periods and ras4 ,there is but one year in the whole ,period which has the same numbers for the three ,cycles of which it is made up3 and therefore1 if historians had remarked in their writings the ,cycles of each year1 there had been no dispute about the time of any action recorded by them4 ,sidenote3 ,to find the year of this ,period4 ,and the ,cycles of that year4 #dca4 ,the ,dionysian or vulgar ra of ,christ's birth was about the end of the year of the ,julian ,period #dgac2 and consequently the first year of his age1 according to that account1 was the #dgadth year of the said ,period4 ,therefore1 if to the current year of ,christ we add #dgac1 the ,sum will be the year of the ,julian ,period4 ,so the year #ageg will be found to be the #fdgjth year of that ,period4 ,or1 to find the year of the ,julian ,period answering to any given year before the first year of ,,christ1 subtract the number of that given year from #dgad1 and the remainder will be the year of the ,julian ,period4 ,thus1 the year #ehe before the first year of ,,christ 7which was the #ehdth before his birth7 was the #dabith year of the said ,period4 ,lastly1 to find the ,cycles of the ,sun1 ,moon1 and ,indiction for any given year of this ,period1 divide the given year by #bh1 #ai1 and #ae2 the three remainders will be the ,cycles sought1 and the ,quotients the numbers of ,cycles run since the beginning of the ,period4 ,so in the above #dgadth year of the ,julian ,period the ,cycle of the ,sun was #aj1 the ,cycle of the ,moon #b1 and the ,cycle of ,indiction #d2 the ,solar ,cycle having run through #afh courses1 the ,lunar #bdh1 and the ,indiction #cad4 ,sidenote3 ,the true ra of ,,christ's birth4 #dcb4 ,the vulgar ra of ,,christ's birth was never settled till the year #ebg2 when ,dionysius ,exiguus1 a ,roman ,abbot1 fixed it to the end of the #dgacth year of the ,julian ,period2 which was certainly four years too late4 ,for1 our ,,saviour was undoubtedly born before the ,death of ,herod the ,great1 who sought to kill him as soon as he heard of his birth4 ,and1 according to the testimony of ,josephus 7,b4 xvii4 c4 #h47 there was an eclipse of the ,moon in the time of ,herod's last illness3 which very eclipse our ,astronomical ,tables shew to have been in the year of the ,julian ,period #dgaj1 ,march #acth1 #c hours #ba minutes after mid-night1 at ,jerusalem4 ,now1 as our ,,saviour must have been born some months before ,herod's death1 since in the interval he was carried into gypt2 the latest time in which we can possibly fix the true ra of his birth is about the end of the #dgjith year of the ,julian ,period4 ,and this is four years before the vulgar ra thereof4 ,sidenote3 ,the time of his crucifixion4 ,in the former edition of this book1 ,i endeavoured to ascertain the time of ,,christ's death2 by shewing in what year1 about the reputed time of the ,passion1 there was a ,passover ,full ,moon on a ,friday3 on which day of the week1 and at the time of the ,passover1 it is evident from ,mark xv4 #db4 that our ,,saviour was crucified4 ,and in computing the times of all the ,passover ,full ,moons from the #bjth to the #djth year of ,,christ1 after the ,jewish manner1 which was to add #ad days to the time when the ,new ,moon next before the ,passover was first visible at ,jerusalem1 in order to have their day of the ,passover ,full ,moon1 ,i found that the only ,passover ,full ,moon which fell on a ,friday1 in all that time1 was in the year of the ,julian ,period #dgdf1 on the third day of ,april3 which year was the #cc;d year of ,,christ's age1 reckoning from the vulgar ra of his birth1 but the #cgth counting from the true ra thereof3 and was also the last year of the #djb;d ,olympiad#hh1 in which very year ,phlegon an ,heathen writer tells us1 there was the most extraordinary ,eclipse of the ,sun that ever was known1 and that it was night at the sixth hour of the day4 ,which agrees exactly with the time that the darkness at the crucifixion began1 according to the three ,evangelists who mention it#hi3 and therefore must have been the very same darkness1 but mistaken by ,phlegon for a natural ,eclipse of the ,sun2 which was impossible on two accounts1 #a4 because it was at the time of ,full ,moon2 and #b4 because whoever takes the pains to calculate1 will find that there could be no regular and total ,eclipse of the ,sun that year in any part of ,judea1 nor any where between ,jerusalem and ,egypt3 so that this darkness must have been quite out of the common course of nature4 ,from the co-incidence of these characters1 ,i made no doubt of having ascertained the true year and day of our ,,saviour's death4 ,but having very lately read what some eminent authors have wrote on the same subject1 of which ,i was really ignorant before2 and heard the opinions of other candid and ingenious enquirers after truth 7which every honest man will follow wherever it leads him7 and who think they have strong reasons for believing that the time of ,,christ's death was not in the year of the ,julian ,period #dgdf1 but in the year #dgdc2 ,i find difficulties on both sides1 not easily got over3 and shall therefore state the case both ways as fairly as ,i can2 leaving the reader to take which side of the ,question he pleases4 ,both ,dr4 ,prideaux and ,sir ,isaac ,newton are of opinion that ,daniel's seventy weeks1 consisting of #dij years 7,dan4 chap4 ix4 v4 #bc-bf7 began with the time when ,ezra received his commission from ,artaxerxes to go to ,jerusalem1 which was in the seventh year of that ,king's reign 7,ezra ch4 vii4 v4 #aa-bf7 and ended with the death of ,,christ4 ,for1 by joining the accomplishment of that prophecy with the expiation of ,sin1 those weeks cannot well be supposed to end at any other time4 ,and both these authors agree that this was ,artaxerxes ,longimanus1 not ,artaxerxes ,mnemon4 ,the ,doctor thinks that the last of those annual weeks was equally divided between ,john's ministry and ,,christ's4 ,and1 as to the half week1 mentioned by ,daniel chap4 ix4 v4 #bg4 ,sir ,isaac thinks it made no part of the above seventy2 but only meant the three years and an half in which the ,romans made war upon the ,jews from spring in ,a4,d4 #fg to autumn in ,a4,d4 #gj1 when a final ,period was put to their sacrifices and oblations by destroying their city and sanctuary1 on which they were utterly dispersed4 ,now1 both by the undoubted ,canon of ,ptolemy1 and the famous ra of ,nabonassar1 which is so well verified by ,eclipses that it cannot deceive us1 the beginning of these seventy weeks1 or the seventh year of the reign of ,artaxerxes ,longimanus1 is pinned down to the year of the ,julian ,period #dbef3 from which count #dij years to the death of ,,christ1 and the same will fall in the above year of the ,julian ,period #dgdf3 which would seem to ascertain the true year beyond dispute4 ,but as ,josephus's ,eclipse of the ,moon in a great measure fixes our ,,saviour's birth to the end of the #dgacth year of the ,julian ,period1 and a ,friday ,passover ,full ,moon fixes the time of his death to the third of ,april in the #dgdfth year of that ,period1 the same as above by ,daniel's weeks1 this supposes our ,,saviour to have been crucified in the #cgth year of his age4 ,and as ,st4 ,luke chap4 iii4 ver4 #bc4 fixes the time of ,,christ's baptism to the beginning of his #cjth year1 it would hence seem that his publick ministry1 to which his baptism was the initiation1 lasted seven years4 ,but1 as it would be very difficult to find account in all the ,evangelists of more than four ,passovers which he kept at ,jerusalem during the time of his ministry1 others think that he suffered in the vulgar #cjth year of his age1 which was really the #cc;d2 namely in the year of the ,julian ,period #dgdc4 ,and this opinion is farther strengthened by considering that our ,,saviour eat his last ,paschal ,supper on a ,thursday evening1 the day immediately before his crucifixion3 and that as he subjected himself to the law1 he would not break the law by keeping the ,passover on the day before the law prescribed2 neither would the ,priests have suffered the ,lamb to be killed for him before the fourteenth day of ,nisan when it was killed for all the people1 ,exod4 xii4 ver4 #f4 ,and hence they infer that he kept this ,passover at the same time with the rest of the ,jews1 in the vulgar #cjth year of his age3 at which time it is evident by calculation that there was a ,passover ,full ,moon on ,thursday ,april the #fth4 ,but this is pressed with two difficulties4 #a4 ,it drops the last half of ,daniel's seventieth week1 as of no moment in the prophecy2 and #b4 it sets aside the testimony of ,phlegon1 as if he had mistaken almost a whole ,olympiad4 ,others again endeavour to reconcile the whole difference1 by supposing1 that as ,,christ expressed himself only in round numbers concerning the time he was to lie in the grave1 ,matt4 xii4 #dj4 so might ,st4 ,luke possibly have done with regard to the year of his baptism3 which would really seem to be the case when we consider1 that the ,jews told our ,,saviour1 sometime before his death1 ,thou art not yet fifty years old1 ,john vii4 #eg4 which indeed was more likely to be said to a person near forty than to one but just turned of thirty4 ,and as to his eating the above ,passover on ,thursday1 which must have been on the ,jewish ,full ,moon day1 they think it may be easily accommodated to the #cgth year of his age2 since1 as the ,jews always began their day in the evening1 their ,friday of course began on the evening of our ,thursday4 ,and it is evident1 as above-mentioned1 that the only ,jewish ,friday ,full ,moon1 at the time of their ,passover1 was in the vulgar #cc;d1 but the real #cgth year of ,,christ's age2 which was the #dgdfth year of the ,julian ,period1 and the last year of the #bjb;d ,olympiad4 ,sidenote3 ras or ,epochas4 #dcc4 ,as there are certain fixed points in the ,heavens from which ,astronomers begin their computations1 so there are certain points of time from which historians begin to reckon2 and these points or roots of time are called ras or ,epochas4 ,the most remarkable ras are those of the ,creation1 the ,greek ,olympiads1 the building of ,rome1 the ra of ,nabonassar1 the death of ,alexander1 the birth of ,,christ1 the ,arabian ,hegira1 and the ,persian ,jesdegird3 ,all which1 together with several others of less note1 have their beginnings in the following ,table fixed to the years of the ,julian ,period1 to the age of the world at those times1 and to the years before and after the birth of ,,christ4 ,julian ,period4 ,y4 of the ,world4 ,before ,christ4 #a4 ,the creation of the world1 according to ,strauchius #gfd #a #cidi #b4 ,the ,deluge1 or ,noah's ,flood #bdbj #afef #bbic #c4 ,the ,assyrian ,monarchy by ,nimrod #becg #aggc #bagf #d4 ,the ,birth of ,abraham #bgab #aidh #bjja #e4 ,the beginning of the ,kingdom of the ,argives #bhef #bjib #aheg #f4 ,the begin4 of the ,kingdom of ,athens by ,cecrops #caeg #bcic #aeef #g4 ,the departure of the ,israelites from ,egypt #cbaf #bdeb #adig #h4 ,their entrance into ,canaan1 or the ,jubilee #cbef #bdib #adeg #i4 ,the destruction of ,troy #cebi #bhfe #aahd #aj4 ,the beginning of ,king ,david's reign #cfec #bhhi #ajfj #aa4 ,the foundation of ,solomon's ,temple #cfif #bicb #ajag #ab4 ,the ,argonautic expedition #cggf #cjab #icg #ac4 ,arbaces1 the first ,king of the ,medes #chch #cjgd #age #ad4 ,mandaucus the second #chfe #caja #hdh #ae4 ,sosarmus the third #ciae #caea #gih #af4 ,artica the fourth #cide #caha #gfh #ag4 ,cardica the fifth #ciif #cbcb #gah #ah4 ,phraortes the sixth #djeg #cbic #fef #ai4 ,cyaxares the seventh #djhj #ccaf #fcc #bj4 ,the beginning of the ,olympiads #cich #cagd #gge #ba4 ,the ,catonian ,epocha of the building of ,rome #cifa #caig #geb #bb4 ,the ra of ,nabonassar #cifg #cbjb #gdf #bc4 ,the destruction of ,samaria #ciij #cbbf #gbc #bd4 ,the ,babylonish captivity #dacc #ccdi #fjj #be4 ,the destruction of ,solomon's ,temple #dabd #ccfj #ehi #bf4 ,the ,persian monarchy founded by ,cyrus #daed #ccij #eei #bg4 ,the battle of ,marathon #dbbd #cdfj #dhi #bh4 ,the begin4 of the reign of ,art4 ,longimanus #dbdi #cdhe #dfd #bi4 ,the beginning of ,daniel's #gj weeks #dbef #cdib #deg #cj4 ,the beginning of the ,peloponnesian war #dbhb #ceah #dca #ca4 ,the death of ,alexander #dcij #cfbf #cbc #cb4 ,the restoration of the ,jews #dedh #cghd #abi #cc4 ,the corr4 of the ,calendar by ,julius ,csar #dffi #cije #dd #cd4 ,the beginning of the reign of ,herod #dfgc #ciji #dj #ce4 ,the ,spanish ra #dfge #ciaa #ch #cf4 ,the battle at ,actium #dfhc #ciai #cj #cg4 ,the taking of ,alexandria #dfhc #ciai #cj #ch4 ,the ,epoch of the title of ,augustus #dfhf #cibb #bg #ci4 ,the true ra of ,,christ's birth #dgji #cide #d #dj4 ,the death of ,herod #dgaj #cidf #c #da4 ,the ,diony4 or vulg4 ra of the birth of ,,christ #dgac #cidi ,,ad#j #db4 ,the true year of ,,christ's death #dgdf #cihb #cc #dc4 ,the destruction of ,jerusalem #dghc #djai #gj #dd4 ,the ,dioclesian persecution #ejae #dbea #cjb #de4 ,the ,epoch of ,constantine the ,great #ejai #dbee #cjf #df4 ,the ,council of ,nice #ejch #dbgd #cbe #dg4 ,the ,epocha of the ,hegira #ecce #dega #fbb #dh4 ,the ,epoch of ,yesdejerd #ecdd #dehj #fca #di4 ,the ,jellalan ,epocha #egia #ejbg #ajgh #ej4 ,the ,epocha of the reformation #fbcj #edff #aeag ---------------------------------------- -------------------------------- ,,tab4 ,i4 ,shewing the ,golden ,number 7which is the same both in the ,old and ,new ,style7 from the ,christian ra to ,a4,d4 #djjj4 ---------------------------------------- -------------------------------- ,years less than an ,hundred4 ---------------------------------------- -------------- #j #a #b #cd #ef #g #h #iajaaabacadaeafagah #aibjbabbbcbdbebfbgbhbicjcacbcccdcecfcg ,hundreds of #chcidjdadbdcdddedfdgdhdiejeaebecedeeef ,years4 #egeheifjfafbfcfdfefffgfhfigjgagbgcgdge #gfggghgihjhahbhchdhehfhghhhiijiaibicid #ieifigihii -------------- #jaijjchjj #a #b #c #d #e #f #g #h #iajaaabacadaeafagahai #ajjbjjjcijj #f #g #h #iajaaabacadaeafagahai #a #b #c #d #e #bjjbajjdjjjaaabacadaeafagahai #a #b #c #d #e #f #g #h #iaj #cjjbbjj c4#afagahai #a #b #c #d #e #f #g #h #iajaaabacadae #djjbcjj -- #b #c #d #e #f #g #h #iajaaabacadaeafagahai #a ---------------------------------------- ---------- #ejjbdjj -- #g #h #iajaaabacadaeafagahai #a #b #c #d #e #f #fjjbejj -- #abacadaeafagahai #a #b #c #d #e #f #g #h #iajaa #gjjbfjj -- #agahai #a #b #c #d #e #f #g #h #iajaaabacadaeaf #hjjbgjj -- #c #d #e #f #g #h #iajaaabacadaeafagahai #a #b #ijjbhjj -- #h #iajaaabacadaeafagahai #a #b #c #d #e #f #g ---------------------------------------- ---------- #ajjjbijj -- #acadaeafagahai #a #b #c #d #e #f #g #h #iajaaab #aajjcjjj -- #ahai #a #b #c #d #e #f #g #h #iajaaabacadaeafag #abjjcajj -- #d #e #f #g #h #iajaaabacadaeafagahai #a #b #c #acjjcbjj -- #iajaaabacadaeafagahai #a #b #c #d #e #f #g #h #adjjccjj -- #adaeafagahai #a #b #c #d #e #f #g #h #iajaaabac ---------------------------------------- ---------- #aejjcdjj -- #ai #a #b #c #d #e #f #g #h #iajaaabacadaeafagah #afjjcejj -- #e #f #g #h #iajaaabacadaeafagahai #a #b #c #d #agjjcfjj -- #ajaaabacadaeafagahai #a #b #c #d #e #f #g #h #i #ahjjcgjj -- #aeafagahai #a #b #c #d #e #f #g #h #iajaaabacad ---------------------------------------- ---------- ---------------------------------------- ---------------------- ,,tab4 ,,ii4 ,shewing the ,number of ,direction1 for finding ,easter ,sunday by the ,golden ,number and ,dominical ,letter4 ---------------------------------------- --- ,g4 ,n4 #a #b #c #d #e #f #g #h #iajaaabacadaeafagahai ---------------------------------------- --- ,a #bfai #ebfabccaiabbfai #ebfab #ebfabccaiab ,b #bgac #fbgaccdbjacbgbj #fbgac #fbjaccdbj #f ,c #bhad #gbaadceba #gbhba #gbhad #gbaadbhba #g ,d #biae #hbbaebibb #hbiae #hbiae #abbaebibb #h ,e #cjaf #bbcafcjbc #icjaf #ibcaf #bbc #icjbc #i ,f #bdag #cbdajcabdajcaagajbdag #cbdajcaagaj ,g #beah #dbeaacbahaacbah #dbeah #dbeaacbahaa ---------------------------------------- --- ,this ,table is adapted to the ,new ,style4 ---------------------------------------- ---------------------- ,,tab4 ,,iii4 ,shewing the ,dominical ,letters1 ,old ,style1 for #dbjj ,years before the ,christian ra4 ---------------------------------------- --------------------------- ,before ,christ ,hundreds of ,years4 ---------------------------------------- --------------------- #j #ajj #bjj #cjj #djj #ejj #fjj #gjj #hjj #ijj #ajjj #aajj #abjj #acjj ,years less #adjj #aejj #afjj #agjj #ahjj #aijj #bjjj than an #bajj #bbjj #bcjj #bdjj #bejj #bfjj #bgjj ,hundred4 #bhjj #bijj #cjjj #cajj #cbjj #ccjj #cdjj #cejj #cfjj #cgjj #chjj #cijj #djjj #dajj ---------------------------------------- ------------------ #j #bh #ef #hd ,d ,c ,c ,b ,b ,a ,a ,g ,g ,f ,f ,e ,e ,d ---------------------------------------- ------------------ #a #bi #eg #he ,e ,d ,c ,b ,a ,g ,f #b #cj #eh #hf ,f ,e ,d ,c ,b ,a ,g #c #ca #ei #hg ,g ,f ,e ,d ,c ,b ,a #d #cb #fj #hh ,b ,a ,a ,g ,g ,f ,f ,e ,e ,d ,d ,c ,c ,b ---------------------------------------- ------------------ #e #cc #fa #hi ,c ,b ,a ,g ,f ,e ,d #f #cd #fb #ij ,d ,c ,b ,a ,g ,f ,e #g #ce #fc #ia ,e ,d ,c ,b ,a ,g ,f #h #cf #fd #ib ,g ,f ,f ,e ,e ,d ,d ,c ,c ,b ,b ,a ,a ,g ---------------------------------------- ------------------ #i #cg #fe #ic ,a ,g ,f ,e ,d ,c ,b #aj #ch #ff #id ,b ,a ,g ,f ,e ,d ,c #aa #ci #fg #ie ,c ,b ,a ,g ,f ,e ,d #ab #dj #fh #if ,e ,d ,d ,c ,c ,b ,b ,a ,a ,g ,g ,f ,f ,e ---------------------------------------- ------------------ #ac #da #fi #ig ,f ,e ,d ,c ,b ,a ,g #ad #db #gj #ih ,g ,f ,e ,d ,c ,b ,a #ae #dc #ga #ii ,a ,g ,f ,e ,d ,c ,b #af #dd #gb ,c ,b ,b ,a ,a ,g ,g ,f ,f ,e ,e ,d ,d ,c ---------------------------------------- ------------------ #ag #de #gc ,d ,c ,b ,a ,g ,f ,e #ah #df #gd ,e ,d ,c ,b ,a ,g ,f #ai #dg #ge ,f ,e ,d ,c ,b ,a ,g #bj #dh #gf ,a ,g ,g ,f ,f ,e ,e ,d ,d ,c ,c ,b ,b ,a ---------------------------------------- ------------------ #ba #di #gg ,b ,a ,g ,f ,e ,d ,c #bb #ej #gh ,c ,b ,a ,g ,f ,e ,d #bc #ea #gi ,d ,c ,b ,a ,g ,f ,e #bd #eb #hj ,f ,e ,e ,d ,d ,c ,c ,b ,b ,a ,a ,g ,g ,f ---------------------------------------- ------------------ #be #ec #ha ,g ,f ,e ,d ,c ,b ,a #bf #ed #hb ,a ,g ,f ,e ,d ,c ,b #bg #ee #hc ,b ,a ,g ,f ,e ,d ,c ---------------------------------------- ------------------ ,,tab4 ,,iv4 ,shewing the ,dominical ,letters1 ,old ,style1 for #dbjj ,years after the ,christian ra4 ---------------------------------------- --------------------------- ,after ,christ ,hundreds of ,years4 ---------------------------------------- --------------------- #j #ajj #bjj #cjj #djj #ejj #fjj #gjj #hjj #ijj #ajjj #aajj #abjj #acjj ,years less #adjj #aejj #afjj #agjj #ahjj #aijj #bjjj than an #bajj #bbjj #bcjj #bdjj #bejj #bfjj #bgjj ,hundred4 #bhjj #bijj #cjjj #cajj #cbjj #ccjj #cdjj #cejj #cfjj #cgjj #chjj #cijj #djjj #dajj ---------------------------------------- ------------------ #j #bh #ef #hd ,d ,c ,e ,d ,f ,e ,g ,f ,a ,g ,b ,a ,c ,b ---------------------------------------- ------------------ #a #bi #eg #he ,b ,c ,d ,e ,f ,g ,a #b #cj #eh #hf ,a ,b ,c ,d ,e ,f ,g #c #ca #ei #hg ,g ,a ,b ,c ,d ,e ,f #d #cb #fj #hh ,f ,e ,g ,f ,a ,g ,b ,a ,c ,b ,d ,c ,e ,d ---------------------------------------- ------------------ #e #cc #fa #hi ,d ,e ,f ,g ,a ,b ,c #f #cd #fb #ij ,c ,d ,e ,f ,g ,a ,b #g #ce #fc #ia ,b ,c ,d ,e ,f ,g ,a #h #cf #fd #ib ,a ,g ,b ,a ,c ,b ,d ,c ,e ,d ,f ,e ,g ,f ---------------------------------------- ------------------ #i #cg #fe #ic ,f ,g ,a ,b ,c ,d ,e #aj #ch #ff #id ,e ,f ,g ,a ,b ,c ,d #aa #ci #fg #ie ,d ,e ,f ,g ,a ,b ,c #ab #dj #fh #if ,c ,b ,d ,c ,e ,d ,f ,e ,g ,f ,a ,g ,b ,a ---------------------------------------- ------------------ #ac #da #fi #ig ,a ,b ,c ,d ,e ,f ,g #ad #db #gj #ih ,g ,a ,b ,c ,d ,e ,f #ae #dc #ga #ii ,f ,g ,a ,b ,c ,d ,e #af #dd #gb ,e ,d ,f ,e ,g ,f ,a ,g ,b ,a ,c ,b ,d ,c ---------------------------------------- ------------------ #ag #de #gc ,c ,d ,e ,f ,g ,a ,b #ah #df #gd ,b ,c ,d ,e ,f ,g ,a #ai #dg #ge ,a ,b ,c ,d ,e ,f ,g #bj #dh #gf ,g ,f ,a ,g ,b ,a ,c ,b ,d ,c ,e ,d ,f ,e ---------------------------------------- ------------------ #ba #di #gg ,e ,f ,g ,a ,b ,c ,d #bb #ej #gh ,d ,e ,f ,g ,a ,b ,c #bc #ea #gi ,c ,d ,e ,f ,g ,a ,b #bd #eb #hj ,b ,a ,c ,b ,d ,c ,e ,d ,f ,e ,g ,f ,a ,g ---------------------------------------- ------------------ #be #ec #ha ,g ,a ,b ,c ,d ,e ,f #bf #ed #hb ,f ,g ,a ,b ,c ,d ,e #bg #ee #hc ,e ,f ,g ,a ,b ,c ,d ---------------------------------------- ------------------ ,,tab4 ,v4 ,the ,dominical ,letter1 ,new ,style1 for #djjj ,years after the ,christian ra4 ---------------------------------------- ------ ,after ,christ4 ,hundreds of ,years4 ---------------------------------------- --- #ajj #bjj #cjj #djj #ejj #fjj #gjj #hjj #ijj #ajjj #aajj #abjj #acjj #adjj #aejj #afjj #agjj #ahjj #aijj #bjjj ,years less than #bajj #bbjj #bcjj #bdjj an ,hundred4 #bejj #bfjj #bgjj #bhjj #bijj #cjjj #cajj #cbjj #ccjj #cdjj #cejj #cfjj #cgjj #chjj #cijj #djjj ------------------------ ,c ,e ,g ,b ,a ---------------------------------------- #a #bi #eg #he ,b ,d ,f ,g #b #cj #eh #hf ,a ,c ,e ,f #c #ca #ei #hg ,g ,b ,d ,e #d #cb #fj #hh ,f ,e ,a ,g ,c ,b ,d ,c ---------------------------------------- #e #cc #fa #hi ,d ,f ,a ,b #f #cd #fb #ij ,c ,e ,g ,a #g #ce #fc #ia ,b ,d ,f ,g #h #cf #fd #ib ,a ,g ,c ,b ,c ,d ,f ,e ---------------------------------------- #i #cg #fe #ic ,f ,a ,c ,d #aj #ch #ff #id ,e ,g ,b ,c #aa #ci #fg #ie ,d ,f ,a ,b #ab #dj #fh #if ,c ,b ,e ,d ,g ,f ,a ,g ---------------------------------------- #ac #da #fi #ig ,a ,c ,e ,f #ad #db #gj #ih ,g ,b ,d ,e #ae #dc #ga #ii ,f ,a ,c ,d #af #dd #gb ,e ,d ,g ,f ,b ,a ,c ,b ---------------------------------------- #ag #de #gc ,c ,e ,g ,a #ah #df #gd ,b ,d ,f ,g #ai #dg #ge ,a ,c ,e ,f #bj #dh #gf ,g ,f ,b ,a ,d ,c ,e ,d ---------------------------------------- #ba #di #gg ,e ,g ,b ,c #bb #ej #gh ,d ,f ,a ,b #bc #ea #gi ,c ,e ,g ,a #bd #eb #hj ,b ,a ,d ,c ,f ,e ,g ,f ---------------------------------------- #be #ec #ha ,g ,b ,d ,e #bf #ed #hb ,f ,a ,c ,d #bg #ee #hc ,e ,g ,b ,c #bh #ef #hd ,d ,c ,f ,e ,a ,g ,b ,a ---------------------------------------- ,,tab4 ,,vi4 ,shewing the ,days of the ,months for both ,styles by the ,dominical ,letters4 ---------------------------------------- - ,week ,day4 ,a ,b ,c ,d ,e ,f ,g ---------------------------------------- - #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad ,january #ca #ae #af #ag #ah #ai #bj #ba ,october #ca #bb #bc #bd #be #bf #bg #bh #bi #cj #ca ---------------- ------------------------- #a #b #c #d #e #f #g #h #i #aj #aa ,feb4 #bh-bi #ab #ac #ad #ae #af #ag #ah ,march #ca #ai #bj #ba #bb #bc #bd #be ,nov4 #cj #bf #bg #bh #bi #cj #ca ---- ------------------------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae ,april #cj #af #ag #ah #ai #bj #ba #bb ,july #ca #bc #bd #be #bf #bg #bh #bi #cj #ca -------------------- --------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai ,august #ca #bj #ba #bb #bc #bd #be #bf #bg #bh #bi #cj #ca -------- --------------------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af ,septemb4 #cj #ag #ah #ai #bj #ba #bb #bc ,decemb4 #ca #bd #be #bf #bg #bh #bi #cj #ca ------------------------ ----------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai #bj ,may #ca #ba #bb #bc #bd #be #bf #bg #bh #bi #cj #ca ------------ ----------------------------- #a #b #c #d #e #f #g #h #i #aj #aa #ab #ac #ad #ae #af #ag ,june #cj #ah #ai #bj #ba #bb #bc #bd #be #bf #bg #bh #bi #cj ---------------------------------------- - ,,chap4 ,,xxii4 ,a ,description of the ,astronomical ,machinery serving to explain and illustrate the foregoing part of this ,treatise4 ,sidenote3 ,fronting the ,title ,page4 ,the ,,orrery4 #dcd4 ,the ,,orrery4 ,this ,machine shews the ,motions of the ,sun1 ,mercury1 ,venus1 ,earth1 and ,moon2 and occasionally1 the superior ,planets1 ,mars1 ,jupiter1 and ,saturn may be put on2 ,jupiter's four ,satellites are moved round him in their proper times by a small ,winch2 and ,saturn has his five ,satellites1 and his ,ring which keeps its parallelism round the ,sun2 and by a ,lamp put in the ,sun's place1 the ,ring shews all the ,phases described in the #bjdth ,article4 ,sidenote3 ,the ,sun4 ,the ,ecliptic4 ,in the ,center1 ,no #a4 represents the ,,sun1 supported by it's ,axis inclining almost #h ,degrees from the ,axis of the ,ecliptic2 and turning round in #be-a_/d days on its ,axis1 of which the ,north ,pole inclines toward the #hth ,degree of ,pisces in the great ,ecliptic 7,no4 #aa47 whereon the ,months and ,days are engraven over the ,signs and ,degrees in which the ,sun appears1 as seen from the ,earth1 on the different days of the year4 ,sidenote3 ,mercury4 ,the nearest ,planet 7,no4 #b7 to the ,sun is ,mercury1 which goes round him in #hg days #bc hours1 or #hg-bc_/bd diurnal rotations of the ,earth2 but has no ,motion round its ,axis in the ,machine1 because the time of its diurnal ,motion in the ,heavens is not known to us4 ,sidenote3 ,venus4 ,the next ,planet in order is ,venus 7,no4 #c7 which performs her annual ,course in #bbd days #ag hours2 and turns round her ,axis in #bd days #h hours1 or in #bd-a_/c diurnal rotations of the ,earth4 ,her ,axis inclines #ge ,degrees from the ,axis of the ,ecliptic1 and her ,north ,pole inclines towards the #bjth ,degree of ,aquarius1 according to the observations of ,bianchini4 ,she shews all the ,phenomena described from the #cjth to the #ddth ,article in ,chap4 ,i4 ,sidenote3 ,the ,earth4 ,next without the ,orbit of ,venus is the ,earth 7,no4 #d7 which turns round its ,axis1 to any fixed point at a great distance1 in #bc hours #ef minutes #d seconds of mean solar time 7#bba seq47 but from the ,sun to the ,sun again in #bd hours of the same time4 ,no4 #f is a sidereal ,dial-,plate under the ,earth2 and ,no4 #g a solar ,dial-,plate on the cover of the ,machine4 ,the ,index of the former shews sidereal1 and of the latter1 solar time2 and hence1 the former ,index gains one entire revolution on the latter every year1 as #cfe solar or natural days contain #cff sidereal days1 or apparent revolutions of the ,stars4 ,in the time that the ,earth makes #cfe-a_/d diurnal rotations on its ,axis1 it goes once round the ,sun in the ,plane of the ,ecliptic2 and always keeps opposite to a moving ,index 7,no4 #aj7 which shews the ,sun's daily change of place1 and also the days of the months4 ,the ,earth is half covered with a black cap for dividing the apparently enlightened half next the ,sun1 from the other half1 which when turned away from him is in the dark4 ,the edge of the cap represents the ,circle bounding ,light and ,darkness1 and shews at what time the ,sun rises and sets to all places throughout the year4 ,the ,earth's ,axis inclines #bc-a_/b ,degrees from the ,axis of the ,ecliptic1 the ,north ,pole inclines toward the beginning of ,cancer2 and keeps its parallelism throughout its annual ,course #dh1 #bjb2 so that in ,summer the northern parts of the ,earth incline towards the ,sun1 and in the ,winter from him3 by which means1 the different lengths of days and nights1 and the cause of the various seasons1 are demonstrated to sight4 ,there is a broad ,horizon1 to the upper side of which is fixed a ,meridian ,semi-circle in the ,north and ,south ,points1 graduated on both sides from the ,horizon to #ij in the ,zenith1 or vertical ,point4 ,the edge of the ,horizon is graduated from the ,east and ,west to the ,south and ,north ,points1 and within these ,divisions are the ,points of the ,compass4 ,on the lower side of this thin ,horizon ,plate stand out four small ,wires1 to which is fixed a ,twilight ,circle #ah ,degrees from the graduated side of the ,horizon all round4 ,this ,horizon may be put upon the ,earth 7when the cap is taken away7 and rectified to the ,latitude of any place3 and then1 by a small ,wire called the ,solar ,ray1 which may be put on so as to proceed directly from the ,sun's ,center towards the ,earth's1 but to come no farther than almost to touch the ,horizon1 the beginning of ,twilight1 time of ,sun-rising1 with his ,amplitude1 ,meridian ,altitude1 time of ,setting1 ,amplitude1 and end of ,twilight1 are shewn for every day of the year1 at that place to which the ,horizon is rectified4 ,sidenote3 ,the ,moon4 ,the ,moon 7,no4 #e7 goes round the ,earth1 from between it and any fixed point at a great distance1 in #bg days #g hours #dc minutes1 or through all the ,signs and ,degrees of her ,orbit2 which is called her ,periodical ,revolution2 but she goes round from the ,sun to the ,sun again1 or from ,change to ,change1 in #bi days #ab hours #de minutes1 which is her ,synodical ,revolution2 and in that time she exhibits all the ,phases already described #bee4 ,when the above-mentioned ,horizon is rectified to the ,latitude of any given place1 the times of the ,moon's rising and setting1 together with her ,amplitude1 are shewn to that place as well as the ,sun's2 and all the various ,phenomena of the ,harvest ,moon #bgc seq4 made obvious to sight4 ,sidenote3 ,the ,nodes4 ,the ,moon's ,orbit 7,no4 #i47 is inclined to the ,ecliptic1 7,no4 #aa47 one half being above1 and the other below it4 ,the ,nodes1 or ,points at #j and #j lie in the ,plane of the ,ecliptic1 as described #cag1 #cah1 and shift backward through all it's ,signs and ,degrees in #ah-b_/c years4 ,the ,degrees of the ,moon's ,latitude1 to the highest at ,,nl 7,north ,latitude7 and lowest at ,,sl 7,south ,latitude7 are engraven both ways from her ,nodes at #j and #j2 and1 as the ,moon rises and falls in her ,orbit according to its inclination1 her ,latitude and ,distance from her ,nodes are shewn for every day2 having first rectified her ,orbit so as to set the ,nodes to their proper places in the ,ecliptic3 and then1 as they come about at different1 and almost opposite times of the year #cai1 and then point towards the ,sun1 all the ,eclipses may be shewn for hundreds of years 7without any new rectification7 by turning the ,machinery backward for time past1 or forward for time to come4 ,at #ag ,degrees distance from each ,node1 on both ,sides1 is engraved a small ,sun2 and at #ab ,degrees distance1 a small ,moon2 which shew the limits of solar and lunar ,eclipses #cag3 and when1 at any change1 the ,moon falls between either of these ,suns and the ,node1 the ,sun will be eclipsed on the day pointed to by the annual ,index 7,no4 #aj17 and as the ,moon has then ,north or ,south ,latitude1 one may easily judge whether that ,eclipse will be visible in the ,northern or ,southern ,hemisphere2 especially as the ,earth's ,axis inclines towards the ,sun or from him at that time4 ,and when1 at any ,full1 the ,moon falls between either of the little ,moon's and ,node1 she will be eclipsed1 and the annual ,index shews the day of that ,eclipse4 ,there is a ,circle of #bi-a_/b equal parts 7,no4 #h47 on the cover of the ,machine1 on which an ,index shews the days of the ,moon's age4 ,sidenote3 ,,plate ,,ix4 ,fig4 ,x4 ,there are two ,semi-circles fixed to an elliptical ,ring1 which being put like a cap upon the ,earth1 and the forked part ,f upon the ,moon1 shews the ,tides as the ,earth turns round within them1 and they are led round it by the ,moon4 ,when the different ,places come to the ,semi-circle ,aa,eb,b1 they have ,tides of ,flood2 and when they come to the ,semicircle ,,ced they have ,tides of ,ebb #cjd1 #cje2 the ,index on the hour ,circle 7,no4 #g47 shewing the times of these ,phenomena4 ,there is a jointed ,wire1 of which one end being put into a hole in the upright stem that holds the ,earth's cap1 and the ,wire laid into a small forked piece which may be occasionally put upon ,venus or ,mercury1 shews the direct and retrograde ,motions of these two ,planets1 with their stationary ,times and ,places as seen from the ,earth4 ,the whole ,machinery is turned by a winch or handle 7,no4 #ab17 and is so easily moved that a clock might turn it without any danger of stopping4 ,to give a ,plate of the wheel-work of this ,machine1 would answer no purpose1 because many of the wheels lie so behind others as to hide them from sight in any view whatsoever4 ,sidenote3 ,another ,,orrery4 ,,plate ,,vi4 ,fig4 ,i4 #dce4 ,another ,,orrery4 ,in this ,machine1 which is the simplest ,i ever saw1 for shewing the diurnal and annual motions of the ,earth1 together with the motion of the ,moon and her ,nodes2 ,a and ,b are two oblong square ,plates held together by four upright pillars2 of which three appear at f1 g1 and g#b4 ,under the ,plate ,a is an endless screw on the ,axis of the handle b1 which works in a wheel fixed on the same ,axis with the double grooved wheel ,e2 and on the top of this ,axis is fixed the toothed wheel i1 which turns the pinion k1 on the top of whose ,axis is the pinion k#b which turns another pinion b#b1 and that other turns a third1 on the ,axis a#b of which is the ,earth ,u turning round2 this last ,axis inclining #bc-a_/b ,degrees4 ,the supporter ,x#b1 in which the ,axis of the ,earth turns1 is fixed to the moveable ,plate ,c4 ,in the fixed ,plate ,b1 beyond ,h1 is fixed the strong wire d1 on which hangs the ,sun ,t so as it may turn round the wire4 ,to this ,sun is fixed the wire or solar ray ,z1 which 7as the ,earth ,u turns round its ,axis7 points to all the places that the ,sun passes vertically over1 every day of the year4 ,the ,earth is half covered with a black cap a1 as in the former ,orrery1 for dividing the day from the night2 and1 as the different places come out from below the edge of the cap1 or go in below it1 they shew the times of ,sun-rising and setting every day of the year4 ,this cap is fixed on the wire b1 which has a forked piece ,c turning round the wire d3 and1 as the ,earth goes round the ,sun1 it carries the ,cap1 ,wire1 and solar ,ray round him2 so that the solar ,ray constantly points towards the ,earth's ,center4 ,on the ,axis of the pinion k is the pinion m1 which turns a wheel on the cock or supporter n1 and on the ,axis of this wheel nearest n is a pinion 7hid from view7 under the ,plate ,c1 which pinion turns a wheel that carries the ,moon ,v round the ,earth ,u2 the ,moon's ,axis rising and falling in the socket ,w1 which is fixed to the triangular piece above ,z2 and this piece is fixed to the top of the ,axis of the last mentioned wheel4 ,the socket ,w is slit on the outermost side2 and in this slit the two pins near ,y1 fixed in the ,moon's ,axis1 move up and down2 one of them being above the inclined ,plane ,,yx1 and the other below it4 ,by this mechanism1 the ,moon ,v moves round the ,earth ,t in the inclined ,orbit q1 parallel to the ,plane of the ,ring ,,yx2 of which the ,descending ,node is at ,x1 and the ,ascending ,node opposite to it1 but hid by the supporter ,x#b4 ,the small wheel ,e turns the large wheels ,d and ,f1 of equal diameters1 by cat-gut strings crossing between them3 and the ,axis of these two wheels are cranked at ,g and ,h1 above the ,plate ,b4 ,the upright stems of these cranks going through the ,plate ,c1 carry it over and over the fixed ,plate ,b1 with a motion which carries the ,earth ,u round the ,sun ,t1 keeping the ,earth's ,axis always parallel to itself2 or still inclining towards the left-hand of the ,plate2 and shewing the vicissitudes of seasons1 as described in the tenth chapter4 ,as the ,earth goes round the ,sun the pinion k goes round the wheel i1 for the ,axis of k never touches the fixed ,plate ,b2 but turns on a wire fixed into the ,plate ,c4 ,on the top of the crank ,g is an ,index ,l1 which goes round the ,circle m#b in the time that the ,earth goes round the ,sun2 and points to the days of the months2 which1 together with the names of the seasons1 are marked in this ,circle4 ,this ,index has a small grooved wheel ,l fixed upon it1 round which1 and the ,plate ,z1 goes a cat-gut string crossing between them2 and by this means the ,moon's inclined ,plane ,,yx with its ,nodes is turned backward1 for shewing the times and returns of ,eclipses #cai1 #cbj4 ,the following parts of this machine must be considered as distinct from those already described4 ,towards the right hand1 let ,s be the ,earth hung on the wire e1 which is fixed into the ,plate ,b2 and let ,o be the ,moon fixed on the ,axis ,m1 and turning round within the cap ,p1 in which1 and in the ,plate ,c the crooked wire ,q is fixed4 ,on the ,axis ,m is also fixed the ,index ,k1 which goes round a ,circle h#b1 divided into #bi-a_/b equal parts1 which are the days of the ,moon's age3 but to avoid confusion in the scheme1 it is only marked with the numeral figures #a #b #c #d1 for the ,quarters4 ,as the crank ,h carries this ,moon round the ,earth ,s in the ,orbit t1 she shews all her ,phases by means of the cap ,p for the different days of her age1 which are shewn by the ,index ,k2 this ,index1 turning just as the ,moon ,o does1 demonstrates her turning round her ,axis as she still keeps the same side towards the ,earth ,s #bfb4 ,sidenote3 ,,pl4 ,,viii4 ,at the other end of the ,plate ,c1 a ,moon ,n goes round an ,earth ,r in the ,orbit p2 but this ,moon's ,axis is stuck fast into the ,plate ,c at ,s#b2 so that neither ,moon nor ,axis can turn round2 and as this ,moon goes round her ,earth she shews herself all round to it2 which proves1 that if the ,moon was seen all round from the ,earth in a ,lunation1 she could not turn round her ,axis4 ,n4 ,b4 ,if there were only the two wheels ,d and ,f1 with a cat-gut string over them1 but not crossing between them1 the ,axis of the ,earth ,u would keep its parallelism round the ,sun ,t1 and shew all the seasons2 as ,i sometimes make these ,machines3 and the ,moon ,o would go round the ,earth ,s1 shewing her ,phases as above2 as likewise would the ,moon ,n round the ,earth ,r2 but then1 neither could the diurnal motion of the ,earth ,u on its ,axis be shewn1 nor the motion of the ,moon ,v round that ,earth4 ,sidenote3 ,the ,,calculator4 #dcf4 ,in the year #agdf ,i contrived a very simple ,machine1 and described it's performance in a small treatise upon the ,phenomena of the ,harvest ,moon1 published in the year #agdg4 ,i improved it soon after1 by adding another wheel1 and called it the ,calculator4 ,it may be easily made by any ,gentleman who has a mechanical ,genius4 ,sidenote3 ,fig4 ,i4 ,the great flat ,ring supported by twelve pillars1 and on which the twelve ,signs with their respective ,degrees are laid down1 is the ,ecliptic2 nearly in the center of it is the ,sun ,s supported by the strong crooked ,wire ,i2 and from the ,sun proceeds a ,wire ,w1 called the ,solar ,ray1 pointing towards the center of the ,earth ,e1 which is furnished with a moveable ,horizon ,h1 together with a brazen ,meridian1 and ,quadrant of ,altitude4 ,r is a small ,ecliptic1 whose ,plane co-incides with that of the great one1 and has the like ,signs and ,degrees marked upon it2 and is supported by two ,wires ,d and ,d1 which enter into the ,plate ,,pp1 but may be taken off at pleasure4 ,as the ,earth goes round the ,sun1 the ,signs of this small ,circle keep parallel to themselves1 and to those of the great ,ecliptic4 ,when it is taken off1 and the solar ,ray ,w drawn farther out1 so as almost to touch the ,horizon ,h1 or the ,quadrant of ,altitude1 the ,horizon being rectified to any given ,latitude1 and the ,earth turned round its ,axis by hand1 the point of the ,wire ,w shews the ,sun's ,declination in passing over the graduated brass ,meridian1 and his height at any given time upon the ,quadrant of ,altitude1 together with his ,azimuth1 or point of ,bearing upon the ,horizon at that time2 and likewise his ,amplitude1 and time of ,rising and ,setting by the hour ,index1 for any day of the year that the annual ,index ,u points to in the ,circle of ,months below the ,sun4 ,m is a solar ,index or ,pointer supported by the ,wire ,l which is fixed into the knob ,k3 the use of this ,index is to shew the ,sun's place in the ,ecliptic every day in the year2 for it goes over the ,signs and ,degrees as the ,index ,u goes over the months and days2 or rather as they pass under the ,index ,u1 in moving the cover plate with the ,earth and its ,furniture round the ,sun2 for the ,index ,u is fixed tight on the immoveable ,axis in the ,center of the ,machine4 ,k is a knob or handle for moving the ,earth round the ,sun1 and the ,moon round the ,earth4 ,as the ,earth is carried round the ,sun1 its ,axis constantly keeps the same oblique direction1 or parallel to itself #dh1 #bjb1 shewing thereby the different lengths of days and nights at different times of the year1 with all the various seasons4 ,and1 in one annual revolution of the ,earth1 the ,moon ,m goes #ab-a_/c times round it from ,change to ,change1 having an occasional provision for shewing her different ,phases4 ,the lower end of the ,moon's ,axis bears by a small friction wheel upon the inclined ,plane ,t1 which causes the ,moon to rise above and sink below the ,ecliptic ,r in every ,lunation2 crossing it in her ,nodes1 which shift backward through all the ,signs and ,degrees of the said ,ecliptic1 by the retrograde ,motion of the inclined ,plane ,t1 in #ah years and #bbe days4 ,on this ,plane the ,degrees and ,parts of the ,moon's ,north and ,south ,latitude are laid down from both the ,nodes1 one of which1 viz4 the ,descending ,node appears at #j1 by ,,dn above ,b2 the other ,node being hid from ,sight on this ,plane by the plate ,,pp2 and from both ,nodes1 at proper distances1 as in the other ,orrery1 the limits of ,eclipses are marked1 and all the solar and lunar ,eclipses are shewn in the same manner1 for any given year1 within the limits of #fjjj1 either before or after the ,christian ra4 ,on the plate that covers the wheel-work1 under the ,sun ,s1 and round the knob ,k are ,astronomical ,tables1 by which the ,machine may be rectified to the beginning of any given year within these limits1 in three or four minutes of time2 and when once set right1 may be turned backward for #cjj years past1 or forward for as many to come1 without requiring any new rectification4 ,there is a method for its adding up the #bith of ,february every fourth year1 and allowing only #bh days to that month for every other three3 but all this being performed by a particular manner of cutting the teeth of the wheels1 and dividing the month circle1 too long and intricate to be described here1 ,i shall only shew how these motions may be performed near enough for common use1 by wheels with grooves and cat-gut strings round them1 only here ,i must put the ,operator in mind that the grooves are to be made sharp 7not round7 bottomed to keep the strings from slipping4 ,the ,moon's ,axis moves up and down in the socket ,n fixed into the bar ,o 7which carries her round the ,earth7 as she rises above or sinks below the ,ecliptic2 and immediately below the inclined ,plane ,t is a flat circular plate 7between ,y and ,t7 on which the different ,excentricities of the ,moon's ,orbit are laid down2 and likewise her mean ,anomaly and elliptic ,equation by which her true ,place may be very nearly found at any time4 ,below this ,apogee-plate1 which shews the ,anomaly1 c4 is a ,circle ,y divided into #bi-a_/b equal parts which are the days of the ,moon's age3 and the forked end ,a of the ,index ,,ab 7,fig ,,ii7 may be put into the ,apogee-part of this plate2 there being just such another ,index to put into the inclined ,plane ,t at the ,ascending ,node2 and then the curved points ,b of these ,indexes shew the direct motion of the ,apogee1 and retrograde motion of the ,nodes through the ,ecliptic ,r1 with their ,places in it at any given time4 ,as the ,moon ,m goes round the ,earth ,e1 she shews her ,place every day in the ,ecliptic ,r1 and the lower end of her ,axis shews her ,latitude and distance from her ,node on the inclined ,plane ,t1 also her distance from her ,apogee and ,perigee1 together with her mean ,anomaly1 the then ,excentricity of her ,orbit1 and her elliptic ,equation1 all on the ,apogee ,plate1 and the day of her age in the ,circle ,y of #bi-a_/b equal parts2 for every day of the year pointed out by the annual ,index ,u in the ,circle of months4 ,having rectified the ,machine by the ,tables for the beginning of any year1 move the ,earth and ,moon forward by the knob ,k1 until the annual ,index comes to any given day of the month2 then stop1 and not only all the above ,phenomena may be shewn for that day1 but also1 by turning the ,earth round its ,axis1 the ,declination1 ,azimuth1 ,amplitude1 ,altitude of the ,moon at any hour1 and the times of her ,rising and ,setting1 are shewn by the ,horizon1 ,quadrant of ,altitude1 and hour ,index4 ,and in moving the ,earth round the ,sun1 the days of all the ,new and ,full ,moons and ,eclipses in any given year are shewn4 ,the ,phenomena of the ,harvest ,moon1 and those of the ,tides1 by such a cap as that in ,plate #i ,fig4 #aj4 put upon the ,earth and ,moon1 together with the solution of many problems not here related1 are made conspicuous4 ,sidenote3 ,,pl4 ,,viii4 ,the easiest1 though not the best way1 that ,i can instruct any mechanical person to make the wheel-work of such a machine1 is as follows2 which is the way that ,i made it1 before ,i thought of numbers exact enough to make it worth the trouble of cutting teeth in the wheels4 ,sidenote3 ,fig4 ,,iii4 ,fig4 #c;d of ,plate #h is a section of this ,machine2 in which ,,abcd is a frame of wood held together by four pillars at the corners1 whereof two appear at ,,ac and ,,bd4 ,in the lower ,plate ,,cd of this ,frame are three small friction-wheels1 at equal distances from each other2 two of them appearing at e and e4 ,as the frame is moved round1 these wheels run upon the fixed bottom ,plate ,,ee which supports the whole work4 ,in the ,center of this last mentioned ,plate is fixed the upright ,axis f ,,ffg1 and on the same ,axis is fixed the wheel ,,hhh in which are four grooves ,i1 ,x1 k1 ,l of different ,diameters4 ,in these grooves are cat-gut strings going also round the separate wheels ,m1 ,n1 ,o and ,p4 ,the wheel ,m is fixed on a solid ,spindle or ,axis1 the lower pivot of which turns at ,r in the under ,plate of the moveable frame ,,abcd2 and on the upper end of this ,axis is fixed the ,plate o o 7which is ,,pp1 under the ,earth1 in ,fig4 ,i47 and to this ,plate is fixed1 at an ,angle of #bc-a_/b ,degrees inclination1 the ,dial-plate below the ,earth ,t2 on the ,axis of which1 the ,index q is turned round by the ,earth4 ,this ,axis1 together with the ,wheel ,m1 and ,plate o o1 keep their parallelism in going round the ,sun ,s4 ,on the ,axis of the wheel ,m is a moveable socket on which the small wheel ,n is fixed1 and on the upper end of this socket is put on tight 7but so as it may be occasionally turned by hand7 the bar ,,zz 7viz4 the bar ,o in ,fig4 ,i47 which carries the ,moon m round the ,earth ,t1 by the ,socket n1 fixed into the bar4 ,as the ,moon goes round the ,earth her ,axis rises and falls in the ,socket n2 because1 on the lower end of her ,axis1 which is turned inward1 there is a small friction ,wheel s running on the inclined ,plane ,x 7which is ,t in ,fig4 ,i47 and so causes the ,moon alternately to rise above and sink below the little ,ecliptic ,,vv 7,r in ,fig4 ,i47 in every ,lunation4 ,on the ,socket or hollow ,axis of the ,wheel ,n1 there is another ,socket on which the ,wheel ,o is fixed2 and the ,moon's inclined ,plane ,x is put tightly on the upper end of this ,socket1 not on a square1 but on a round1 that it may be occasionally set by hand without wrenching the ,wheel or ,axle4 ,lastly1 on the hollow ,axis of the ,wheel ,o is another ,socket on which is fixed the ,wheel ,p1 and on the upper end of this ,socket is put on tightly the ,apogee-plate ,y1 7that immediately below ,t in ,fig4 ,i47 all these ,axles turn in the upper ,plate of the moveable frame at ,q which ,plate is covered with the thin ,plate cc 7screwed to it7 whereon are the fore-mentioned ,tables and month ,circle in ,fig4 ,i4 ,the middle part of the thick fixed ,wheel ,,hhh is much broader than the rest of it1 and comes out between the ,wheels ,m and ,o almost to the ,wheel ,n4 ,to adjust the diameters of the grooves of this fixed wheel to the grooves of the separate ,wheels ,m1 ,n1 ,o and ,p1 so as they may perform their motions in the proper times1 the following method must be observed4 ,the ,groove of the ,wheel ,m1 which keeps the parallelism of the ,earth's ,axis1 must be precisely of the same ,diameter as the lower ,groove ,i of the fixed ,wheel ,,hhh2 but1 when this ,groove is so well adjusted as to shew1 that in ever so many annual revolutions of the ,earth1 its ,axis keeps its parallelism1 as may be observed by the solar ,ray ,w 7,fig4 ,i47 always coming precisely to the same ,degree of the small ,ecliptic ,r at the end of every annual revolution1 when the ,index ,m points to the like ,degree in the great ,ecliptic2 then1 with the edge of a thin ,file give the ,groove of the ,wheel ,m a small rub all round2 and by that means1 lessening the ,diameter of the ,groove1 perhaps about the #bjth part of a hair's breadth1 it will cause the ,earth to shew the precession of the ,equinoxes2 which1 in many annual revolutions will begin to be sensible as the ,earth's ,axis slowly deviates from its parallelism #bdf1 towards the antecedent ,signs of the ,ecliptic4 ,the ,diameter of the ,groove of the ,wheel ,n1 which carries the ,moon round the ,earth1 must be to the ,diameter of the ,groove ,x as a ,lunation is to a year2 that is1 as #bi-a_/b to #cfe-a_/d4 ,the ,diameter of the ,groove of the ,wheel ,o1 which turns the inclined ,plane ,x with the ,moon's ,nodes backward1 must be to the ,diameter of the ,groove k as #bj to #ah-bbe_/cfe4 ,and1 ,lastly1 the ,diameter of the ,groove of the ,wheel ,p1 which carries the ,moon's ,apogee forward1 must be to the ,diameter of the ,groove ,l as #gj to #fb4 ,sidenote3 ,,plate ,,iv4 ,but1 after all this nice adjustment of the ,grooves to the proportional times of their respective ,wheels turning round1 and which seems to promise very well in ,theory1 there will still be found a necessity of a farther adjustment by hand2 because proper allowance must be made for the ,diameters of the cat-gut strings3 and the ,grooves must be so adjusted by hand1 as1 that in the time the ,earth is moved once round the ,sun1 the ,moon must perform #ab synodical revolutions round the ,earth1 and be almost #aa days old in her #acth revolution4 ,the inclined ,plane with its ,nodes must go once round backward through all the ,signs and ,degrees of the small ,ecliptic in #ah annual revolutions of the ,earth and #bbe days over4 ,and the ,apogee-plate must go once round forward1 so as its ,index may go over all the ,signs and ,degrees of the small ,ecliptic in eight years 7or so many annual revolutions of the ,earth7 and #cab days over4 ,n4 ,b4 ,the string which goes round the ,grooves ,x and ,n for the ,moon's ,motion must cross between these ,wheels2 but all the rest of the strings go in their respective ,grooves ,,im1 k,o1 and ,,lp without crossing4 ,sidenote3 ,the ,,cometarium4 #dcg4 ,the ,,cometarium4 ,this curious ,machine shews the ,motion of a ,comet or excentric ,body moving round the ,sun1 describing equal ,areas in equal times #aeb1 and may be so contrived as to shew such a ,motion for any ,degree of ,excentricity4 ,it was invented by the late ,dr4 ,desaguliers4 ,sidenote3 ,fig4 ,,iv4 ,the dark elliptical ,groove round the letters abcdefghiklm is the ,orbit of the ,comet ,y3 this ,comet is carried round in the ,groove according to the order of letters1 by the ,wire ,w1 fixed in the ,sun ,s1 and slides on the ,wire as it approaches nearer to or recedes farther from the ,sun1 being nearest of all in the ,perihelion a1 and farthest in the ,aphelion g4 ,the ,areas a,sb1 b,sc1 c,sd c4 or contents of these several ,triangles are all equal2 and in every turn of the ,winch ,n the ,comet ,y is carried over one of these ,areas2 consequently in as much time as it moves1 from f to g1 or from g to h1 it moves from m to a1 or from a to b2 and so of the rest1 being quickest of all at a1 and slowest at g4 ,thus1 the ,comet's velocity in its ,orbit continually decreases from the ,perihelion a to the ,aphelion g2 and increases in the same proportion from g to a4 ,sidenote3 ,,plate ,,iv4 ,the elliptic ,orbit is divided into #ab equal ,parts or ,signs with their respective ,degrees1 and so is the ,circle n o p q r s t n which represents a great ,circle in the ,heavens1 and to which all the fixed ,stars in the ,comet's way are referred4 ,whilst the ,comet moves from f to g in its ,orbit it appears to move only about #e ,degrees in this ,circle1 as is shewn by the small knob on the end of the ,wire ,w2 but in as short time as the ,comet moves from m to a1 or from a to b1 and it appears to describe the large space tn or no in the ,heavens1 either of which spaces contains #abj ,degrees or four ,signs4 ,were the ,excentricity of its ,orbit greater1 the greater still would be the difference of its ,motion1 and vice vers4 ,,abcdefghiklma is a circular ,orbit for shewing the equable ,motion of a ,body round the ,sun ,s1 describing equal ,areas ,,asb1 ,,bsc1 c4 in equal times with those of the ,body ,y in its elliptical ,orbit above mentioned2 but with this difference1 that the circular ,motion describes the equal ,arcs ,,ab1 ,,bc1 c4 in the same equal times that the elliptical ,motion describes the unequal ,arcs ab1 bc1 c4 ,now1 suppose the two ,bodies ,y and ,i to start from the ,points a and ,a at the same moment of time1 and each having gone round its respective ,orbit1 to arrive at these ,points again at the same instant1 the ,body ,y will be forwarder in its ,orbit than the ,body ,i all the way from a to g1 and from ,a to ,g2 but ,i will be forwarder than ,y through all the other half of the ,orbit2 and the difference is equal to the ,equation of the ,body ,y in its ,orbit4 ,at the ,points a1 ,a1 and g1 ,g1 that is1 in the ,perihelion and ,aphelion1 they will be equal2 and then the ,equation vanishes4 ,this shews why the ,equation of a ,body moving in an elliptic ,orbit1 is added to the mean or supposed circular ,motion from the ,perihelion to the ,aphelion1 and subtracted from the ,aphelion to the ,perihelion1 in ,bodies moving round the ,sun1 or from the ,perigee to the ,apogee1 and from the ,apogee to the ,perigee in the ,moon's ,motion round the ,earth1 according to the ,precepts in the #ceeth ,article2 only we are to consider1 that when ,motion is turned into ,time1 it reverses the titles in the ,table of ,the ,moon's elliptic ,equation4 ,sidenote3 ,fig4 ,v4 ,this curious ,motion is performed in the following manner4 ,,abc is a wooden bar 7in the box containing the wheel-work7 above which are the wheels ,d and ,e2 and below it the elliptic ,plates ,,ff and ,,gg2 each ,plate being fixed on an ,axis in one of its ,focuses1 at ,e and ,k2 and the ,wheel ,e is fixed on the same ,axis with the ,plate ,,ff4 ,these ,plates have ,grooves round their edges precisely of equal ,diameters to one another1 and in these ,grooves is the cat-gut string gg1 gg crossing between the ,plates at h4 ,on ,h1 the ,axis of the handle or winch ,n in ,fig4 #dth1 is an endless screw in ,fig4 #e1 working in the ,wheels ,d and ,e1 whose numbers of teeth being equal1 and should be equal to the number of lines a,s1 b,s1 c,s1 c4 in ,fig4 #d1 they turn round their ,axes in equal times to one another1 and to the ,motion of the elliptic ,plates4 ,for1 the ,wheels ,d and ,e having equal numbers of teeth1 the ,plate ,,ff being fixed on the same ,axis with the ,wheel ,e1 and the ,plate ,,ff turning the equally big ,plate ,,gg by a cat-gut string round them both1 they must all go round their ,axes in as many turns of the handle ,n as either of the ,wheels has teeth4 ',tis easy to see1 that the end h of the elliptical ,plate ,,ff being farther from its ,axis ,e than the opposite end i is1 must describe a ,circle so much the larger in proportion2 and therefore move through so much more space in the same time2 and for that reason the end h moves so much faster than the end i1 although it goes no sooner round the ,center ,e4 ,but then1 the quick-moving end h of the ,plate ,,ff leads about the short end h,k of the ,plate ,,gg with the same velocity2 and the slow moving end i of the ,plate ,,ff coming half round as to ,b1 must then lead the long end k of the ,plate ,,gg as slowly about3 ,so that the elliptical ,plate ,,ff and it's ,axis ,e move uniformly and equally quick in every part of its revolution2 but the elliptical ,plate ,,gg1 together with its ,axis ,k must move very unequally in different parts of its revolution2 the difference being always inversely as the distance of any point of the ,circumference of ,,gg from its ,axis at ,k3 or in other words1 to instance in two points1 if the distance ,kk be four1 five1 or six times as great as the distance ,kh1 the ,point h will move in that position four1 five1 or six times as fast as the ,point k does1 when the ,plate ,,gg has gone half round3 and so on for any other ,excentricity or difference of the ,distances ,kk and ,kh4 ,the tooth i on the ,plate ,,ff falls in between the two teeth at k on the ,plate ,,gg1 by which means the revolution of the latter is so adjusted to that of the former1 that they can never vary from one another4 ,on the top of the ,axis of the equally moving ,wheel ,d1 in ,fig4 #eth1 is the ,sun ,s in ,fig4 #dth2 which ,sun1 by the ,wire ,z fixed to it1 carries the ,ball ,i round the ,circle ,,abcd1 c4 with an equable ,motion according to the order of the letters3 and on the top of the ,axis ,k of the unequally moving ,ellipsis ,,gg1 in ,fig4 #eth1 is the ,sun ,s in ,fig4 #dth1 carrying the ,ball ,y unequably round in the elliptical ,groove a b c d1 c4 ,n4,b4 ,this elliptical ,groove must be precisely equal and similar to the verge of the ,plate ,,gg1 which is also equal to that of ,,ff4 ,in this manner1 ,machines may be made to shew the true ,motion of the ,moon about the ,earth1 or of any ,planet about the ,sun2 by making the elliptical ,plates of the same ,excentricities1 in proportion to the ,radius1 as the ,orbits of the ,planets are whose ,motions they represent3 and so1 their different ,equations in different parts of their ,orbits may be made plain to sight2 and clearer ,ideas of these ,motions and ,equations acquired in half an hour1 than could be gained from reading half a day about such ,motions and ,equations4 ,sidenote3 ,the improved ,,celestial ,,globe4 ,,plate ,,iii4 ,fig4 ,,iii4 #dch4 ,the ,improved ,celestial ,globe4 ,on the ,north ,pole of the ,axis1 above the ,hour ,circle1 is fixed an ,arch ,,mkh of #bc-a_/b ,degrees2 and at the end ,h is fixed an upright pin ,,hg1 which stands directly over the ,north ,pole of the ,ecliptic1 and perpendicular to that part of the surface of the ,globe4 ,on this pin are two moveable ,collets at ,d and ,h1 to which are fixed the quadrantal ,wires ,n and ,o1 having two little ,balls on their ends for the ,sun and ,moon1 as in the ,figure4 ,the ,collet ,d is fixed to the circular ,plate ,f whereon the #bi-a_/b days of the ,moon's age are engraven1 beginning just under the ,sun's ,wire ,n2 and as this ,wire is moved round the ,globe1 the ,plate ,f turns round with it4 ,these ,wires are easily turned if the ,screw ,g be slackened2 and when they are set to their proper places1 the ,screw serves to fix them there so1 as in turning the ,ball of the ,globe1 the ,wires with the ,sun and ,moon go round with it2 and these two little ,balls rise and set at the same times1 and on the same points of the ,horizon1 for the day to which they are rectified1 as the ,sun and ,moon do in the ,heavens4 ,because the ,moon keeps not her course in the ,ecliptic 7as the ,sun appears to do7 but has a ,declination of #e-a_/c ,degrees on each side from it in every ,lunation #cag1 her ,ball may be screwed as many ,degrees to either side of the ,ecliptic as her ,latitude or ,declination from the ,ecliptic amounts to at any given time2 and for this purpose ,s is a small piece of pasteboard1 of which the curved edge ,s is to be set upon the ,globe at right ,angles to the ,ecliptic1 and the dark line over ,s to stand upright upon it4 ,from this line1 on the convex edge1 are drawn the #e-a_/c ,degrees of the ,moon's ,latitude on both sides of the ,ecliptic2 and when this piece is set upright on the ,globe1 it's graduated edge reaches to the ,moon on the ,wire ,o1 by which means she is easily adjusted to her ,latitude found by an ,ephemeris4 ,the ,horizon is supported by two semicircular ,arches1 because ,pillars would stop the progress of the ,balls when they go below the ,horizon in an oblique sphere4 ,sidenote3 ,to rectify it4 ,to rectify the ,globe4 ,elevate the ,pole to the ,latitude of the ,place2 then bring the ,sun's place in the ,ecliptic for the given day to the brasen ,meridian1 and set the ,hour ,index to ,,xii at noon1 that is1 to the upper ,,xii on the ,hour ,circle2 keeping the ,globe in that situation1 slacken the ,screw ,g1 and set the ,sun directly over his place on the ,meridian2 which done1 set the ,moon's ,wire under the number that expresses her age for that day on the ,plate ,f1 and she will then stand over her place in the ,ecliptic1 and shew what ,constellation she is in4 ,lastly1 fasten the ,screw ,g1 and laying the curved edge of the pasteboard ,s over the ,ecliptic below the ,moon1 adjust the ,moon to her ,latitude over the graduated edge of the pasteboard2 and the ,globe will be rectified4 ,sidenote3 ,it's use4 ,having thus rectified the ,globe1 turn it round1 and observe on what points of the ,horizon the ,sun and ,moon ,balls rise and set1 for these agree with the points of the ,compass on which the ,sun and ,moon rise and set in the ,heavens on the given day2 and the ,hour ,index shews the times of their rising and setting2 and likewise the time of the ,moon's passing over the ,meridian4 ,this simple ,apparatus shews all the varieties that can happen in the rising and setting of the ,sun and ,moon2 and makes the forementioned ,phenomena of the ,harvest ,moon 7,chap4 xvi47 plain to the ,eye4 ,it is also very useful in reading ,lectures on the ,globes1 because a large company can see this ,sun and ,moon going round1 rising above and setting below the ,horizon at different times1 according to the seasons of the year2 and making their appulses to different fixed ,stars4 ,but1 in the usual way1 where there is only the places of the ,sun and ,moon in the ,ecliptic to keep the ,eye upon1 they are easily lost sight of1 unless covered with ,patches4 ,sidenote3 ,the ,,planetary ,,globe4 ,,pl4 ,,viii4 ,fig4 ,,iv4 #dci4 ,the ,planetary ,globe4 ,in this ,machine1 ,t is a terrestrial ,globe fixed on its ,axis standing upright on the ,pedestal ,,cde1 on which is an ,hour ,circle1 having its ,index fixed on the ,axis1 which turns somewhat tightly in the ,pedestal1 so that the ,globe may not be liable to shake2 to prevent which1 the ,pedestal is about two ,inches thick1 and the ,axis goes quite through it1 bearing on a shoulder4 ,the ,globe is hung in a graduated brasen ,meridian1 much in the usual way2 and the thin ,plate ,n1 ,,ne1 ,e1 is a moveable ,horizon1 graduated round the outer edge1 for shewing the ,bearings and ,amplitudes of the ,sun1 ,moon1 and ,planets4 ,the brasen ,meridian is grooved round the outer edge2 and in this ,groove is a slender ,semi-circle of brass1 the ends of which are fixed to the ,horizon in its ,north and ,south ,points3 this ,semi-circle slides in the ,groove as the ,horizon is moved in rectifying it for different ,latitudes4 ,to the middle of the ,semi-circle is fixed a ,pin which always keeps in the ,zenith of the ,horizon1 and on this ,pin the ,quadrant of ,altitude q turns2 the lower end of which1 in all ,positions1 touches the ,horizon as it is moved round the same4 ,this ,quadrant is divided into #ij ,degrees from the ,horizon to the zenithal ,pin on which it is turned1 at #ij4 ,the great flat ,circle or ,plate ,,ab is the ,ecliptic1 on the outer edge of which1 the ,signs and ,degrees are laid down2 and every fifth ,degree is drawn through the rest of the surface of this ,plate towards its ,center4 ,on this ,plate are seven ,grooves1 to which seven little ,balls are adjusted by sliding ,wires1 so that they are easily moved in the ,grooves1 without danger of starting out of them4 ,the ,ball next the terrestrial ,globe is the ,moon1 the next without it is ,mercury1 the next ,venus1 the next the ,sun1 then ,mars1 then ,jupiter1 and lastly ,saturn2 and in order to know them1 they are separately stampt with the following ,characters2 1 1 1 1 1 1 4 ,this ,plate or ,ecliptic is supported by four strong ,wires1 having their lower ends fixed into the ,pedestal1 at ,c1 ,d1 and ,e1 the fourth being hid by the ,globe4 ,the ,ecliptic is inclined #bc-a_/b ,degrees to the ,pedestal1 and is therefore properly inclined to the ,axis of the ,globe which stands upright on the ,pedestal4 ,sidenote3 ,to rectify it4 ,to rectify this ,machine4 ,set all the planetary ,balls to their geocentric places in the ,ecliptic for any given time by an ,ephemeris3 then1 set the ,north ,point of the ,horizon to the ,latitude of your place on the brasen ,meridian1 and the ,quadrant of ,altitude to the ,south ,point of the ,horizon2 which done1 turn the ,globe with its ,furniture till the ,quadrant of ,altitude comes right against the ,sun1 viz4 to his place in the ,ecliptic2 and keeping it there1 set the ,hour ,index to the ,,xii next the letter ,c2 and the ,machine will be rectified1 not only for the following ,problems1 but for several others1 which the ,artist may easily find out4 ,,problem ,i4 ,to find the ,amplitudes1 ,meridian ,altitudes1 and times of ,rising1 ,culminating1 and ,setting1 of the ,sun1 ,moon1 and ,planets4 ,sidenote3 ,it's use4 ,turn the ,globe round eastward1 or according to the order of ,signs2 and as the eastern edge of the ,horizon comes right against the ,sun1 ,moon1 or any ,planet1 the ,hour ,index will shew the time of it's rising2 and the inner edge of the ,ecliptic will cut it's rising ,amplitude in the ,horizon4 ,turn on1 and as the ,quadrant of ,altitude comes right against the ,sun1 ,moon1 or ,planets1 the ,ecliptic cuts their meridian ,altitudes in the ,quadrant1 and the ,hour ,index shews the times of their coming to the ,meridian4 ,continue turning1 and as the western edge of the ,horizon comes right against the ,sun1 ,moon1 or ,planets1 their setting ,amplitudes are cut in the ,horizon by the ,ecliptic2 and the times of their setting are shewn by the ,index on the ,hour ,circle4 ,,problem ,,ii4 ,to find the ,altitude and ,azimuth of the ,sun1 ,moon1 and ,planets1 at any time of their being above the ,horizon4 ,turn the ,globe till the ,index comes to the given time in the ,hour ,circle2 then keep the ,globe steady1 and moving the ,quadrant of ,altitude to each ,planet respectively1 the edge of the ,ecliptic will cut the ,planet's mean ,altitude on the ,quadrant1 and the ,quadrant will cut the ,planet's ,azimuth1 or ,point of ,bearing on the ,horizon4 ,,problem ,,iii4 ,the ,sun's ,altitude being given at any time either before or after ,noon1 to find the ,hour of the ,day1 and the ,variation of the ,compass1 in any known ,latitude4 ,with one hand hold the edge of the ,quadrant right against the ,sun2 and1 with the other hand1 turn the ,globe westward1 if it be in the forenoon1 or eastward if it be in the afternoon1 until the ,sun's place at the inner edge of the ,ecliptic cuts the ,quadrant in the ,sun's observed ,altitude2 and then the ,hour ,index will point out the time of the day1 and the ,quadrant will cut the true ,azimuth1 or ,bearing of the ,sun for that time3 the difference between which1 and the ,bearing shewn by the ,azimuth ,compass1 shews the variation of the ,compass in that place of the ,earth4 ,sidenote3 ,the ,,trajectorium ,,lunare4 ,,pl4 ,,vii4 ,fig4 ,v4 #ddj4 ,the ,trajectorium ,lunare4 ,this ,machine is for delineating the paths of the ,earth and ,moon1 shewing what sort of ,curves they make in the etherial regions2 and was just mentioned in the #bffth ,article4 ,s is the ,sun1 and ,e the ,earth1 whose ,centers are #ha ,inches distant from each other2 every ,inch answering to a ,million of ,miles #dg4 ,m is the ,moon1 whose ,center is #bd_/ajj parts of an ,inch from the ,earth's in this ,machine1 this being in just proportion to the ,moon's distance from the ,earth #eb4 ,,aa is a ,bar of ,wood1 to be moved by hand round the ,axis g which is fixed in the ,wheel ,y4 ,the ,circumference of this ,wheel is to the ,circumference of the small ,wheel ,l 7below the other end of the ,bar7 as #cfe-a_/d days is to #bi-a_/b2 or as a ,year is to a ,lunation4 ,the ,wheels are grooved round their edges1 and in the ,grooves is the cat-gut string ,,gg crossing between the ,wheels at ,x4 ,on the ,axis of the ,wheel ,l is the ,index ,f1 in which is fixed the ,moon's ,axis ,m for carrying her round the ,earth ,e 7fixed on the ,axis of the ,wheel ,l7 in the time that the ,index goes round a ,circle of #bi-a_/b equal parts1 which are the days of the ,moon's age4 ,the ,wheel ,y has the ,months and ,days of the year all round it's ,limb2 and in the ,bar ,,aa is fixed the ,index ,i1 which points out the ,days of the ,months answering to the ,days of the ,moon's age1 shewn by the ,index ,f1 in the ,circle of #bi-a_/b equal parts at the other end of the ,bar4 ,on the ,axis of the ,wheel ,l is put the piece ,d1 below the ,cock ,c1 in which this ,axis turns round2 and in ,d are put the ,pencils e and m1 directly under the ,earth ,e and ,moon ,m2 so that m is carried round e as ,m is round ,e4 ,sidenote3 ,it's use4 ,lay the ,machine on an even ,floor1 pressing gently on the ,wheel ,y to cause its spiked ,feet 7of which two appear at ,p and ,p1 the third being supposed to be hid from sight by the ,wheel7 enter a little into the ,floor to secure the ,wheel from turning4 ,then lay a paper about four foot long under the ,pencils e and m1 cross-wise to the ,bar3 which done1 move the ,bar slowly round the ,axis g of the ,wheel ,y2 and1 as the ,earth ,e goes round the ,sun ,s1 the ,moon ,m will go round the ,earth with a duly proportioned velocity2 and the friction ,wheel ,w running on the ,floor1 will keep the ,bar from bearing too heavily on the ,pencils e and m1 which will delineate the paths of the ,earth and ,moon1 as in ,fig4 #b;d1 already described at large1 #bff1 #bfg4 ,as the ,index ,i points out the ,days of the ,months1 the ,index ,f shews the ,moon's age on these ,days1 in the ,circle of #bi-a_/b equal parts4 ,and as this last ,index points to the different ,days in it's ,circle1 the like numeral ,figures may be set to those parts of the ,curves of the ,earth's ,path and ,moon's1 where the ,pencils e and m are at those times respectively1 to shew the places of the ,earth and ,moon4 ,if the ,pencil e be pushed a very little off1 as if from the ,pencil m1 to about #a_/dj part of their distance1 and the ,pencil m pushed as much towards e1 to bring them to the same distances again1 though not to the same points of space2 then as m goes round e1 e will go as it were round the ,center of ,gravity between the ,earth e and ,moon m #bih3 but this ,motion will not sensibly alter the ,figure of the ,earth's ,path or the ,moon's4 ,if a ,pin as p be put through the ,pencil m1 with its head towards that of the ,pin q in the ,pencil e1 its head will always keep thereto as m goes round e1 or as the same side of the ,moon is still obverted to the ,earth4 ,but the ,pin p1 which may be considered as an equatoreal ,diameter of the ,moon1 will turn quite round the ,point m1 making all possible ,angles with the ,line of its progress or line of the ,moon's ,path4 ,this is an ocular proof of the ,moon's turning round her ,axis4 ,sidenote3 ,the ,,tide ,,dial4 ,,plate ,,ix4 ,fig4 ,,vii4 ,it's use4 #dda4 ,the ,,tide-,,dial4 ,the outside parts of this ,machine consist of1 #a4 ,an eight-sided ,box1 on the top of which at the corner is shewn the ,phases of the ,moon at the ,octants1 ,quarters1 and ,full4 ,within these is a ,circle of #bi-a_/b equal parts1 which are the days of the ,moon's age accounted from the ,sun at ,new ,moon round to the same again4 ,within this ,circle is one of #bd hours divided into their respective ,halves and ,quarters4 #b4 ,a moving elliptical ,plate painted blue to represent the rising of the ,tides under and opposite to the ,moon2 and has the words1 ,high ,water1 ,tide falling1 ,low ,water1 ,tide rising1 marked upon it4 ,to one end of this ,plate is fixed the ,moon ,m by the ,wire ,w1 and goes along with it4 #c4 ,above this elliptical ,plate is a round one1 with the ,points of the ,compass upon it1 and also the names of above #bjj places in the large ,machine 7but only #cb in the ,figure to avoid confusion7 set over those ,points on which the ,moon bears when she raises the ,tides to the greatest heights at these ,places twice in every lunar day3 and to the ,north and ,south ,points of this ,plate are fixed two ,indexes ,i and ,k1 which shew the times of ,high ,water in the ,hour ,circle at all these places4 #d4 ,below the elliptical ,plate are four small ,plates1 two of which project out from below its ends at ,new and ,full ,moon2 and so1 by lengthening the ,ellipse shew the ,spring ,tides1 which are then raised to the greatest heights by the united attractions of the ,sun and ,moon #cjb4 ,the other two of these small ,plates appear at low water when the ,moon is in her ,quadratures1 or at the sides of the elliptic ,plate1 to shew the ,nepe ,tides2 the ,sun and ,moon then acting cross-wise to each other4 ,when any two of these small ,plates appear1 the other two are hid2 and when the ,moon is in her ,octants they all disappear1 there being neither ,spring nor ,nepe ,tides at those times4 ,within the ,box are a few ,wheels for performing these ,motions by the ,handle or ,winch ,h4 ,illustration3 ,plate ,,xiii4 ,j4 ,ferguson inv4 et del4 ,j4 ,mynde ,sculp4 ,turn the ,handle until the ,moon ,m comes to any given day of her age in the ,circle of #bi-a_/b equal parts1 and the ,moon's ,wire ,w will cut the time of her coming to the ,meridian on that day1 in the ,hour ,circle2 the ,,xii under the ,sun being ,mid-day1 and the opposite ,,xii ,mid-night3 then looking for the name of any given place on the round ,plate 7which makes #bi-a_/b rotations whilst the ,moon ,m makes only one revolution from the ,sun to the ,sun again7 turn the ,handle till that place comes to the word ,high ,water under the ,moon1 and the ,index which falls among the ,afternoon ,hours will shew the time of high water at that place in the ,afternoon of the given day3 then turn the ,plate half round1 till the same place comes to the opposite ,high ,water ,mark1 and the ,index will shew the time of ,high ,water in the ,forenoon at that place4 ,and thus1 as all the different places come successively under and opposite to the ,moon1 the ,indexes shew the times of ,high ,water at them in both parts of the day3 and when the same places come to the ,low ,water ,marks the ,indexes shew the times of ,low ,water4 ,for about two days before and after the times of ,new and ,full ,moon1 the two small ,plates come out a little way from below the ,high ,water ,marks on the elliptical ,plate1 to shew that the ,tides rise still higher about these times3 and about the ,quarters1 the other two ,plates come out a little from under the ,low ,water ,marks towards the ,sun and on the opposite side1 shewing that the ,tides of ,flood rise not then so high1 nor do the ,tides of ,ebb fall so low1 as at other times4 ,by pulling the ,handle a little way outward1 it is disengaged from the ,wheel-work1 and then the upper ,plate may be turned round quickly by hand so1 as the ,moon may be brought to any given day of her age in about a quarter of a minute4 ,sidenote3 ,the inside work described4 ,fig4 ,,viii4 ,on ,,ab1 the ,axis of the ,handle ,h1 is an endless ,screw ,c which turns the ,wheel ,,fed of #bd teeth round in #bd revolutions of the ,handle3 this ,wheel turns another ,,ong of #dh teeth1 and on its ,axis is the ,pinion ,,pq of four leaves which turns the ,wheel ,,lki of #ei teeth round in #bi-a_/b turnings or rotations of the ,wheel ,,fed1 or in #gjh revolutions of the ,handle1 which is the number of ,hours in a synodical revolution of the ,moon4 ,the round ,plate with the names of ,places upon it is fixed on the ,axis of the ,wheel ,,fed2 and the ,elliptical or ,tide-,plate with the ,moon fixed to it is upon the ,axis of the ,wheel ,,lki2 consequently1 the former makes #bi-a_/b revolutions in the time that the latter makes one4 ,the whole ,wheel ,,fed with the endless ,screw ,c1 and dotted part of the ,axis of the ,handle ,,ab1 together with the dotted part of the ,wheel ,,ong1 lie hid below the large ,wheel ,,lki4 ,fig4 #ith represents the under side of the ,elliptical or ,tide-,plate abcd1 with the four small ,plates ,,abcd1 ,,efgh1 ,,iklm1 ,,nopq upon it3 each of which has two slits as ,,tt1 ,,ss1 ,,rr1 ,,uu sliding on two ,pins as nn1 fixed in the elliptical ,plate4 ,in the four small ,plates are fixed four ,pins at ,w1 ,x1 ,y1 and ,z2 all of which work in an elliptic ,groove oooo on the cover of the ,box below the elliptical ,plate2 the longest ,axis of this ,groove being in a right line with the ,sun and ,full ,moon4 ,consequently1 when the ,moon is in ,conjunction or ,opposition1 the ,pins ,w and ,x thrust out the ,plates ,,abcd and ,,iklm a little beyond the ends of the elliptic ,plate at d and b1 to f and e2 whilst the ,pins ,y and ,z draw in the ,plates ,,efgh and ,,nopq quite under the elliptic ,plate to g and h4 ,but1 when the ,moon comes to her first or third ,quarter1 the elliptic ,plate lies across the fixed elliptic ,groove in which the ,pins work2 and therefore the end ,plates ,,abcd and ,,iklm are drawn in below the great ,plate1 and the other two ,plates ,,efgh and ,,nopq are thrust out beyond it to a and c4 ,when the ,moon is in her ,octants the ,pins ,v1 ,x1 ,y1 ,z are in the parts o1 o1 o1 o of the elliptic ,groove1 which parts are at a mean between the greatest and least distances from the ,center q1 and then all the four small ,plates disappear below the great one4 ,sidenote3 ,the ,,eclipsareon4 ,pl4 ,,xiii4 #ddb4 ,the ,,eclipsareon4 ,this ,piece of ,mechanism exhibits the ,time1 ,quantity1 ,duration1 and ,progress of solar ,eclipses1 at all ,parts of the ,earth4 ,the principal parts of this ,machine are1 #a4 ,a terrestrial ,globe ,a turned round its ,axis ,b by the ,handle or ,winch ,m2 the ,axis ,b inclines #bc-a_/b ,degrees1 and has an ,index which goes round the ,hour ,circle ,d in each rotation of the ,globe4 #b4 ,a circular ,plate ,e on the ,limb of which the ,months and ,days of the year are inserted4 ,this ,plate supports the ,globe1 and gives its ,axis the same position to the ,sun1 or to a candle properly placed1 that the ,earth's ,axis has to the ,sun upon any day of the year #cch1 by turning the ,plate till the given ,day of the ,month comes to the fixed ,pointer or annual ,index ,g4 #c4 ,a crooked ,wire ,f which points towards the middle of the ,earth's enlightened ,disc at all times1 and shews to what place of the ,earth the ,sun is vertical at any given time4 #d4 ,a ,penumbra1 or thin circular ,plate of brass ,i divided into #ab ,digits by #ab concentric ,circles1 which represent a ,section of the ,moon's ,penumbra1 and is proportioned to the size of the ,globe2 so that the shadow of this ,plate1 formed by the ,sun1 or a candle placed at a convenient distance1 with it's ,rays transmitted through a convex ,lens to make them fall parallel on the ,globe1 covers exactly all those places upon it that the ,moon's ,shadow and ,penumbra do on the ,earth3 so that the ,phenomena of any solar ,eclipse may be shewn by this ,machine with candle-light1 almost as well as by the light of the ,sun4 #e4 ,an upright frame ,,hhhh1 on the sides of which are ,scales of the ,moon's ,latitude or ,declination from the ,ecliptic4 ,to these ,scales are fitted two ,sliders ,k and ,k1 with ,indexes for adjusting the ,penumbra's ,center to the ,moon's ,latitude1 as it is ,north or ,south ,ascending or ,descending4 #f4 ,a solar ,horizon ,c1 dividing the enlightened ,hemisphere of the ,globe from that which is in the dark at any given time1 and shewing at what places the general ,eclipse begins and ends with the rising or setting ,sun4 #g4 ,a ,handle ,m1 which turns the ,globe round it's ,axis by wheel-work1 and at the same time moves the ,penumbra across the frame by threads over the ,pullies ,l1 ,l1 ,l1 with the velocity duly proportioned to that of the ,moon's shadow over the ,earth1 as the ,earth turns on its ,axis4 ,and as the ,moon's ,motion is quicker or slower1 according to her different distances from the ,earth1 the penumbral ,motion is easily regulated in the ,machine by changing one of the ,pullies4 ,sidenote3 ,to rectify it4 ,to rectify the ,machine for use4 ,the true time of ,new ,moon and her ,latitude being known by the foregoing ,precepts #cee1 #cfc1 if her ,latitude exceeds the number of minutes or divisions on the ,scales 7which are on the side of the frame hid from view in the ,figure of the ,machine7 there can be no ,eclipse of the ,sun at that ,conjunction2 but if it does not1 the ,sun will be eclipsed to some places of the ,earth2 and1 to shew the times and various appearances of the ,eclipse at those places1 proceed in order as follows4 ,to rectify the ,machine for performing by the ,light of the ,sun4 #a4 ,move the ,sliders ,,kk till their ,indexes point to the ,moon's ,latitude on the ,scales1 as it is ,north and ,south ,ascending or ,descending1 at that time4 #b4 ,turn the ,month ,plate ,e till the day of the given ,new ,moon comes to the annual ,index ,g4 #c4 ,unscrew the ,collar ,n a little on the ,axis of the ,handle1 to loosen the contiguous ,socket on which the threads that move the ,penumbra are wound2 and set the ,penumbra by ,hand till its ,center comes to the perpendicular thread in the middle of the frame2 which thread represents the ,axis of the ,ecliptic #cga4 #d4 ,turn the ,handle till the ,meridian of ,london on the ,globe comes just under the point of the crooked ,wire ,f2 then stop1 and turn the ,hour ,circle ,d by ,hand till ,,xii at ,noon comes to its ,index4 #e4 ,turn the ,handle till the ,hour ,index points to the time of ,new ,moon in the ,circle ,d2 and holding it there1 screw fast the ,collar ,n4 ,lastly1 elevate the ,machine till the ,sun shines through the ,sight-,holes in the small upright ,plates ,o1 ,o1 on the ,pedestal2 and the whole ,machine will be rectified4 ,to rectify the ,machine for shewing the ,candle-,light1 proceed in every respect as above1 except in that part of the last paragraph where the ,sun is mentioned2 instead of which place a ,candle before the ,machine1 about four yards from it1 so as the shadow of ,intersection of the cross threads in the middle of the frame may fall precisely on that part of the ,globe to which the crooked ,wire ,f points3 then1 with a pair of ,compasses take the distance between the ,penumbra's ,center and ,intersection of the threads2 and equal to that distance set the ,candle higher or lower as the ,penumbra's ,center is above or below the said ,intersection4 ,lastly1 place a large convex ,lens between the ,machine and ,candle1 so as the ,candle may be in the ,focus of the ,lens1 and then the ,rays will fall parallel1 and cast a strong light on the ,globe4 ,sidenote3 ,it's use4 ,these things done1 which may be sooner than expressed1 turn the ,handle backward until the ,penumbra almost touches the side ,,hf of the frame2 then turning it gradually forward1 observe the following ,phenomena4 #a4 ,where the eastern edge of the ,shadow of the penumbral ,plate ,i first touches the ,globe at the solar ,horizon1 those who inhabit the corresponding part of the ,earth see the ,eclipse begin on the uppermost edge of the ,sun1 just at the time of its rising4 #b4 ,in that place where the ,penumbra's ,center first touches the ,globe1 the inhabitants have the ,sun rising upon them centrally eclipsed4 #c4 ,when the whole ,penumbra just falls upon the ,globe1 its western edge1 at the solar ,horizon1 touches and leaves the place where the ,eclipse ends at ,sun-rise on his lowermost edge4 ,continue turning1 and1 #d4 the cross lines in the ,center of the ,penumbra will go over all those places on the ,globe where the ,sun is centrally eclipsed4 #e4 ,when the eastern edge of the ,shadow touches any place of the ,globe1 the ,eclipse begins there3 when the vertical line in the ,penumbra comes to any place1 then is the greatest obscuration at that place2 and when the western edge of the ,penumbra leaves the place1 the ,eclipse ends there2 the times of all which are shewn on the ,hour ,circle3 and from the beginning to the end1 the ,shadows of the concentric penumbral ,circles shew the number of ,digits eclipsed at all the intermediate times4 #f4 ,when the eastern edge of the ,penumbra leaves the ,globe at the solar ,horizon ,c1 the inhabitants see the ,sun beginning to be eclipsed on his lowermost edge at its setting4 #g4 ,where the ,penumbra's ,center leaves the ,globe1 the inhabitants see the ,sun set centrally eclipsed4 ,and lastly1 where the ,penumbra is wholly departing from the ,globe1 the inhabitants see the ,eclipse ending on the uppermost part of the ,sun's edge1 at the time of its disappearing in the ,horizon #cdc4 ,n4,b4 ,if any given day of the year on the ,plate ,e be set to the annual ,index ,g1 and the ,handle turned till the ,meridian of any place comes under the point of the crooked ,wire1 and then the ,hour ,circle ,d set by the hand till ,,xii comes to its ,index2 in turning the ,globe round by the ,handle1 when the said place touches the eastern edge of the ,hoop or solar ,horizon ,c1 the ,index shews the time of ,sun-setting at that place2 and when the place is just coming out from below the other edge of the ,hoop ,c1 the ,index shews the time that the evening ,twilight ends to it4 ,when the place has gone through the dark part ,a1 and comes about so to touch under the back of the ,hoop ,c on the other side1 the ,index shews the time that the ,morning ,twilight begins2 and when the same place is just coming out from below the edge of the ,hoop next the frame1 the ,index points out the time of ,sun-rising4 ,and thus1 the times of ,sun-rising and setting are shewn at all places in one rotation of the ,globe1 for any given day of the year3 and the point of the crooked ,wire ,f shews all the places that the ,sun passes vertically over on that day4 ,,finis4 ,,index4 ,the numeral ,figures refer to the ,articles1 and the small n to the ,notes on the ,articles4 ,a4 ,acceleration of the ,stars1 #bba4 ,angle1 what1 #ahe4 ,annual ,parallax of the ,stars1 #aif4 ,anomaly1 what1 #bci4 ,antients1 their superstitious notions of ,eclipses1 #cbi4 ,their method of dividing the ,zodiac1 #cih4 ,antipodes1 what1 #abb4 ,apsides1 line of1 #bch4 ,,archimedes1 his ideal ,problem for moving the ,earth1 #aei4 ,areas described by the ,planets1 equal in times1 #aec4 ,astronomy1 the great advantages arising from it both in our religious and civil concerns1 #a ,discovers the laws by which the ,planets move1 and are retained in their ,orbits1 #b ,atmosphere1 the higher the thinner1 #agd4 ,it's prodigious expansion1 ib4 ,it's whole weight on the ,earth1 #age4 ,generally thought to be heaviest when it is lightest1 #agf4 ,without it the ,heavens would appear dark in the day-time1 #agg4 ,is the cause of twilight1 ib4 ,it's height1 ib4 ,refracts the ,sun's rays1 #agh4 ,causeth the ,sun and ,moon to appear above the ,horizon when they are really below it1 ib4 ,foggy1 deceives us in the bulk and distance of objects1 #ahe4 ,attraction1 #aja-aje4 ,decreases as the square of the distance increases1 #ajf4 ,greater in the larger than in the smaller ,planets1 #aeh4 ,greater in the ,sun than in all the ,planets if put together1 ib4 ,axes of the ,planets1 what1 #ai4 ,their different positions with respect to one another1 #abj4 ,axis of the ,earth1 it's parallelism1 #cjb4 ,it's position variable as seen from the ,sun or ,moon1 #cch4 the ,phenomena thence arising1 #cdj4 ,b4 ,bodies1 on the ,earth1 lose of their weight the nearer they are to the ,equator1 #aag4 ,how they might lose all their weight1 #aah1 ,how they become visible1 #afg4 ,c4 ,calculator1 7an ,instrument7 described1 #dcf4 ,calendar1 how to inscribe the ,golden ,numbers rightly in it for shewing the days of ,new ,moons1 #dbc4 ,cannon-,ball1 it's swiftness1 #hi4 ,in what times it would fly from the ,sun to the different ,planets and fixed ,stars1 ib4 ,,cassini1 his account of a double ,star eclipsed by the ,moon1 #eh4 ,his ,diagrams of the ,paths of the ,planets1 #ach4 ,catalogue of the ,eclipses1 #cbg4 ,of the ,constellations and ,stars1 #cfg4 ,of remarkable ras and events1 #dcc4 ,celestial ,globe improved1 #dch4 ,centripetal and centrifugal forces1 how they alternately overcome each other in the motions of the ,planets1 #aeb-aed4 ,changes in the ,heavens1 #djc4 ,chords1 line of1 how to make1 #cfi4 ,circles1 of perpetual ,apparition and ,occultation1 #abh4 ,of the ,sphere1 #aih4 ,contain #cfj ,degrees whether they be great or small1 #bjg4 ,civil ,year1 what1 #daa4 ,,columbus 7,,christopher7 his story concerning an ,eclipse1 #ccj4 ,clocks and ,watches1 an easy method of knowing whether they go true or false1 #bbc4 ,why they seldom agree with the ,sun if they go true1 #bbh-bde4 ,how to regulate them by ,equation ,tables and a ,meridian line1 #bbe1 #bbf4 ,cloudy ,stars1 #djb4 ,cometarium 7an ,instrument7 described1 #dcg4 ,constellations1 antient1 their number1 #cif4 ,the number of ,stars in each1 according to different ,astronomers1 #cii4 ,cycle1 ,solar1 ,lunar1 and ,romish1 #dbj4 ,of ,easter1 #dbe4 ,d4 ,darkness at our ,,saviour's crucifixion supernatural1 #ceb1 #dcb4 ,day1 natural and artificial1 what1 #dag4 ,and ,night1 always equally long at the ,equator1 #abf4 ,natural1 not compleated in an absolute turn of the ,earth on it's ,axis1 #bbb4 ,degree1 what1 #bjg4 ,digit1 what1 #cba1 n4 ,direction1 7,number of7 #dbf4 ,distances of the ,planets from the ,sun1 an idea thereof1 #hi4 ,a ,table thereof1 #ih4 ,how found1 #aij4 ,diurnal and annual ,motions of the ,earth illustrated1 #bjj1 #bjb4 ,dominical ,letter1 #dbg4 ,double projectile force1 a balance to a ,quadruple ,power of ,gravity1 #aec4 ,star covered by the ,moon1 #eh4 ,e4 ,earth1 it's bulk but a point as seen from the ,sun1 #c ,it's ,diameter1 annual ,period1 and ,distance from the ,sun1 #dg4 ,turns round it's ,axis1 ib4 ,velocity of it's equatoreal ,parts1 ib4 ,velocity in it's annual ,orbit1 ib4 ,inclination of it's ,axis1 #dh4 ,proof of it's being globular1 or nearly so1 #di1 #cad4 ,measurement of it's surface1 #ej1 #ea4 ,difference between it's ,equatoreal and ,polar ,diameters1 #gf4 ,it's motion round the ,sun demonstrated by gravity1 #ajh1 #aaa4 by ,dr4 ,,bradley's observations1 #aac4 by the ,eclipses of ,jupiter's ,satellites1 #bai4 ,it's diurnal motion highly probable from the absurdity that must follow upon supposing it not to move1 #aaa4 #abj4 and demonstrable from it's figure1 #aaf4 this motion cannot be felt1 #aai4 ,objections against it's motion answered1 #aab1 #aba4 ,it has no such thing as an upper or under side1 #abb4 in what case it might1 #abc4 ,the swiftness of it's motion in it's ,orbit compared with the velocity of light1 #aig4 ,it's diurnal and annual motions illustrated by an easy experiment1 #bjj4 ,proved to be less than the ,sun and bigger than the ,moon1 #cae4 ,easter ,cycle1 #dbe4 ,eclipsareon 7an ,instrument7 described1 #ddb4 ,eclipses1 of ,jupiter's ,satellites1 how the ,longitude is found by them1 #bjg-bah4 they demonstrate the velocity of light1 #baf4 ,of the ,sun and ,moon1 #cab-cbg4 ,why they happen not in every month1 #caf4 ,when they must be1 #cag4 ,their limits1 ib4 ,their ,period1 #cbj1 #cbf4 ,a dissertation on their progress1 #cba-cbd4 ,a large catalogue of them1 #cbg4 ,historical ones1 #cbh4 ,more of the ,sun than of the ,moon1 and why1 #cca4 ,the proper ,elements for their calculation and projection1 #cec-cij4 ,ecliptic1 it's ,signs1 their names and characters1 #ia4 ,makes different ,angles with the ,horizon every hour and minute1 #bge4 how these ,angles may be estimated by the position of the ,moon's horns1 #bfj4 ,it's obliquity to the ,equator less now than it was formerly1 #dje4 ,how it's ,signs are numbered1 #ced4 ,elongations1 of the ,planets1 as seen by an observer at rest on the outside of all their ,orbits1 #acc4 ,of ,mercury and ,venus as seen from the ,earth1 illustrated1 #adb4 it's quantity1 #adc4 ,of ,mercury1 ,venus1 the ,earth1 ,mars1 and ,jupiter2 it's quantity as seen from ,saturn1 #adg4 ,epochas or ras1 #dcc4 ,equation of time1 #bbd-bde4 ,of the ,moon's ,place1 #cee4 ,of the ,sun's ,place1 ib4 ,of the ,nodes1 #cfc4 ,equator1 day and night always equal there1 #abf4 ,makes always the same ,angle with the ,horizon of the same place2 the ,ecliptic not1 #bgd1 #bge4 ,equinoctial ,points in the ,heavens1 their precession1 #bdf1 a very different thing from the recession or anticipation of the ,equinoxes on ,earth1 the one no ways occasioned by the other1 #bdi4 ,excentricities of the ,planets ,orbits1 #aee4 ,f4 ,fallacies in judging of the bulk of objects by their apparent distance1 #ahe2 applied to the solution of the horizontal ,moon1 #ahg4 ,first ,meridian1 what1 #bjg4 ,fixed ,stars1 why they appear of less magnitude when viewed through a telescope than by the bare eye1 #cia4 ,their number1 #cib4 ,their division into different ,classes and ,constellations1 #cie-cii4 ,g4 ,general ,phenomena of a superior ,planet as seen from an inferior1 #adi4 ,gravity1 demonstrable1 #aja-ajd4 ,keeps all bodies on the ,earth to it's surface1 or brings them back when thrown upward2 and constitutes their weight1 #aja1 #abb4 ,retains all the ,planets in their ,orbits1 #ajc4 ,decreases as the square of the distance increases1 #ajf4 ,proves the ,earth's annual motion1 #ajh4 ,demonstrated to be greater in the larger ,planets than in the smaller2 and stronger in the ,sun than in all the ,planets together1 #aeh4 ,hard to understand what it is1 #afj4 ,acts every moment1 #afb4 ,globe1 improved celestial1 #dch4 ,great ,year1 #bea4 ,h4 ,harmony of the celestial motions1 #aaa4 ,harvest-,moon1 #bgc-bic4 ,none at the ,equator1 #bgc4 ,remarkable at the ,polar ,circles1 #bhe4 ,in what years most and least advantageous1 #bib4 ,heat1 decreases as the square of the distance from the ,sun increases1 #afi4 ,why not greatest when the ,earth is nearest the ,sun1 #bje4 ,why greater about three o',clock in the afternoon than when the ,sun is on the ,meridian1 #cjj4 ,heavens1 seem to turn round with different velocities as seen from the different ,planets2 and on different ,axes as seen from most of them1 #abj4 ,only one ,hemisphere of them seen at once from any one ,planet's surface1 #abe4 ,the ,sun's ,center the only point from which their true ,motions could be seen1 #ace4 ,changes in them1 #djc4 ,horizon1 what1 #abe1 n4 ,horizontal-,moon explained1 #ahg4 ,horizontal ,parallax1 of the ,moon1 #aij2 of the ,sun1 #aia2 best observed at the ,equator1 #aic4 ,hour-,circles1 what1 #bjh4 ,hour of time equal to #ae degrees of motion1 ib4 ,how divided by the ,jews1 ,chaldeans1 and ,arabians1 #dai4 ,,huygenius1 his thoughts concerning the distance of some ,stars1 #e ,i4 ,j4 ,inclination of ,venus's ,axis1 #bi4 ,of the ,earth's1 #dh4 ,of the ,axis or ,orbit of a ,planet only relative1 #bja4 ,inhabitants of the ,earth 7or any other ,planet7 stand on opposite sides with their feet toward one another1 yet each thinks himself on the upper side1 #abb4 ,julian ,period1 #dcj4 ,jupiter1 it's distance1 diameter1 diurnal and annual revolutions1 #fg-fi4 ,the ,phenomena of it's ,belts1 #gj4 ,has no difference of seasons1 #ga4 ,has four ,moons1 #gb1 their grand ,period1 #gc1 the ,angles which their ,orbits subtend as seen from the ,earth1 #gd1 most of them are eclipsed in every revolution1 #ge4 ,the great difference between it's equatoreal and polar ,diameters1 #gf4 ,the inclination of it's ,orbit1 and place of it's ,ascending ,node1 #gg4 ,the ,sun's light #cjjj times as strong on it as ,full ,moon-light is on the ,earth1 #he4 ,is probably inhabited1 #hf4 ,the amazing strength required to put it in motion1 #aeh4 ,the figures of the ,paths described by it's ,satellites1 #bfi4 ,l4 ,light1 the inconceivable smallness of it's particles1 #afe1 and the dreadful mischief they would do if they were larger1 #aff4 ,it's surprising velocity1 #aff1 compared with the swiftness of the ,earth's annual motion1 #aig4 ,decreases as the square of the distance from the luminous body increases1 #afi4 ,is refracted in passing through different ,mediums1 #aga-agc4 ,affords a proof of the ,earth's annual motion1 #aig1 #bai4 ,in what time it comes from the ,sun to the ,earth1 #baf1 this explained by a figure1 #bag4 ,limits of ,eclipses1 #cag4 ,line1 of the ,nodes1 what1 #cag2 has a retrograde motion1 #cai4 ,of ,sines and ,chords1 how to make1 #cfi4 ,,long 7,rev4 ,dr47 his method of comparing the quantity of the surface of dry land with that of the ,sea1 #ea4 ,his glass sphere1 #abf4 ,longitude1 how found1 #bjg-bac4 ,lucid ,spots in the ,heavens1 #dja4 ,lunar ,cycle deficient1 #dbb4 ,m4 ,magellanic ,clouds1 #djb4 ,man1 of a middle size1 how much pressed by the weight of the ,atmosphere1 #age2 why this pressure is not felt1 ib4 ,mars1 it's ,diameter1 ,period1 ,distance1 and other ,phenomena1 #fd-fg4 ,matter1 it's properties1 #ii4 ,mean ,anomaly1 what1 #bci4 ,mercury1 it's ,diameter1 ,period1 ,distance1 c4 #bb4 ,appears in all the shapes of the ,moon1 #bc4 ,when it will be seen on the ,sun1 #bd4 ,the inclination of it's ,orbit and ,place of it's ,ascending ,node1 ib4 ,it's ,path delineated1 #ach4 ,experiment to shew it's ,phases and apparent ,motion1 #adb4 ,mercury 7,quicksilver7 in the ,barometer1 why not affected by the ,moon's raising ,tides in the ,air1 #caa4 ,meridian1 first1 #bjg4 ,line1 how to draw one1 #bbf4 ,milky ,way1 what1 #djj4 ,months1 ,jewish1 ,arabian1 ,egyptian1 and ,grecian1 #dae4 ,moon1 her ,diameter and ,period1 #eb4 ,her phases1 #ec1 #bee4 ,shines not by her own light1 #ed4 ,has no difference of seasons1 #ee4 ,the ,earth is a ,moon to her1 #ef4 ,has no ,atmosphere of any visible ,density1 #eh2 nor ,seas1 #ei4 ,how her inhabitants may be supposed to measure their year1 #fb4 ,her light compared with day-light1 #he4 ,the excentricity of her ,orbit1 #ih4 ,is nearer the ,earth now than she was formerly1 #afc4 ,appears bigger in the ,horizon than at any considerable height above it1 and why1 #ahg2 yet is seen much under the same ,angle in both cases1 #ahh4 ,her surface mountainous1 #beb3 if smooth she could give us no light1 ib4 ,why no hills appear round her edge1 #bec4 ,has no ,twilight1 #bed4 ,appears not always quite round when full1 #bef4 ,her phases agreeably represented by a globular ,stone viewed in ,sun-shine when she is above the ,horizon1 and the observer placed as if he saw her on the top of the ,stone1 #beh4 ,turns round her ,axis1 #bfb4 ,the length of her ,solar and ,sidereal ,day1 ib4 ,her periodical and synodical revolution represented by the motions of the hour and minute hands of a ,watch1 #bfd4 ,her ,path delineated1 and shewn to be always concave to the ,sun1 #bfe-bfh4 ,her motion alternately retarded and accelerated1 #bfg4 ,her gravity toward the ,sun greater than toward the ,earth at her ,conjunction1 and why she does not then abandon the ,earth on that account1 #bfh4 ,rises nearer the time of ,sun-set when about the full in harvest for a whole week than when she is about the full at any other time of the year1 and why1 #bgc-bhd3 this rising goes through a course of increasing and decreasing benefit to the farmers every #ai years1 #bib4 ,continues above the ,horizon of the ,poles for fourteen of our natural ,days together1 #bic4 ,proved to be globular1 #cad4 and to be less than the ,earth1 #cae4 ,her ,nodes1 #cag4 ascending and descending1 #cah4 their retrograde motion1 #cai4 ,her acceleration proved from antient ,eclipses1 #cbb1 n4 ,her ,apogee and ,perigee1 #ccf4 ,not invisible when she is totally eclipsed1 and why1 #cdf4 ,how to calculate her ,conjunctions1 ,oppositions1 and ,eclipses1 #cee-cij4 ,how to find her age in any ,lunation by the ,golden ,number1 #dbc4 ,morning and ,evening ,star1 what1 #ade4 ,motion1 naturally rectilineal1 #ajj4 ,apparent1 of the ,planets as seen by a spectator at rest on the outside of all their ,orbits1 #acc2 and of the ,heavens as seen from any ,planet1 #aed4 ,n4 ,natural ,day1 not compleated in the time that the ,earth turns round it's ,axis1 #bbb4 ,new and ,full ,moon1 to calculate the times of #cee4 ,new ,stars1 #djc1 cannot be ,comets1 #djd4 ,new ,style1 it's original1 #dad4 ,,nicias's ,eclipse1 #cbh4 ,nodes1 of the ,planet's ,orbits1 their places in the ,ecliptic1 #bj4 ,of the ,moon's ,orbit1 #cag4 their retrograde motion1 #cai4 ,nonagesimal ,degree1 what1 #bei4 ,number of ,direction1 #dbf4 ,o4 ,objects1 we often mistake their bulk by mistaking their distance1 #ahe4 ,appear bigger when seen through a fog than through clear ,air1 and why1 ib4 this applied to the solution of the ,horizontal ,moon1 #ahg4 ,oblique ,sphere1 what1 #aca4 ,olympiads1 what1 #cbc4 n4 ,orbits of the ,planets not solid1 #ba4 ,orrery described1 #dcd1 #dce1 #dcf4 ,p4 ,parallax1 ,horizontal1 what1 #aij4 ,parallel ,sphere1 what1 #aca4 ,path of the ,moon1 #bfe1 #bff1 #bfg4 ,of ,jupiter's ,moons1 #bfi4 ,pendulums1 their vibrating slower at the ,equator than near the ,poles proves that the ,earth turns on it's ,axis1 #aag4 ,penumbra1 what1 #ccf4 ,it's velocity on the ,earth in ,solar ,eclipses1 #ccg4 ,period of ,eclipses1 #cbj1 #cbf4 ,phases of the ,moon1 #beb-bfh4 ,planets1 much of the same nature with the ,earth1 #aa4 ,some have ,moons belonging to them1 #ab4 ,move all the same way as seen from the ,sun1 but not as seen from one another1 #ah4 ,their ,moons denote them to be inhabited1 #hf4 ,the proportional breadth of the ,sun's ,disc as seen from each of them1 #hg4 ,their proportional bulks as seen from the ,sun1 #hh4 ,an idea of their distances from the ,sun1 #hi4 ,appear bigger and less by turns1 and why1 #ij4 ,are kept in their ,orbits by the power of gravity1 #aja1 #aej-aeh4 ,their motions very irregular as seen from the ,earth1 #acg4 ,the apparent motions of ,mercury and ,venus delineated by ,pencils in an ,orrery1 #ach4 ,elongations of all the rest as seen from ,saturn1 #adg4 ,describe equal areas in equal times1 #aec4 ,the excentricities of their ,orbits1 #aee4 ,in what times they would fall to the ,sun by the power of gravity1 #aeg4 ,disturb one another's motions1 the consequence thereof1 #afc4 ,appear dimmer when seen through telescopes than by the bare eye1 the reason of this1 #agj4 ,planetary ,globe described1 #dci4 ,polar ,circles1 #aih4 ,poles1 of the ,planets1 what1 #ai4 ,of the world1 what1 #abb4 ,celestial1 seem to keep on the same points of the ,heavens all the year1 and why1 #aif4 ,projectile ,force1 #aej2 if doubled would require a quadruple power of gravity to retain the ,planets in their ,orbits1 #aec4 ,is evidently an impulse from the hand of the ,,almighty1 #afa4 ,precession of the ,equinoxes1 #bdf-bea4 ,ptolemean ,system absurd1 #if1 #adj4 ,r4 ,rays of ,light1 if not disturbed1 move in straight lines1 and hinder not one another's motions1 #afh4 ,are refracted in passing through different mediums1 #aga4 ,reflection of the ,atmosphere causes the ,twilight1 #agg4 ,refraction of the ,atmosphere bends the rays of light from straight lines1 and keeps the ,sun and ,moon longer in sight than they would otherwise be1 #agh4 ,a surprising instance of this1 #ahc4 ,must be allowed for in taking the ,altitudes of the celestial bodies1 ib4 ,right ,sphere1 #aca4 ,s4 ,satellites2 the times of their revolutions round their primary ,planets1 #eb1 #gc1 #hj4 ,their ,orbits compared with each other1 with the ,orbits of the primary ,planets1 and with the ,sun's circumference1 #bga4 ,what sort of ,curves they describe1 #bgb4 ,saturn1 with his ,ring and ,moon's1 their ,phenomena1 #gh1 #gi1 #hb4 ,the ,sun's light #ajjj times as strong to him as the light of the ,full ,moon is to us1 #he4 ,the ,phenomena of his ,ring farther explained1 #bjd4 ,our blessed ,,saviour1 the darkness at his crucifixion supernatural1 #ceb4 ,the prophetic year of his crucifixion found to agree with an astronomical calculation1 #dcb4 ,seasons1 different1 illustrated by an easy experiment1 #bjj2 by a figure1 #bjb4 ,shadow1 what1 #cab4 ,sidereal ,time1 what1 #bba2 the number of ,sidereal ,days in a year exceeds the number of ,solar ,days by one1 and why1 #bbb4 ,an easy method for regulating ,clocks and ,watches by it1 #bbc4 ,signs of the ,zodiac1 their names and characters1 #ia1 #cfe4 ,how they are numbered by ,astronomers1 #ced4 ,sines1 line of1 how to make1 #cfi4 ,,smith1 7,rev4 ,dr47 his companion between ,moon-light and ,day-light1 #he4 ,his demonstration that light decreases as the square of the distance from the luminous body increases1 #afi4 7,mr4 ,,george7 his ,dissertation on the ,progress of a ,solar ,eclipse1 #cba-cbd4 ,solar ,astronomer1 the judgment he might be supposed to make concerning the ,planets and ,stars1 #ace1 #acf4 ,sphere1 parallel1 oblique1 and right1 #aca4 ,it's ,circles1 #aih4 ,spring and ,neap ,tides1 #cjb4 ,stars1 their vast distance from the ,earth1 #c1 #aif4 ,probably not all at the same distance1 #d ,shine by their own light1 and are therefore ,suns #g1 probably to other worlds1 #h ,a demonstration that they do not move round the ,earth1 #aaa4 ,have an apparent slow motion round the ,poles of the ,ecliptic1 and why1 #bea4 ,a catalogue of them1 #cii4 ,cloudy1 #djb4 ,new1 #djc4 ,some of them change their places1 #djd4 ,starry ,heavens have the same appearance from any part of the ,solar ,system1 #acb4 ,,sun appears bigger than the ,stars1 and why1 #d ,turns round his ,axis1 #ah4 ,his proportional breadth as seen from the different ,planets1 #hg4 ,describes unequal arcs above and below the ,horizon at different times1 and why1 #acj4 ,his ,center the only place from which the true motions of the ,planets could be seen1 #ace4 ,is for half a year together visible at each ,pole in it's turn1 and as long in visible1 #bjj1 #bid4 ,is nearer the ,earth in ,winter than in ,summer1 #bje4 ,why his motion agrees so seldom with the motion of a well regulated ,clock1 #bbd-bde4 ,would more than fill the ,moon's ,orbit1 #bga4 ,proved to be much bigger than the ,earth1 and the ,earth to be bigger than the ,moon1 #cae4 ,to calculate his true place1 #cfj4 ,systems1 the ,solar1 #ag-ie2 the ,ptolemean1 #if2 the ,tychonic1 #ig4 ,t4 ,table1 of the ,periods1 ,revolutions1 ,magnitudes1 ,distances1 c4 of the ,planets1 facing #ii4 ,of the ,air's rarity1 compression1 and expansion at different heights1 #agd4 ,of refractions1 #ahb4 ,for converting time into motion1 and the reverse1 #bbj4 ,for shewing how much of the celestial ,equator passes over the ,meridian in any part of a mean ,solar ,day2 and how much the ,stars accelerate upon the mean ,solar time for a month1 #bba4 ,of the first part of the ,equation of time1 #bbi2 of the second part1 #bda4 ,of the precession of the ,equinox1 #bdg4 ,of the length of ,sidereal1 ,julian1 and ,tropical ,years1 #bea4 ,of the ,sun's place and ,anomaly1 following #bea4 ,of the ,equation of natural ,days1 following #bea ,of the ,conjunctions of the hour and minute hands of a ,watch1 #bfd4 ,of the ,curves described by the ,satellites1 #bgb4 ,of the difference of time in the ,moon's rising and setting on the parallel of ,london every day during her course round the ,ecliptic1 #bgg4 ,of ,eclipses1 #cbg4 ,for calculating ,new and ,full ,moons and ,eclipses1 following #cij4 ,of the ,constellations and number of the ,stars1 #cii4 ,of the ,jewish1 ,egyptian1 ,arabic1 and ,grecian months1 #dae4 ,for inserting the ,golden ,numbers right in the ,calendar1 #dbc4 ,of the times of all the ,new ,moons for #gf years1 #dbd4 ,of remarkable ras or ,events1 #dcc4 ,of the ,golden ,number1 ,number of ,direction1 ,dominical ,letter and ,days of the ,months1 following #dcc4 ,,thales's ,eclipse1 #cbc4 ,,thucydides's ,eclipse #cbd4 ,tides1 their ,cause and ,phenomena1 #bie-caa4 ,tide-,dial described1 #dda4 ,trajectorium ,lunare described1 #ddj4 ,tropics1 #aih4 ,twilight1 none in the ,moon1 #bed4 ,tychonic ,system absurd1 #ig4 ,u4 ,universe1 the ,work of ,almighty ,power1 #e1 #afa4 ,up and down1 only relative terms1 #abb4 ,upper or under side of the ,earth no such thing1 #abc4 ,v4 ,velocity of ,light compared with the velocity of the ,earth in it's annual ,orbit1 #aig4 ,venus1 her bulk1 distance1 period1 length of days and nights1 #bf4 ,shines not by her own light1 ib4 ,is our morning and evening ,star1 #bh4 ,her ,axis1 how situated1 #bi4 ,her surprising ,phenomena1 #bi-dc4 ,the inclination of her ,orbit1 #de4 ,when she will be seen on the ,sun1 ib4 ,how it may probably be soon known if she has a ,satellite1 #df4 ,appears in all the ,shapes of the ,moon1 #bc1 #ada4 ,an experiment to shew her phases and apparent motion1 #ada4 ,vision1 how caused1 #afg4 ,w4 ,weather1 not hottest when the ,sun is nearest to us1 and why1 #bje4 ,weight1 the cause of it1 #abb4 ,world not eternal1 #afd4 ,y4 ,year1 #djg1 ,great1 #bea1 ,tropical1 #djh1 ,sidereal1 #djj1 ,lunar1 #daj1 ,civil1 #daa1 ,bissextile1 ib4 ,roman1 #dac1 ,jewish1 ,egyptian1 ,arabic1 and ,grecian1 #dae1 how long it would be if the ,sun moved round the ,earth1 #aaa4 ,z4 ,zodiac1 what1 #cig4 ,how divided by the antients1 #cih4 ,zones1 what1 #aii4 ,,directions to the ,,bookbinder4 ,the ,,orrery ,,plate is to front the ,title ,page4 ,,plate ,i fronting ,page #e ,,ii #ci ,,iii #di ,,iv #gc ,v #ha ,,vi #ig ,,vii #abe ,,viii #adg ,,ix #adg ,x #aeg ,,xi #agi ,,xii #bjc ,,xiii #bgi ,footnotes ,footnote #a3 ,dr4 ,,young's ,night ,thoughts4 ,footnote #b3 ,if a thread be tied loosely round two pins stuck in a table1 and moderately stretched by the point of a black lead pencil carried round by an even motion and light pressure of the hand1 an oval or ellipsis will be described2 the two points where the pins are fixed being called the foci or focuses thereof4 ,the ,orbits of all the ,planets are elliptical1 and the ,sun is placed in or near to one of the foci of each of them3 and that in which he is placed1 is called the lower focus4 ,footnote #c3 ,astronomers are not far from the truth1 when they reckon the ,sun's center the lower focus of all the ,planetary ,orbits4 ,though strictly speaking1 if we consider the focus of ,mercury's ,orbit to be in the ,sun's center1 the focus of ,venus's ,orbit will be in the common center of gravity of the ,sun and ,mercury2 the focus of the ,earth's ,orbit in the common center of gravity of the ,sun1 ,mercury1 and ,venus2 the focus of the ,orbit of ,mars in the common center of gravity of the ,sun1 ,mercury1 ,venus1 and the ,earth2 and so of the rest4 ,yet1 the focuses of the ,orbits of all the ,planets1 except ,saturn1 will not be sensibly removed from the center of the ,sun2 nor will the focus of ,saturn's ,orbit recede sensibly from the common center of gravity of the ,sun and ,jupiter4 ,footnote #d3 ,as represented in ,plate ,,iii4 ,fig4 ,i4 and described in #ach4 ,footnote #e3 ,when he is between the ,earth and the ,sun in the nearer part of his ,orbit4 ,footnote #f3 ,the time between the ,sun's rising and setting4 ,footnote #g3 ,one entire revolution1 or #bd hours4 ,footnote #h3 ,these are lesser circles parallel to the ,equator1 and as many degrees from it1 towards the ,poles1 as the ,axis of the ,planet is inclined to the ,axis of it's ,orbit4 ,when the ,sun is advanced so far north or south of the ,equator as to be directly over either ,tropic1 he goes no farther2 but returns towards the other4 ,footnote #i3 ,these are lesser circles round the ,poles1 and as far from them as the ,tropics are from the ,equator4 ,the ,poles are the very north and south points of the ,planet4 ,footnote #aj3 ,a ,degree is a #cfjth part of any ,circle4 ,see #ba4 ,footnote #aa3 ,the ,limit of any inhabitant's view1 where the ,sky seems to touch the ,planet all round him4 ,footnote #ab3 ,this is not strictly true1 as will appear when we come to treat of the ,recession of the ,equinoctial ,points in the ,heavens #bdf2 which recession is equal to the deviation of the ,earth's ,axis from it's parallelism3 but this is rather too small to be sensible in an age1 except to those who make very nice observations4 ,footnote #ac3 ,memoirs d',acad4 ann4 #agbj4 ,footnote #ad3 ,the ,moon's ,orbit crosses the ,ecliptic in two opposite points called the ,moon's ,nodes2 so that one half of her ,orbit is above the ,ecliptic1 and the other half below it4 ,the ,angle of it's ,obliquity is #e-a_/c degrees4 ,footnote #ae3 ,,cassini ,elements d',astronomie1 ,liv4 ix4 ,chap4 #c4 ,footnote #af3 ,optics1 ,art4 #ie4 ,footnote #ag3 ,mr4 ,,whiston1 in his ,astronomical ,principles of ,religion4 ,footnote #ah3 ,as will be demonstrated in the ninth ,chapter4 ,footnote #ai3 ,optics1 ,b4 ,i4 #aagh4 ,footnote #bj3 ,astronomy1 ,b4 ,,ii4 4 #hch4 ,footnote #ba3 ,philosophy1 ,vol4 ,i4 p4 #dja4 ,footnote #bb3 ,account of ,sir ,isaac ,newton's ,philosophical ,discoveries1 ,b4 ,,iii4 c4 #b4 #c4 ,footnote #bc3 ,elements d',astronomie1 #cha4 ,footnote #bd3 ,the face of the ,sun1 ,moon1 or any ,planet1 as it appears to the eye1 is called it's ,disc4 ,footnote #be3 ,the utmost limit of a person's view1 where the ,sky seems to touch the ,earth all around1 is called his ,horizon2 which shifts as the person changes his place4 ,footnote #bf3 ,the ,plane of a ,circle1 or a thin circular ,plate1 being turned edgewise to the eye appears to be a straight line4 ,footnote #bg3 ,a ,degree is the #cfjth part of a ,circle4 ,footnote #bh3 ,here we do not mean such a conjunction1 as that the nearer ,planet should hide all the rest from the observer's sight2 7for that would be impossible unless the intersections of all their ,orbits were coincident1 which they are not1 ,see #ba47 but when they were all in a line crossing the standard ,orbit at right ,angles4 ,footnote #bi3 ,the ,,orrery fronting the ,title-page4 ,footnote #cj3 ,to make the projectile force balance the gravitating power so exactly as that the body may move in a ,circle1 the projectile velocity of the body must be such as it would have acquired by gravity alone in falling through half the radius4 ,footnote #ca3 ,astronomical ,principles of ,religion1 p4 #ff4 ,footnote #cb3 1 1 i4 e4 ,give me a place to stand on1 and ,i shall move the ,earth4 ,footnote #cc3 ,if the ,sun was not agitated about the common center of gravity of the whole ,system1 and the ,planets did not act mutually upon one another1 their ,orbits would be elliptical1 and the areas described by them would be exactly proportionate to the times of description #aec4 ,but observations prove that these areas are not in such exact proportion1 and are most varied when the greatest number of ,planets are in any particular quarter of the ,heavens4 ,when any two ,planets are in conjunction1 their mutual attractions1 which tend to bring them nearer to one another1 draws the inferior one a little farther from the ,sun1 and the superior one a little nearer to him2 by which means1 the figure of their ,orbits is somewhat altered2 but this alteration is too small to be discovered in several ages4 ,footnote #cd3 ,religious ,philosopher1 ,vol4 ,,iii4 page #fe4 ,footnote #ce3 ,this will be demonstrated in the eleventh ,chapter4 ,footnote #cf3 ,a fine net-work membrane in the bottom of the eye4 ,footnote #cg3 ,book ,i4 ,art4 #eg4 ,footnote #ch3 ,a medium1 in this sense1 is any transparent body1 or that through which the rays of light can pass2 as water1 glass1 diamond1 air2 and even a vacuum is sometimes called a ,medium4 ,footnote #ci3 ,,newton's ,system of the ,world1 p4 #abj4 ,footnote #dj3 ,this is evident from pumps1 since none can draw water higher than #cc foot4 ,footnote #da3 ,namely #ajjjj times the distance of ,saturn from the ,sun2 p4 #id4 ,footnote #db3 ,see his ,astronomy1 p4 #bcb4 ,footnote #dc3 ,as far as one can see round him on the ,earth4 ,footnote #dd3 ,sidenote3 ,fig4 ,v4 ,an ,angle is the inclination of two right lines1 as ,,ih and ,,kh1 meeting in a point at ,h2 and in describing an ,angle by three letters1 the middle letter always denotes the angular point3 thus1 the above lines ,,ih and ,,kh meeting each other at ,h1 make the ,angle ,,ihk4 ,and the point ,h is supposed to be the center of a ,circle1 the circumference of which contains #cfj equal parts called degrees4 ,a fourth part of a ,circle1 called a ,quadrant1 as ,,ge1 contains #ij degrees2 and every ,angle is measured by the number of degrees in the arc it cuts off2 as the angle ,,ehp is #de degrees1 the ,angle ,,ehf #cc1 c3 and so the ,angle ,,ehf is the same with the angle ,,chn1 and also with the ,angle ,,ahm1 because they all cut off the same arc or portion of the ,quadrant ,,eg2 and so likewise the ,angle ,,ehf is greater than the ,angle ,,chd or ,,ahl1 because it cuts off a greater arc4 ,the nearer an object is to the eye the bigger it appears1 and under the greater ,angle is it seen4 ,to illustrate this a little1 suppose an ,arrow in the position ,,ik1 perpendicular to the right line ,,ha drawn from the eye at ,h through the middle of the ,arrow at ,o4 ,it is plain that the ,arrow is seen under the ,angle ,,ihk1 and that ,,ho1 which is it's distance from the eye1 divides into halves both the ,arrow and the ,angle under which it is seen3 viz4 the ,arrow into ,,io1 ,,ok1 and the ,angle into ,,iho and ,,kho3 and this will be the case whatever distance the ,arrow is placed at4 ,let now three ,arrows1 all of the same length with ,,ik1 be placed at the distances ,,ha1 ,,hc1 ,,he1 still perpendicular to1 and bisected by the right line ,,ha2 then will ,,ab1 ,,cd1 ,,ef1 be each equal to1 and represent ,,io2 and ,,ab 7the same as ,,io7 will be seen from ,h under the ,angle ,,ahb2 but ,,cd 7the same as ,,io7 will be seen under the ,angle ,,chd or ,,ahl2 and ,,ef 7the same as ,,io7 will be seen under the ,angle ,,ehf1 or ,,chn1 or ,,ahm4 ,also1 ,,ef or ,,io at the distance ,,he will appear as long as ,,cn would at the distance ,,hc1 or as ,,am would at the distance ,,ha3 and ,,cd or ,,io at the distance ,,hc will appear as long as ,,al would at the distance ,,ha4 ,so that as an object approaches the eye1 both it's magnitude and the ,angle under which it is seen increase2 and as the object recedes1 the contrary4 ,footnote #de3 ,the fields which are beyond the gate rise gradually till they are just seen over it2 and the arms1 being red1 are often mistaken for a house at a considerable distance in those fields4 ,i once met with a curious deception in a gentleman's garden at ,hackney1 occasioned by a large pane of glass in the garden-wall at some distance from his house4 ,the glass 7through which the fields and sky were distinctly seen7 reflected a very faint image of the house2 but the image seemed to be in the ,clouds near the ,horizon1 and at that distance looked as if it were a huge castle in the ,air4 ,yet1 the ,angle under which the image appeared1 was equal to that under which the house was seen3 but the image being mentally referred a much greater distance than the house1 appeared much bigger to the imagination4 ,footnote #df3 ,the ,sun and ,moon subtend a greater ,angle on the ,meridian than in the ,horizon1 being nearer the ,earth in the former case than the latter4 ,footnote #dg3 ,the ,altitude of any celestial ,phenomenon is an arc of the ,sky intercepted between the ,horizon and the ,phenomenon4 ,in ,fig4 ,,vi4 of ,plate ,,ii4 let ,,hox be a horizontal line1 supposed to be extended from the eye at ,a to ,x1 where the ,sky and ,earth seem to meet at the end of a long and level plain2 and let ,s be the ,sun4 ,the arc ,,xy will be the ,sun's height above the ,horizon at ,x1 and is found by the instrument ,,edc1 which is a quadrantal board1 or plate of metal1 divided into #ij equal parts or degrees on its limb ,,dpc2 and has a couple of little brass plates1 as a and b1 with a small hole in each of them1 called ,sight-,holes1 for looking through1 parallel to the edge of the ,quadrant whereon they stand4 ,to the center ,e is fixed one end of a thread ,f1 called the ,plumb-,line1 which has a small weight or plummet ,p fixed to it's other end4 ,now1 if an observer holds the ,quadrant upright1 without inclining it to either side1 and so that the ,horizon at ,x is seen through the sight-holes a and b1 the plumb-line will cut or hang over the beginning of the degrees at o1 in the edge ,,ec2 but if he elevates the ,quadrant so as to look through the sight-holes at any part of the ,heavens1 suppose to the ,sun at ,s2 just so many degrees as he elevates the sight-hole b above the horizontal line ,,hox1 so many degrees will the plumb-line cut in the limb ,,cp of the ,quadrant4 ,for1 let the observer's eye at ,a be in the center of the celestial arc ,,xyv 7and he may be said to be in the center of the ,sun's apparent diurnal ,orbit1 let him be on what part of the ,earth he will7 in which arc the ,sun is at that time1 suppose #be degrees high1 and let the observer hold the ,quadrant so that he may see the ,sun through the sight-holes2 the plumb-line freely playing on the quadrant will cut the #beth degree in the limb ,,cp equal to the number of degrees of the ,sun's ,altitude at the time of observation4 ,n4 ,b4 ,whoever looks at the ,sun1 must have a smoaked glass before his eyes to save them from hurt4 ,the better way is not to look at the ,sun through the sight-holes1 but to hold the ,quadrant facing the eye1 at a little distance1 and so that the ,sun shining through one hole1 the ray may be seen to fall on the other4 ,footnote #dh3 ,see the ,note on #ahe4 ,footnote #di3 ,here proper allowance must be made for the ,refraction1 which being about #cd minutes of a degree in the ,horizon1 will cause the ,moon's center to appear #cd minutes above the ,horizon when her center is really in it4 ,footnote #ej3 ,by this is meant1 that if a line be supposed to be drawn parallel to the ,earth's ,axis in any part of it's ,orbit1 the ,axis keeps parallel to that line in every other part of it's ,orbit3 as in ,fig4 ,i4 of ,plate ,v2 where abcdefgh represents the ,earth's ,orbit in an oblique view1 and ,ns the ,earth's ,axis keeping always parallel to the line ,,mn4 ,footnote #ea3 ,,smith's ,optics1 #aaig4 ,footnote #eb3 ,all ,circles appear ellipses in an oblique view1 as is evident by looking obliquely at the rim of a bason4 ,for the true figure of a ,circle can only be seen when the eye is directly over it's center4 ,the more obliquely it is viewed1 the more elliptical it appears1 until the eye be in the same plane with it1 and then it appears like a straight line4 ,footnote #ec3 ,here we must suppose the ,sun to be no bigger than an ordinary point 7as 7 because he only covers a ,circle half a degree in diameter in the ,heavens2 whereas in the figure he hides a whole sign at once from the ,earth4 ,footnote #ed3 ,here we must suppose the ,earth to be a much smaller point than that in the preceding note marked for the ,sun4 ,footnote #ee3 ,if the ,earth were cut along the ,equator1 quite through the center1 the flat surface of this section would be the plane of the ,equator2 as the paper contained within any ,circle may be justly termed the plane of that ,circle4 ,footnote #ef3 ,the two opposite points in which the ,ecliptic crosses the ,equinoctial1 are called the ,equinoctial ,points3 and the two points where the ,ecliptic touches the ,tropics 7which are likewise opposite1 and #ij degrees from the former7 are called the ,solstitial ,points4 ,footnote #eg3 ,the ,equinoctial ,circle intersects the ,ecliptic in two opposite points1 called ,aries and ,libra1 from the ,signs which always keep in these points3 ,they are called the ,equinoctial ,points1 because when the ,sun is in either of them1 he is directly over the terrestrial ,equator2 and then the days and nights are equal4 ,footnote #eh3 ,in this discourse1 we may consider the ,orbits of all the ,satellites as circular1 with respect to their primary ,planets2 because the excentricities of their ,orbits are too small to affect the ,phenomena here described4 ,footnote #ei3 ,if a ,globe be cut quite through upon any ,circle1 the flat surface where it is so divided1 is the plane of that circle4 ,footnote #fj3 ,the ,figure shews the ,globe as if only elevated about #dj degrees1 which was occasioned by an oversight in the drawing3 but it is still sufficient to explain the ,phenomena4 ,footnote #fa3 ,the ,ecliptic1 together with the fixed ,stars1 make #cff-a_/d apparent diurnal revolutions about the ,earth in a year2 the ,sun only #cfe-a_/d4 ,therefore the ,stars gain #c minutes #ef seconds upon the ,sun every day3 so that a ,sidereal day contains only #bc hours #ef minutes of mean ,solar time2 and a natural or ,solar day #bd hours4 ,hence #ab ,sidereal hours are #a minute #eh seconds shorter than #ab ,solar4 ,footnote #fb3 ,the ,sun advances almost a degree in the ,ecliptic in #bd hours1 the same way that the ,moon moves3 and therefore1 the ,moon by advancing #ac-a_/f degrees in that time goes little more than #ab degrees farther from the ,sun than she was on the day before4 ,footnote #fc3 ,this center is as much nearer the ,earth's center than the ,moon's as the ,earth is heavier1 or contains a greater quantity of matter than the ,moon1 namely about #dj times4 ,if both bodies were suspended on it they would hang in quilibria4 ,so that dividing #bdj1jjj miles1 the ,moon's distance from the ,earth's center1 by #dj the excess of the ,earth's weight above the ,moon's1 the quotient will be #fjjj miles1 which is the distance of the common center of gravity of the ,earth and ,moon from the ,earth's center4 ,footnote #fd3 ,the ,penumbra is a faint kind of shadow all around the perfect shadow of the ,planet or ,satellite2 and will be more fully explained by and by4 ,footnote #fe3 ,which is the time that the ,eclipse would be at the greatest obscuration1 if the motions of the ,sun and ,moon were equable1 or the same in all parts of their ,orbits4 ,footnote #ff3 ,the above period of #ah years #aa days #g hours #dc minutes1 which was found out by the ,chaldeans1 and by them called ,saros4 ,footnote #fg3 ,a ,digit is a twelfth part of the diameter of the ,sun or ,moon4 ,footnote #fh3 ,there are two antient ,eclipses of the ,moon1 recorded by ,ptolemy from ,hipparchus1 which afford an undeniable proof of the ,moon's acceleration4 ,the first of these was observed at ,babylon1 ,december the #bb;d1 in the year before ,,christ #chc3 when the ,moon began to be eclipsed about half an hour before the ,sun rose1 and the ,eclipse was not over before the ,moon set3 but by our best ,astronomical ,tables1 the ,moon was set at ,babylon half an hour before the ,eclipse began2 in which case1 there could have been no possibility of observing it4 ,the second ,eclipse was observed at ,alexandria1 ,september the #bb;d1 the year before ,,christ #bja2 where the ,moon rose so much eclipsed1 that the ,eclipse must have begun about half an hour before she rose3 whereas by our ,tables the beginning of this ,eclipse was not till about #aj minutes after the ,moon rose at ,alexandria4 ,had these ,eclipses begun and ended while the ,sun was below the ,horizon1 we might have imagined1 that as the antients had no certain way of measuring time1 they might have been so far mistaken in the hours1 that we could not have laid any stress on the accounts given by them4 ,but1 as in the first ,eclipse the ,moon was set1 and consequently the ,sun risen1 before it was over2 and in the second ,eclipse the ,sun was set1 and the ,moon not risen1 till some time after it began2 these are such circumstances as the observers could not possibly be mistaken in4 ,mr4 ,struyk in the following ,catalogue1 notwithstanding the express words of ,ptolemy1 puts down these two ,eclipses as observed at ,athens2 where they might have been seen as above1 without any acceleration of the ,moon's motion3 ,athens being #bj degrees ,west of ,babylon1 and #g degrees ,west of ,alexandria4 ,footnote #fi3 ,each ,olympiad began at the time of ,full ,moon next after the ,summer ,solstice1 and lasted four years1 which were of unequal lengths because the time of ,full ,moon differs #aa days every year3 so that they might sometimes begin on the next day after the ,solstice1 and at other times not till four weeks after it4 ,the first ,olympiad began in the year of the ,julian ,period #cich1 which was #ggf years before the first year of ,,christ1 or #gge before the year of his birth2 and the last ,olympiad1 which was the #bic;d1 began ,a4 ,d4 #cic4 ,at the expiration of each ,olympiad1 the ,olympic ,games were celebrated in the ,elean fields1 near the river ,alpheus in the ,peloponnesus 7now ,morea7 in honour of ,,jupiter ,,olympus4 ,see ,,strauchius's ,breviarium ,chronologium1 p4 #bdg-bea4 ,footnote #gj3 ,the reader may probably find it difficult to understand why ,mr4 ,,smith should reckon this ,eclipse to have been in the #dth year of the #dhth ,olympiad2 as it was only in the end of the third year3 and also why the #bhth of ,may1 in the #eheth year before ,,christ should answer to the present #ajth of that month4 ,but we hope the following explanation will remove these difficulties4 ,the month of ,may 7when the ,sun was eclipsed7 in the #eheth year before the first year of ,,christ1 which was a leap-year1 fell in the latter end of the third year of the #dhth ,olympiad2 and the fourth year of that ,olympiad began at the ,summer ,solstice following3 but perhaps ,mr4 ,,smith begins the years of the ,olympiad from ,january1 in order to make them correspond more readily with ,julian years2 and so reckons the month of ,may1 when the ,eclipse happened1 to be in the fourth year of that ,olympiad4 ,the ,place or ,longitude of the ,sun at that time was #bi #dc #ag1 to which same place the ,sun returned 7after #bcjj years1 viz47 ,a4 ,d4 #agaf1 on ,may1 #i;d4 #e;h4 #fm4 after noon3 so that1 with respect to the ,sun's place1 the #ith of ,may1 #agaf answers to the #bhth of ,may in the #eheth year before the first year of ,,christ2 that is1 the ,sun had the same ,longitude on both those days4 ,footnote #ga3 ,before ,,christ #dac1 ,august #bg4 ,footnote #gb3 ,before ,,christ #afh1 ,june #bj4 ,footnote #gc3 ,,struyk's ,eclipses are to the ,old ,style1 all the rest to the ,new4 ,footnote #gd3 ,this ,eclipse happened in the first year of the ,peloponnesian war4 ,footnote #ge3 ,although the ,sun and ,moon are spherical bodies1 as seen from the ,earth they appear to be circular planes1 and so would the ,earth if it were seen from the ,moon4 ,the apparently flat surfaces of the ,sun and ,moon are called their ,disks by ,astronomers4 ,footnote #gf3 ,a ,digit is a twelfth part of the diameter of the ,sun and ,moon4 ,footnote #gg3 ,this is the same with the annual ,argument of the ,moon4 ,footnote #gh3 ,when the ,romans divided the ,empire1 which was about #ch years before ,,christ1 ,spain fell to ,augustus's share3 in memory of which1 the ,spaniards dated all their memorable events ab exordio ,regni ,augusti2 as ,christians do from the birth of our ,,saviour4 ,but in process of time1 only the initial letters ,,aera of these words were used instead of the words themselves4 ,and thus1 according to some1 came the word ,,ra1 which is made use of to signify a point of time from whence historians begin to reckon4 ,footnote #gi3 ,when the ,sun's ,anomaly is #j signs #j degrees1 or #f signs #j degrees1 neither the ,sun nor the ,moon's ,anomaly have any ,equation2 which is the case in this ,example4 ,footnote #hj3 ,see the ,remark1 p4 #aie4 ,footnote #ha3 ,babylon is #db deg4 #df min4 east from the ,meridian of ,london1 which is equal to #b hours #ea min4 of time nearly4 ,see #bbj4 ,footnote #hb3 ,our ,,saviour was born in a leap-year1 and therefore every fourth year both before and after is a leap-year in the ,old ,stile3 but the ,tables begin with the year next after that of his birth4 ,footnote #hc3 ,when only one of the ,nodes is mentioned1 it is the ,ascending ,node that is meant1 to which the ,descending ,node is exactly opposite4 ,footnote #hd3 ,when the ,moon is ,north of the ,ecliptic and going farther from it1 her ,latitude or ,declination from the ,ecliptic is called ,north ,ascending3 when she is ,north of the ,ecliptic and going toward it1 her ,latitude is ,north ,descending3 when she is ,south of the ,ecliptic and going farther from it1 her ,latitude is ,south ,descending3 and lastly1 when she is ,south of the ,ecliptic and going toward it1 her ,latitude is ,south ,ascending4 ,footnote #he3 ,see ,page #aic1 ,example ,,ii4 ,footnote #hf3 ,m4 ,maupertuis1 in his dissertation on the figures of the ,celestial ,bodies 7p4 #fa-fc7 is of opinion that some ,stars1 by their prodigious quick rotations on their ,axes1 may not only assume the figures of oblate spheroids1 but that by the great centrifugal force1 arising from such rotations1 they may become of the figures of mill-stones2 or be reduced to flat circular planes1 so thin as to be quite invisible when their edges are turned towards us2 as ,saturn's ,ring is in such positions4 ,but when very excentric ,planets or ,comets go round any flat ,star1 in ,orbits much inclined to it's ,equator1 the attraction of the ,planets or ,comets in their perihelions must alter the inclination of the ,star2 on which account it will appear more or less large and luminous as it's broad side is more or less turned towards us4 ,and thus he imagines we may account for the apparent changes of magnitude and lustre in those ,stars1 and likewise for their appearing and disappearing4 ,footnote #hg3 ,see this word explained in the note at the foot of page #aid4 ,footnote #hh3 ,see the note on #cbc4 ,footnote #hi3 ,matt4 xxvii4 #de4 ,mark xv4 #dc4 ,luke xxiii4 #dd4 ,transcriber's ,note ,this book uses inconsistent spelling and hyphenation1 which were retained in the ebook version4 ,some corrections have been made to the text1 including correcting the errata and normalizing punctuation4 ,further corrections are noted below3 ,errata3 l4 #ae from botton - l4 #ae from bottom p4 #i3 forward in the ,eliptic - forward in the ,ecliptic p4 #ca3 is at it were - is as it were p4 #cf1 ,footnote #bb moved from referring to ,rutherfurth to ,maclaurin1 additionally #8,isacc ,newton' changed to #8,isaac ,newton'4 ,footnote marker on ,rutherfurth removed as there was no footnote associated with it4 p4 #ch3 on the the same ,axis - on the same ,axis ,footnote #cb - p4 #fi3 who were suprised to find - who were surprised to find p4 #fi3 than those whch - than those which p4 #gb3 than tie a thread - then tie a thread p4 #gd3 is is equal to - is equal to p4 #gd3 the graduaded limb - the graduated limb ,footnote #di3 bove the horizon - above the horizon p4 #gh3 different lenghts - different lengths p4 #gh3 from the the ,equator - from the ,equator p4 #ij3 is not instantaneons - is not instantaneous p4 #ib3 ,degreees and ,parts of the ,equtor- ,degrees and ,parts of the ,equator p4 #acb3 appear supprising - appear surprising p4 #acc3 ,when ,jupiter at - ,when ,jupiter is at ,sidenote p4 #acf3 ,the reason of of this - the reason of this p4 #adj the opposite points rises - the opposite point rises ,sidenote p4 #ada3 ,harvest aad ,hunter's - ,harvest and ,hunter's p4 #aed3 espeically as to the - especially as to the ,sidenote p4 #aee3 aereal ,tides - aerial ,tides p4 #aeh3 the the ,earth - the ,earth p4 #afj3 goes round him #hg days - goes round him in #hg days p4 #afa3 ,eclipses and revolulution - ,eclipses and revolution p4 #afg3 ,jacobus ,ptlaumen - ,jacobus ,pflaumen p4 #afh3 set set down - set down p4 #agb ,table #b1 #ast column1 #fth row3 #achh - #adhh p4 #agd3 duplicate entry for #afjf ,sept #b4 removed p4 #agg3 foretold by ,thalls - foretold by ,thales p4 #ahj3 the ,eclipse is annualar - the ,eclipse is annular p4 #aic3 ,,eaample ,,ii4 - ,,example ,,ii p4 #bjb3 these two ,fquations - these two ,equations p4 #bjc3 their ,sun will be - their ,sum will be p4 #baj3 the page number was printed as #aaj and has been corrected p4 #baj3 ,motion and ,semi diameter - ,motion and ,semi-diameter p4 #bcb3 - p4 #bcb3 - p4 #bch3 oblate spheriod - oblate spheroid p4 #bfa #ah ,degres - #ah ,degrees ,index ,mercury 7,quicksiver7 - ,mercury 7,quicksilver7 ,list of ,plates ,page number for ,plate ,,iv corrected from #ae to #ig