,transcriber's ,notes3 ,underscores 80 before and after a word or phrase indicate italics in the original text4 ,small capitals have been converted to ,,solid capitals4 ,old or antiquated spellings have been preserved4 ,typographical errors have been silently corrected4 ,illustration3 ,the ,,great ,,orrery ,four ,feet in ,diameter ,made by ,,tho3 ,,wright ,mathematical ,instrument-maker ,,to ,,his ,,majesty ,for the ,royal ,academy at ,,portsmouth ,now ,b4 ,cole1 at the same shop4 ,who makes ,orrery's of different sorts as may be seen at his ,shop in ,,fleet ,,street ,where is ,sold a ,large ,print of the ,orrery with the ,explanation on a ,sheet of ,imperial ,paper4 ,price #bs4 ,,the ,description and ,use ,,of ,,the ,,globes1 ,,and ,,the ,,orrery4 ,to which is prefix'd1 ,by ,way of ,,introduction1 ,a brief ,account of the ,,solar ,,system4 ,by ,,joseph ,,harris1 ,,teacher of the ,,mathematics4 ,,the ,,eleventh ,,edition4 ,,london3 ,printed for ,b4 ,,cole1 at the ,orrery1 near the ,globe ,tavern1 in ,fleet street1 late the ,shop of ,mr4 ,,thomas ,,wright1 ,instrument-maker to his late ,,majesty2 and ,e4 ,,cushee1 near ,st4 ,dunstan's ,church1 ,fleet ,street4 ,,mdcclxxiii4 ,advertisement4 ,the great encouragement ,mr4 ,,wright has had for many years past in making large ,orreries1 with the motions of all the ,planets and ,satellites1 and the true motion of ,saturn's ,ring1 has made him so ready and perfect1 that ,gentlemen may depend on having them made reasonable and sound1 not liable to be out of ,order4 ,as may be seen by one he made for ,mr4 ,watt's ,academy in ,tower-street4 ,another for his ,majesty at ,kensington4 ,another for the ,new ,royal ,academy at ,portsmouth4 ,another for his ,grace the ,duke of ,argyle 7late ,lord ,ila47 ,and several other large ones for ,noblemen and ,gentlemen4 ,the above1 and all other ,mathematical1 ,philosophical1 and ,optical ,instruments1 are now made in the most complete manner1 by ,b4 ,,cole1 ,servant to ,mr4 ,,wright1 at the time of the above being made1 and successor to him in the same ,trade and ,business4 ,,the ,,contents4 ,the ,,introduction3 ,containing a brief ,account of the ,solar ,system1 and of the ,fixed ,stars4 ,,sect4 ,i4 ,of the ,order and ,periods of the ,primary ,planets revolving about the ,sun2 and of the ,secondary ,planets round their respective ,primaries4 ------ ,of the ,primary ,planets #a ------ ,of the ,secondary ,planets #e ------ ,of the ,annual and ,diurnal ,motion of the ,planets #g ------ ,that the ,planets are ,opaque and ,globular #i ------ ,that the ,earth is placed betwixt the ,orbits of ,mars and ,venus ibid4 ------ ,that the ,planets turn round the ,sun ibid4 ------ ,that the ,earth also turns round the ,sun #ae ------ ,how the ,annual and ,diurnal ,motion of the ,planets are computed ibid4 ------ ,how the relative ,distance of the ,planets from the ,sun are determined #ah ------ ,how their absolute ,distances from the ,sun are computed #bc ------ ,how the ,magnitudes of the ,planets are determined #bf ------ ,why the ,moon appears bigger than any of the ,planets #bg ------ ,a ,table of the ,distances1 ,magnitudes1 ,periodical1 and ,diurnal ,revolutions of the ,planets #bh ------ ,of ,comets #bi ,,sect4 ,,ii4 ,of the ,fixed ,stars #cb ------ ,that the fixed ,stars are luminous ,bodies1 at immense ,distances from us ibid4 ------ ,of ,telescopical ,stars #ce ------ ,the ,stars digested into ,constellations #cf ------ ,of the ,galaxy1 or ,milky ,way #ch ,illustration ,the ,,description and ,,use of the ,,celestial and ,,terrestrial ,,globes4 ,the ,geometrical ,definition of a ,globe1 and of the principal ,use of the ,artificial ,globes #db ,that there will be the same prospect of the ,fixed ,stars1 whether the ,spectator be placed in the ,sun1 or on the ,earth #de ,,sect4 ,i4 ,an ,explanation of the ,circles of the ,sphere1 and of some ,astronomical ,terms arising therefrom #dg ------ ,of the ,division of ,time #fi ------ ,of the ,atmosphere #ha ,,sect4 ,,ii4 ,geographical ,definitions #hd ------ ,of the ,situation of ,places upon the ,earth ibid4 ------ ,of ,zones and ,climates #ij ------ ,of the ,poetical ,rising and ,setting of the ,stars #if ------ ,of the surface of the ,earth1 considered as it is composed of ,land and ,water ibid4 ------ ,of the appurtenances of the ,globes #aja ,,sect4 ,,iii4 ,the ,use of the ,globes #ajd ,,problem ,i4 ,to find the ,latitude and ,longitude of any given place upon the ,globe2 and on the contrary1 the ,latitude and ,longitude being given to find the ,place ibid4 ,,prob4 ,,ii4 ,to find the ,difference of ,latitude betwixt any two given places #ajf ,,prob4 ,,iii4 ,to find the ,difference of ,longitude betwixt any two given places ibid4 ,,prob4 ,,iv4 ,any ,place being given2 to find all those places that are in the same ,latitude with the said place #ajg ,,prob4 ,v4 ,the ,day of the ,month being given2 to find the ,sun's place in the ,ecliptic1 and his ,declination #ajh ,,prob4 ,,vi4 ,to rectify the ,globe for the ,latitude1 ,zenith1 and ,sun's place #aji ,,prob4 ,,vii4 ,to find the ,distance between any two given ,places upon the ,globe1 and to find all those places upon the ,globe that are at the same ,distance from a given place #aaj ,,prob4 ,,viii4 ,to find the ,angle of a ,position of ,places2 or the angle formed by the ,meridian of one place1 and a great circle passing through both the places #aaa ,,prob4 ,,ix4 ,to find the ,antci1 ,perici1 and ,antipodes1 to any given place #aac ,,prob4 ,x4 ,the ,hour of the ,day at one ,place being given2 to find the correspondent ,hour 7or what o',clock it is at that time7 at any other place #aad ,,prob4 ,,xi4 ,the ,day of the ,month being given2 to find those places on the ,globe where the ,sun will be ,vertical1 or in the ,zenith1 that ,day #aae ,,prob4 ,,xii4 ,a place being given in the ,torrid ,zone2 to find those two ,days in which the ,sun will be ,vertical to the same #aaf ,,prob4 ,,xiii4 ,to find where the ,sun is ,vertical at any given time assigned2 or1 the ,day of the ,month and the ,hour at any place 7suppose ,london7 being given1 to find in what place the ,sun is ,vertical at that very time ibid4 ,,prob4 ,,xiv4 ,the ,day1 and the ,hour of the ,day at one place1 being given2 to find all those places upon the ,earth where the ,sun is then ,rising1 ,setting1 ,culminating 7or on the ,meridian72 also where it is ,day-light1 ,twilight1 ,dark ,night1 ,midnight2 where the ,twilight then begins1 and where it ends2 the ,height of the ,sun in any part of the illuminated ,hemisphere2 also his ,depression in the obscure ,hemisphere #aag ,,prob4 ,,xv4 ,the ,day of the ,month being given1 to show1 at one ,view1 the ,length of ,days and ,nights in all ,places upon the ,earth1 at that time2 and to explain how the ,vicissitudes of ,day and ,night are really made by the motion of the ,earth round her ,axis1 in #bd ,hours1 the ,sun standing still #aai ,,prob4 ,,xvi4 ,to ,explain in general the ,alteration of ,seasons1 or ,length of the ,days and ,nights1 made in all places of the ,world1 by the ,sun's1 or the ,earth's ,annual motion in the ,ecliptic #aba ,,prob4 ,,xvii4 ,to shew by the ,globe1 at one ,view1 the ,length of the ,days and ,nights1 at any particular place1 at all times of the ,year #abh ,,prob4 ,,xviii4 ,the ,latitude of any place1 not exceeding #fi ,degrees1 and the ,day of the ,month being given2 to the time of ,sun-rising and ,setting1 and the length of the ,day and ,night #acf ,,prob4 ,,xix4 ,to find the length of the longest and shortest ,day and ,night in any given place1 not exceeding #ff ,degrees of ,latitude #acg ,,prob4 ,,xx4 ,to find in what ,latitude the longest ,day is1 of any given length less than #bd ,hours #aci ,,prob4 ,,xxi4 ,a ,place being given in one of the ,frigid ,zones 7suppose the ,northern7 to find what number of ,days 7of #bd ,hours each7 the ,sun doth constantly shine upon the same1 how long he is absent1 and also the first and last day of his appearance #adj ,,prob4 ,,xxii4 ,to find in what ,latitude the longest ,day is1 of any given length1 less than #ahb natural ,days #ada ,,prob4 ,,xxiii4 ,the ,day of the ,month being given2 to find when the ,morning and ,evening ,twilight begins and ends1 in any place upon the ,globe #adb ,,prob4 ,,xxiv4 ,to find the time when total ,darkness ceases1 or when the ,twilight continues from ,sun-setting to ,sun-rising1 in any given place #add ,,prob4 ,,xxv4 ,the ,day of the ,month being given2 to find those places of the ,frigid ,zones1 where the ,sun begins to shine constantly without setting2 and also those places where he begins to be totally absent #adf ,,prob4 ,,xxvi4 ,the ,latitude1 the ,sun's ,place1 and his ,altitude being given2 to find the ,hour of the ,day1 and ,sun's ,azimuth from the ,meridian #adi ,,prob4 ,,xxvii4 ,the ,latitude1 ,hour of the ,day1 and the ,sun's ,place being given2 to find the ,sun's ,altitude #aej ,,prob4 ,,xxviii4 ,the ,latitude of the ,place1 and the ,day of the ,month being given2 to find the depression of the ,sun below the ,horizon1 and his ,azimuth1 at any ,hour of the ,night #aea ,,prob4 ,,xxix4 ,the ,latitude of the ,sun's ,place1 and his ,azimuth being given2 to find his ,altitude1 and the ,hour #aeb ,,prob4 ,,xxx4 ,the ,latitude1 the ,sun's ,altitude1 and his ,azimuth being given2 to find his ,place on the ,ecliptic1 and the ,hour ibid4 ,,prob4 ,,xxxi4 ,the ,declination1 and ,meridian ,altitude of the ,sun1 or of any ,star being given2 to find the ,latitude of the ,place #aec ,,prob4 ,,xxxii4 ,the ,day and ,hour of a ,lunar ,eclipse being known2 to find all those ,places upon the ,globe in which the same will be visible #aed ,,prob4 ,,xxxiii4 ,the ,day of the ,month1 and ,hour of the ,day1 according to our way of reckoning in ,england1 being given2 to find thereby the ,babylonish1 ,italic1 and ,jewish1 or ,judaical ,hour #aee ,,prob4 ,,xxxiv4 ,to find the ,right ,ascension and ,declination of the ,sun1 or any ,fixed ,star #aef ,,prob4 ,,xxxv4 ,to find the ,longitude and ,latitude of a given ,star #aeh ,,prob4 ,,xxxvi4 ,the ,latitude of the ,place1 the ,day of the ,month1 and the ,hour being given2 to find what ,stars are then rising and setting1 what ,stars are culminating1 or on the ,meridian1 and the ,altitude and ,azimuth of any ,star above the ,horizon2 and also how to distinguish the ,stars in the ,heavens one from the other1 and to know them by their proper ,names #aei ,,prob4 ,,xxxvii4 ,the ,latitude of the ,place being given2 to find the ,amplitude1 ,oblique ,ascension1 and ,descension1 ,ascensional ,difference1 ,semi-diurnal ,arch1 and the time of ,continuance above the ,horizon1 of any given ,point in the ,heavens #afb ,,prob4 ,,xxxviii4 ,the ,latitude and the ,day of the ,month being given2 to find the ,hour when any known ,star will be on the ,meridian1 and also the time of its ,rising and ,setting #afe ,,prob4 ,,xxxix4 ,to find at what time of the ,year a given ,star will be upon the ,meridian1 at a given ,hour of the ,night #aff ,,prob4 ,,xl4 ,the ,day of the ,month and the ,azimuth1 of any known ,star being given2 to find the ,hour of the ,night #afg ,,prob4 ,,xli4 ,two known ,stars1 having the same ,azimuth1 or the same ,height1 being given2 to find the ,hour of the ,night #afh ,,prob4 ,,xlii4 ,the ,latitude1 ,day of the ,month1 and the ,altitude of any known ,star being given2 to find the ,hour of the ,night #afi ,,prob4 ,,xliii4 ,having the ,latitude of the ,place1 to find the ,degree of the ,ecliptic1 which rises or sets with a given ,star2 and from thence to determine the time of its ,cosmical and ,achronical ,rising and ,setting #aga ,,prob4 ,,xliv4 ,having the ,latitude of the ,place2 to find the time when a ,star rises and sets ,heliacally #agb ,,prob4 ,,xlv4 ,to find the ,place of any ,planet upon the ,globe1 so by that ,means to find its ,place in the ,heavens2 also to find at what ,hour any ,planet will rise or set1 or be on the ,meridian1 at any ,day in the ,year #agc ,,prob4 ,,xlvi4 ,to find all that space upon the ,earth where an ,eclipse of one of the ,satellites of ,jupiter will be visible #age ,the ,,description of the ,,orrery #agg ,of the ,motions of the ,planets in general #ahc ,of the ,stations and ,retrogadations of the ,planets #ahf ,of the ,annual and ,diurnal ,motion of the ,earth #aid ,of the ,phases of the ,moon1 and of her ,motion in her ,orbit #bja ,of the ,eclipses of the ,sun and ,moon #bjh ,of the ,eclipses of ,jupiter's ,satellites #bab ,illustration ,,the ,,introduction1 ,,containing ,a ,brief ,account of the ,,solar ,,system1 and of the ,,fixed ,,stars4 ,,sect4 ,i4 ,of the ,order and ,periods of the ,primary ,planets revolving about the ,sun2 and of the ,secondary ,planets round their respective ,primaries4 ,sidenote3 ,planets4 ,the ,sun is placed in the midst of an immense space1 wherein six opaque spherical bodies revolve about him as their center4 ,these wandering globes are called the ,planets1 who1 at different distances1 and in different periods1 perform their revolutions from ,west to ,east1 in the following order3 #a4 ,mercury is nearest to the ,sun of all the planets1 and performs its course in about three months4 #b4 ,venus in about seven months and a half4 #c4 ,the ,earth in a year4 #d4 ,mars in about two years4 #e4 ,jupiter in twelve4 ,and lastly1 ,saturn1 whose#a,orbit includes all the rest1 spends almost #cj years in one revolution round the ,sun4 ,the distances of the ,planets from the ,sun are nearly in the same proportion as they are represented in ,plate #a4 viz4 ,supposing the distance of the ,earth from the ,sun to be divided into #aj equal parts2 that of ,mercury will be about #d of these parts2 of ,venus #g2 of ,mars #ae2 of ,jupiter #eb2 and that of ,saturn #ie4 ,the ,characters placed before the names of the ,planets1 are for brevity's sake commonly made use of by ,astronomers1 instead of the words at length1 as 1 for ,venus1 c4 ,illustration3 ,plate #a4 ,,the ,,solar ,,system ,or the ,orbits of the ,planets according to their mean distances from the ,sun4 ,sidenote3 ,nodes4 ,the orbits of the ,planets are not all in the same plane1 but variously inclined to one another2 so that supposing one of them to coincide with the above scheme1 the others will have one half above1 and the other half below it2 intersecting one another in a line passing through the ,sun4 ,the plane of the ,earth's orbit is called the ,ecliptic2 and this the astronomers make the standard to which the planes of the other orbits are judged to incline4 ,the right line passing thro' the ,sun1 and the common intersection of the plane of the orbit of any planet and the ,ecliptic1 is called the ,line of the ,nodes of that planet2 and the points themselves1 wherein the orbit cuts the ,ecliptic are called the ,nodes4 ,sidenote3 ,excentricity4 ,the inclinations of the orbits of the ,planets to the plane of the ecliptic1 are as follows1 viz4 the orbit of ,mercury makes an angle with it of almost #g degrees2 that of ,venus something above #c degrees2 of ,mars a little less than #b degrees2 of ,jupiter1 #a degree2 and of ,saturn1 about #b degrees4 ,the orbits of the ,planets are not circles1 but ellipses or ovals4 ,what an ellipsis is1 may be easily understood from the following description4 ,imagine two small pegs fixed upright on any plane1 and suppose them tied with the ends of a thread somewhat longer than their distance from one another3 ,now if a pin be placed in the double of the thread and turned quite round 7always stretching the thread with the same force7 the curved described by this motion is an ,ellipsis4 ,the two points where the pegs stood1 7about which the thread was turned7 are called the foci of that ellipsis2 and if1 without changing the length of the thread1 we alter the position of the pegs1 we shall then have an ellipsis of a different kind from the former2 and the nearer the focus's are together1 the nearer will the curve described be to a circle2 until at last1 the two focus's coincide1 and then the pin in the doubling of the thread will describe a perfect circle4 ,the orbits of all the ,planets have the ,sun in one of their focus's1 and half the distance between the two focus's is called the ,excentricity of the orbits4 ,this excentricity is different in all the planets1 but in most of them so small1 that in little schemes or instruments1 made to represent the planetary orbits1 it need not be considered4 ,sidenote3 ,primary ,planets4 ,sidenote3 ,secondary ,planets4 ,the six ,planets above-mentioned1 are called ,primaries1 or ,primary ,planets2 but besides these1 there are ten other lesser ,planets1 which are called ,secondaries1 ,moons1 or ,satellites4 ,these moons always accompany their respective primaries1 and perform their ,revolutions round them1 whilst both together are also carried round the ,sun4 ,of the six ,primary ,planets1 there are but three1 as far as observation can assure us1 that have these attendants1 viz4 the ,earth1 ,jupiter1 and ,saturn4 ,the ,earth is attended by the ,moon1 who performs her revolution in about #bg ,days1 at the distance of about #cj ,diameters of the ,earth from it2 and once a ,year is carried round the ,sun along with the ,earth4 ,sidenote3 ,jupiter's four ,moons4 ,jupiter has four ,moons1 or ,satellites2 the first1 or innermost1 performs its revolution in about one ,day1 and #ah ,hours1 at the distance of #e ,semidiameters of ,jupiter1 from his ,center2 the second revolves about ,jupiter in #c ,days1 #ac ,hours1 at the distance of #i of his ,semidiameters2 the third in #g ,days1 and #d ,hours1 at the distance of #ad ,semidiameters2 the fourth1 and outermost1 performs its course in the space of #af ,days1 #ag ,hours2 and is distant from ,jupiter's center1 #be of his ,semidiameters4 ,sidenote3 ,saturn has five ,moons4 ,saturn has no less than five ,satellites2 the first1 or innermost1 revolves about him in #a ,day1 and #ba ,hours1 at the distance of #d ,semidiameters of 1 from his center2 the second compleats his period in #b ,days1 at the distance of #e_/ of his ,semidiameters2 the third1 in about #d ,days1 at the distance of #h ,semidiameters2 the fourth performs its course in about #af ,days1 at the distance of #ah ,semidiameters2 the fifth1 and outermost1 takes #gi ,days1 to finish his course1 and is #ed ,semidiameters of ,saturn distant from his center4 ,the ,satellites1 as well as their primaries1 perform their revolutions from ,west to ,east3 ,the planes of the ,orbits of the ,satellites of the same ,planet are variously inclined to one another1 and consequently are inclined to the plane of the ,orbit of their primary4 ,sidenote3 ,saturn's ,ring4 ,besides these attendants1 ,saturn is encompassed with a thin plain ,ring1 that does no where touch his body2 ,the diameter of this ,ring is to the diameter of ,saturn1 as #i to #d2 and the void space between the ,ring and the body of ,saturn is equal to the breadth of the ,ring itself2 so that in some situations the ,heavens may be seen between the ,ring and his body4 ,this surprizing phnomenon of ,saturn's ,ring1 is a modern discovery2 neither were the ,satellites of ,jupiter and ,saturn known to the ancients4 ,the ,jovial ,planets were first discovered by the famous ,italian philosopher ,galilus1 by a telescope which he first invented2 and the celebrated ,cassini1 the ,french king's astronomer1 was the first that saw all the ,satellites of ,saturn2 which by reason of their great distances from the ,sun1 and the smallness of their own bodies1 cannot be seen by us1 but by the help of very good glasses4 ,sidenote3 ,annual ,motion4 ,sidenote3 ,diurnal ,motion4 ,the motion of the primary ,planets round the ,sun 7as also of the ,satellites round their respective primaries7 is called their ,annual ,motion2 because they have one ,year1 or alteration of ,seasons compleat1 in one of these revolutions4 ,besides this annual motion1 four of the ,planets1 viz4 ,venus1 the ,earth1 ,mars1 and ,jupiter revolve about their own ,axis1 from ,west to ,east2 and this is called their ,diurnal ,motion4 ,for by this rotation1 each point of their surfaces is carried successively towards or from the ,sun1 who always illuminates the hemisphere which is next to him1 the other remaining obscure2 and while any place is in the hemisphere1 illuminated by the ,sun1 it is ,day1 but when it is carried to the obscure hemisphere1 it becomes ,night2 and so continues1 until by this rotation the said place is again enlightened by the ,sun4 ,sidenote3 ,diurnal ,motion of the 1 1 and 4 ,sidenote3 and likewise turn round their ,axis4 ,the ,earth performs its revolution round its axis in #bc ,hours1 #ef ,minutes2#b,venus1 in #bd ,days1 #h ,hours2 ,mars1 in #bd ,hours1 and #dj ,minutes2 and ,jupiter moves round his own axis in #i ,hours1 and #ef ,minutes4 ,the ,sun also is found to turn round his axis from ,west to ,east1 in #bg ,days3 ,and the ,moon1 which is nearest to us of all the ,planets1 revolves about her axis in a ,month1 or in the same space of time that she turns round the ,earth2 so that the ,lunarians have but #a ,day throughout the ,year4 ,sidenote3 ,the ,planets are ,opaque and ,globular4 ,i4 ,the ,planets are all ,opaque bodies1 having no light but what they borrow from the ,sun2 for that side of them which is next towards the ,sun1 has always been observed to be illuminated1 in what position soever they be2 but the opposite side1 which the ,solar rays do not reach1 remains dark and obscure2 whence it is evident that they have no light but what proceeds from the ,sun2 for if they had1 all parts of them would be lucid1 without any darkness or shadow4 ,the ,planets are likewise proved to be ,globular2 because let what part soever of them be turned towards the ,sun1 its boundary1 or the line separating that part from the opposite1 always appears to be circular2 which could not happen1 if they were not globular4 ,sidenote3 ,the ,planets turn round the ,sun4 ,,ii4 ,that the ,earth is placed betwixt the ,orbs of ,mars and ,venus1 and that 1 1 1 and 1 do all turn round the ,sun1 is proved from observations as follow3 ,sidenote3 ,plate #b4 ,fig4 #a4 #b4 #a4 ,whenever ,venus is in conjunction with the ,sun1 that is1 when she is in the same direction from the ,earth1 or towards the same part of the ,heavens the ,sun is in2 she either appears with a bright and round face1 like a ,full ,moon1 or else disappears3 ,or1 if she is visible1 she appears horned1 like a new ,moon2 which phnomena could never happen if did not turn round the ,sun1 and was not betwixt him and the ,earth3 ,for since all the ,planets borrow their light from the ,sun1 it is necessary that 's lucid face should be towards the ,sun2 and when she appears fully illuminated1 she shews the same face to the ,sun and ,earth2 and at that time she must be above or beyond the ,sun2 for in no other position could her illuminated face be seen from the ,earth4 ,farther1 when she disappears1 or if visible1 appears horned2 that face of her's which is towards the ,sun is either wholly turned from the ,earth1 or only a small part of it can be seen by the ,earth2 and in this case she must of necessity be betwixt us and the ,sun4 ,let ,s be the ,sun1 ,t the ,earth1 and ,v ,venus1 having the same face presented both towards the ,sun and ,earth2 here it is plain that the ,sun is betwixt us and ,venus and therefore we must either place ,venus in an ,orbit round the ,sun1 and likewise betwixt him and us1 as in ,fig4 #a4 or else we must make the ,sun to move round the ,earth in an ,orbit within that of ,venus1 as in ,fig4 #b4 ,again1 after ,venus disappears1 or becomes horned1 at her#c with the 1 she then must be betwixt us and the ,sun1 and must move either in an ,orbit round the ,sun and betwixt us and him1 as in ,fig4 #a4 or else round the ,earth1 and betwixt us and the ,sun1 as in ,fig4 #b4 ,but ,venus cannot move sometimes within the ,sun's ,orbit1 and sometimes without it1 as we must suppose if she moves round the ,earth2 therefore it is plain that her motion is round the ,sun4 ,sidenote3 ,why ,venus is always either our ,morning or ,evening ,star4 ,besides the forgoing1 there is another argument to prove that ,venus turns round the ,sun in an ,orbit that is within the ,earth's1 because she is always observed to keep near the ,sun1 and in the same quarter of the ,heavens that he is in1 never receding from him more than about of a whole circle2 and therefore she can never come in opposition to him2 which would necessarily happen1 did she perform her course round the ,earth either in a longer or shorter time than a ,year4 ,and this is the reason why ,venus is never to be seen near midnight1 but always either in the ,morning or ,evening1 and at most not above three or four ,hours before ,sun-rising or after ,sun-setting4 ,from the time of 's superior conjunction 7or when she is above the ,sun7 she is more ,easterly than the ,sun1 and therefore sets later1 and is seen after ,sun-setting2 and then she is commonly called the ,evening ,star4 ,but from the time of her inferior conjunction1 'till she comes again to the superior1 she then appears more ,westerly than the ,sun1 and is only to be seen in the morning before ,sun-rising1 and is then called the ,morning ,star4 ,after the same manner we prove that ,mercury turns round the ,sun1 for he always keeps in the ,sun's neighbourhood1 and never recedes from him so far as ,venus does2 and therefore the ,orbit of must lie within that of 2 and on the account of his nearness to the ,sun1 he can seldom be seen without a ,telescope4 ,sidenote3 ,the ,orbit of ,mars includes the ,earth's4 ,sidenote3 ,fig4 #c4 ,mars is observed to come in opposition1 and likewise to have all other aspects with the ,sun2 he always preserves a round1 full1 and bright face1 except when he is near his quadrate aspect1 when he appears somewhat gibbous1 like the ,moon three or four ,days before or after the full3 ,therefore the ,orbit of must include the ,earth within it1 and also the ,sun2 for if he was betwixt the ,sun and us at the time of his inferior conjunction1 he would either quite disappear1 or appear horned1 as ,venus and the ,moon do in that position4 ,let ,s be the ,sun1 ,t the ,earth1 and ,a ,p ,mars1 both in his conjunction and opposition to the ,sun1 and in both positions full2 and ,b ,c ,mars at his quadratures1 when he appears somewhat gibbous from the ,earth at ,t4 ',tis plain hence1 that the ,orbit of ,mars does include the ,earth1 otherwise he could not come in opposition to the ,sun2 and that it likewise includes the ,sun1 else he could appear full at his conjunction4 ,mars when he is in opposition to the ,sun1 looks almost seven times larger in diameter than when he is in conjunction with him1 and therefore must needs be almost seven times nearer to us in one position than in the other2 for the apparent magnitudes of far distant objects increase or decrease in proportion to their distances from us3 ,but ,mars keeps always nearly at the same distance from the ,sun2 therefore it is plain that it is not the ,earth1 but the ,sun1 that is the center of his motion4 ,it is proved in the same way1 that ,jupiter and ,saturn have both the ,sun and the ,earth within their ,orbits1 and that the ,sun1 and not the ,earth1 is the center of their motions2 altho' the disproportion of the distances from the ,earth is not so great in ,jupiter1 as it is in ,mars1 nor so great in ,saturn1 as it is in ,jupiter1 by reason that they are at a much greater distance from the ,sun4 ,sidenote3 ,inferior and ,superior ,planets4 ,we have now shewn that all the ,planets turn round the ,sun1 and that ,mercury and ,venus are included between him and the ,earth1 whence they are called the ,inferior ,planets1 and that the ,earth is placed between the ,orbits of ,mars and ,venus1 and therefore included within the ,orbits of ,mars1 ,jupiter1 and ,saturn1 whence they are called the ,superior ,planets3 ,and since the ,earth is in the middle of these moveable bodies1 and is of the same nature with them1 we may conclude that she has the same sort of motions2 but that she turns round the ,sun is proved thus3 ,sidenote3 ,the ,earth does not stand still1 but turns round the ,sun4 ,sidenote3 ,fig4 #d4 ,all the ,planets seen from the ,earth appear to move very unequally1 as sometimes to go faster1 at other times slower2 sometimes to go backwards1 and sometimes to be stationary1 or not to move at all2 which could not happen if the ,earth stood still4 ,let ,s be the ,sun1 ,t the ,earth1 the great circle ,a ,b ,c ,d the ,orbit of ,mars1 and the numbers #a1 #b1 #c1 c4 its equable motion round the ,sun2 the correspondent numbers #a1 #b1 #c1 c4 in the circle a1 b1 c1 d1 the motion of ,mars1 as it would be seen from the ,earth4 ,it is plain from this ,figure1 that if the ,earth stood still1 the motion of ,mars1 will be always progressive1 7tho' sometimes very unequal27 but since observations prove the contrary1 it necessarily follows1 that the ,earth turns round the ,sun4 ,sidenote3 ,the ,annual and ,diurnal ,motions of the ,planets1 how computed4 ,the annual periods of the ,planets round the ,sun are determined by carefully observing the length of time since their departure from a certain point in the ,heavens1 7or from a fix'd ,star7 until they arrive to the same again4 ,by these sort of observations the ancients determined the periodical revolutions of the ,planets round the ,sun1 and were so exact in their computations1 as to be capable of predicting ,eclipses of the ,sun and ,moon4 ,but since the invention of telescopes1 astronomical observations are made with greater accuracy2 and of consequence1 our tables are far more perfect than those of the ancients4 ,and in order to be as exact as possible1 astronomers compare observations made at a great distance of time from one another1 including several periods2 by which means1 the error that might be in the whole1 is in each period subdivided into such little parts as to be inconsiderable4 ,thus the mean length of a ,solar ,year is known1 even to ,seconds4 ,the ,diurnal rotation of the ,planets round their axis1 was discovered by certain spots which appear on the surfaces4 ,these spots appear first in the margin of the ,planet's disk1 7or the edge of their surfaces7 and seem by degrees to creep toward their middle1 and so on1 going still forward1 'till they come to the opposite side or edge of the disk1 where they set or disappear2 and after they have been hid for the same space of time1 that they were visible1 they again appear to rise in or near the same place1 as they did at first1 then to creep on progressively1 taking the same course as they did before4 ,these spots have been observed on the surfaces of the ,sun1 ,venus1 ,mars1 and ,jupiter2 by which means it has been found that these bodies turn round their own axis1 in the times before-mentioned4 ,it is very probable that ,mercury and ,saturn have likewise a motion round their axis1 that all the parts of their surface may alternately enjoy the light and heat of the ,sun1 and receive such changes as are proper and convenient for their nature4 ,but by reason of the nearness of to the ,sun1 and 's immense distance from him1 no observations have hitherto been made whereby their spots 7if they have any7 could be discovered1 and therefore their ,diurnal motions could not be determined4 ,the ,diurnal motion of the ,earth is computed from the apparent revolution of the ,heavens1 and of all the ,stars round it1 in the space of a natural ,day4 ,the ,solar spots do not always remain the same1 but sometimes old ones vanish1 and afterwards others succeed in their room2 sometimes several small ones gather together and make one large spot1 and sometimes a large spot is seen to be divided into many small ones4 ,but1 notwithstanding these changes1 they all turn round with the ,sun in the same time4 ,sidenote3 ,how the relative distances of the ,planets from the ,sun are determined4 ,the relative distances of the ,planets from the ,sun1 and likewise from each other1 are determined by the following methods3 ,first1 the distance of the two inferior ,planets and from the ,sun1 in respect of the ,earth's distance from him1 is had by observing their greatest ,elongation from the ,sun as they are seen from the ,earth4 ,sidenote3 ,fig4 #e4 ,elongation4 ,the greatest ,elongation of ,venus is found by observation to be about #dh degrees1 which is the angle ,s ,t 2 whence1 by the known rules of ,trigonometry1 the proportion of ,s 1 the mean distance of ,venus from the ,sun to ,,st1 the mean distance of the ,earth from him may be easily found4 ,after the same manner1 in the right-angled triangle ,s ,t 1 may be found the distance ,s of ,mercury from the ,sun4 ,and if the mean distance of the ,earth from the ,sun ,s ,t be made #ajjj1 the mean distance of ,venus ,s from the ,sun will be #gbc2 and of ,mercury ,s #chg3 ,and if the ,planets moved round the ,sun in circles1 having him for their center1 the distances here found would be always their true distances3 ,but as they move in ,ellipses1 their distances from the ,sun will be sometimes greater1 and sometimes less4 ,their ,excentricities are computed to be as follows1 viz4 ,mercury #hj of the parts ,excent4 of ,venus #e above-mentioned4 ,earth #afi ,sidenote3 ,heliocentric and ,geocentric ,place1 what4 ,the distances of the superior ,planets1 viz4 1 1 and 1 are found by comparing their true places1 as they are seen from the ,sun1 with their apparent places1 as they are seen from the ,earth4 ,let ,s be the ,sun1 the circle ,,abc the ,earth's orbit1 ,,ag a line touching the ,earth's orbit1 in which we'll suppose the superior ,planets are seen from the ,earth in the points of their orbits 1 1 2 and let ,,defgh be a portion of a great circle in the ,heavens1 at an infinite distance3 ,then the place of ,mars seen from the ,sun is ,d1 which is called his true1 or ,heliocentric ,place2 but from the ,earth1 he will be seen in ,g1 which is called his apparent1 or ,geocentric ,place4 ,so likewise ,jupiter and ,saturn will be seen from the ,sun in the points ,e and ,f1 their ,heliocentric places2 but a spectator from the ,earth will see them in the point of the ,heavens ,g1 which is their ,geocentric place4 ,the arches ,,dg1 ,,eg1 ,,fg1 the differences between the true and apparent places of the ,superior ,planets1 are called the ,parallaxes of the ,earth's annual ,orb1 as seen from these ,planets4 ,if thro' the ,sun we draw ,,sh parallel to ,,ag1 the angles ,a ,s1 ,a ,s1 ,a ,s1 will be respectively equal to the angles ,d ,s ,h1 ,e ,s ,h1 and ,f ,s ,h2 and the angle ,a ,g ,s is equal to the angle ,,gsh1 whose measure is the arch ,,gh2 which therefore will be the measure of the angle ,,ags1 the angle under which the semidiameter ,a ,s of the ,earth's orbit1 is seen from the ,starry ,heavens4 ,but this semidiameter is nothing in respect of the immense distance of the ,heavens or ,fixed ,stars2 for from thence it would appear under no sensible angle1 but look like a point4 ,and therefore in the ,heavens1 the angle ,g ,s ,h1 or the arch ,g ,h vanishes2 and the ,points ,g and ,h coincide2 and the arches ,d ,h1 ,e ,h1 ,f ,h1 may be considered as being of the same bigness with the arches ,d ,g1 ,e ,g1 and ,f ,g1 which are the measures of the angles ,a ,s1 ,a ,s1 ,a ,s2 which angles are nearly the greatest elongation of the ,earth from the ,sun1 if the ,earth be observed from the respective ,planets1 when the line ,g ,a1 touches the ,earth's orbit in ,a4 ,the nearer any of the superior ,planets is to the ,sun1 the greater is the ,parallax of the annual ,orb1 or the angle under which the semidiameter of the ,earth's orbit is seen from that ,planet4 ,in ,mars the angle ,s1 7which is the visible elongation of the ,earth seen from ,mars1 or the ,parallax of the annual ,orb seen from that ,planet7 is about #db degrees1 and therefore the ,earth is always to the inhabitants of ,mars either their ,morning or ,evening ,star1 and is never seen by them so far distant from the ,sun as we see ,venus4 ,the greatest elongation of the ,earth seen from ,jupiter1 being nearly equal to the angle ,a ,s1 is about #aa degrees4 ,in ,saturn the angle ,a ,s is but #f degrees1 which is not much above part of the greatest elongation we observe in ,mercury4 ,and since ,mercury is so rarely seen by us1 probably the astronomers of ,saturn 7except they have better ,optics than we have7 have not yet discovered that there is such a body as our ,earth in the ,universe4 ,the ,parallax of the annual ,orb1 or the greatest elongation of the ,earth's orbit seen from any of the superior ,planets1 being given2 the distance of that ,planet from the ,sun1 in respect of the ,earth's distance from him1 may be found by the same methods as the distances of the inferior ,planets were4 ,thus1 to find the distance of ,mars from the ,sun1 it will be as the ,sine of the angle ,s ,a is to the ,radius1 so is the distance ,,as 7the distance of the ,earth from the ,sun7 to ,s 1 the distance from the ,sun to ,mars4 ,after the same manner the distances of ,jupiter and ,saturn are also found4 ,the mean distance of the ,earth from the ,sun being made #ajjj1 the mean distances of the superior ,planets from the ,sun are1 viz4 the mean distance from the ,sun of #aebd #ada #ebja and the ,excentricity #bej #iech #edg ,to which1 if you add or subtract their mean distances1 we shall have the greatest or least distances of those ,planets from the ,sun4 ,there are other methods by which the relative distances of the ,planets might be found2 but that which hath been here illustrated1 is sufficient to evince the certainty of that ,problem4 ,sidenote3 ,how the absolute distances of the ,planets from the ,sun are computed4 ,sidenote3 ,parallax of the ,earth's ,semidiameter4 ,sidenote3 ,fig4 #g4 ,hitherto we have only considered the distances of the ,planets in relation to one another1 without determining them by any known measure2 but in order to find their absolute distances in some determinate measure1 there must be something given1 whose measure is known4 ,now the circumference of the ,earth is divided into #cfj degrees1 and each of these degrees into #fj ,geographical miles1 so that the whole circumference contains #bafjj2 and by the known proportion for finding the diameter of a circle from its circumference1 the ,earth's diameter will be found to be #fhgb miles1 and its semidiameter #cdcf miles4 ,the ,parallax of the ,earth's semidiameter1 or the angle under which it is seen from a certain ,planet1 may be found by comparing the true place of the ,planet1 as it would be seen from the center of the ,earth 7which is known by computation7 with its apparent place1 as it is seen from some point on the ,earth's surface4 ,let ,,cza be the ,earth1 ,,zc its semidiameter1 some ,planet1 and ,,bht arch of a great circle in the ,heavens1 at an infinite distance4 ,now the ,planet will appear from the ,earth's center ,c1 in the point of the ,heavens ,h2 but a spectator from the point ,z upon the ,earth's surface1 will see the same object in the point of the ,heavens ,b2 and the arch ,,bh the difference1 is equal to the angle ,b ,h ,z ,c1 the ,parallax2 which being known1 the side ,c the distance of the ,planet from the center of the ,earth1 at that time1 may be easily found4 ,now if this distance of the ,planet from the ,earth be determined1 when the centers of the ,sun1 the said ,planet1 and of the ,earth1 are in the same right line1 we have the absolute distance of the ,planet's orbit from the ,earth's in known measure2 then it will be1 as the relative distance betwixt the ,earth's orbit and that of the ,planet is to the relative distance of the said ,planet from the ,sun2 so is the distance of the ,planet's orbit from the ,earth's in known measure to the distance of the said ,planet from the ,sun in the same measure3 ,which being known1 the distance of all the other ,planets from the ,sun may be found4 ,for it will be1 as the relative distance of any ,planet from the ,sun1 is to its distance from him in a known measure2 so is the relative distance of any other ,planet from him to its distance in the same measure4 ,this may be done by finding the distance of the ,planet ,mars1 when he is in opposition to the ,sun1 after the same manner as we find the distance of a tree1 or the like1 by two stations4 ,let be ,mars1 ,d the point on the ,earth's superficies1 where ,mars is vertical when he is in opposition to the ,sun1 which may be found exactly enough by calculation1 at which time let an observer1 at the point ,z 7whose situation from ,d must be known7 take the altitude of ,mars1 whose complement will be the angle ,,zr2 then in the triangle ,,zc will be given the angle ,z ,c1 the angle ,c 7whose measure is the arch ,,dz7 and consequently the angle ,z ,c the ,parallax1 and also the side ,z ,c the semidiameter of the ,earth2 by which we may find ,c the distance of ,mars from the ,earth4 ,the extreme nicety required in this observation1 makes it very difficult to determine the exact distances of the ,planets from the ,sun2 but the celebrated ,dr4 ,halley has1 in the ,philosophical ,transactions1 shewed us a more certain method for finding the distances of the ,planets2 which is by observing the ,transit of ,venus over the ,sun4 ,sidenote3 ,how the ,magnitudes of the ,planets are determined4 ,sidenote3 ,fig4 #h4 ,the eye judgeth of the magnitudes of far distant objects1 according to the quantities of the angles under which they are seen 7which are called their apparent magnitudes27 and these angles appear greater or less in a certain proportion to their distances4 ,wherefore the distances of the ,planets from the ,earth1 and their apparent diameters being given1 their true diameters 7and from thence their magnitudes7 may be found4 ,how the distances of the ,planets may be found has been already shewn2 their apparent diameters are found by a telescope1 having a machine fix'd to it for measuring of angles1 called a ,micrometer4 ,let ,,bd1 or the angle ,,bad be the apparent diameter of any ,planet1 and ,,ab1 or ,,ad1 7which by reason of the great distance of the ,planets in respect of their magnitudes7 may be considered as being the distance of the said ,planet from the observer4 ,now in the triangle ,,abd1 having the sides ,,ab1 ,,ad1 given1 and the angle1 ,a1 we have also the other angles ,b and ,d1 7because the ,side ,,ab1 ,,ad1 are equal7 whence the side ,,bd the diameter of the ,planet may be easily found by ,trigonometry4 ,sidenote3 ,why the ,moon appears bigger than any of the ,planets4 ,from hence it appears1 that the same body at different distances1 will seem to have very different magnitudes4 ,thus the diameter ,,bd will appear from the point ,e1 to be twice as large as from the point ,a4 ,it also follows1 that a small body1 when at no great distance from us1 may appear to be equal1 or even to exceed another at a great distance1 tho' immensely bigger4 ,thus b d appears under the same angle1 and consequently of the same bigness from the point ,a1 that the line ,b ,d doth1 tho' one vastly exceeds the other4 ,and this is the reason1 why the ,moon1 which is much less than any of the ,planets1 appears to us vastly bigger than either of them1 and even to equal the ,sun himself1 which is many thousand times greater in magnitude4 ,the distances of the ,planets1 and periods round the ,sun1 their diameters and velocities round their own axis1 according to modern computations1 are as follows3 ,revolves about the ,distance in ,sun in the space of ,miles ,y4 ,d4 ,h ,saturn #bi3afg3bb #ggg4jjj4jjj ,jupiter #aa3cad3ab #dbd4jjj4jjj ,mars #a3cba3bc #abc4jjj4jjj ,earth #j3cfe3 #f #ha4jjj4jjj ,venus #j3bbd3af #ei4jfj4jjj ,mercury #j3 #hg3bc #cb4jjj4jjj ,moon ,round the ,d4 ,h4 ,m4 ,earth4 #bg3 #g3 #dc #bdj4jjj ,periods round ,diameters their own axis4 in ,miles4 ,d4 ,h4 ,m4 ,sun #be3 #f3 #j #gfc4jjj ,saturn #fa4jjj ,jupiter #j3 #i3 #ef #ha4jjj ,mars #a3 #j3 #dj #d4ddj ,earth #j3 #bc3 #ef #g4igj ,venus #bd3 #h3 #j #g4ijj ,mercury #d4bdj ,moon #bg3 #g3 #dc #b4agj ,the cause of ,eclipses and ,phases of the ,moon1 and some other phnomena not here explained1 shall be shewed when we come to give a ,description of the ,orrery4 ,illustration3 ,plate #b4 ,besides the ,planets already mentioned1 there are other great bodies that sometimes visit our system1 which are a sort of temporary ,planets2 for they come and abide with us for a while1 and afterwards withdraw from us1 for a certain space of time1 after which they again return4 ,these wandering bodies are called ,comets4 ,sidenote3 ,of ,comets4 ,the motion of ,comets in the ,heavens1 according to the best observations hitherto made1 seem to be regulated by the same immutable law that rules the ,planets2 for their orbits are elliptical1 like those of the ,planets1 but vastly narrower1 or more excentric4 ,yet they have not all the same direction with the ,planets1 who move from ,west to ,east1 for some of the ,comets move from ,east to ,west2 and their orbits have different inclinations to the ,earth's orbit2 some inclining ,northwardly1 others ,southwardly1 much more than any of the ,planetary orbits do4 ,altho' both the ,comets and the ,planets move in elliptic orbits1 yet their motions seem to be vastly different3 ,for the excentricities of the ,planet's orbits are so small1 that they differ but little from circles2 but the excentricities of the ,comets are so very great1 that the motions of some of them seem to be almost in right lines1 tending directly towards the ,sun4 ,now1 since the orbits of the ,comets are so extremely excentric1 their motions1 when they are in their ,perihelia1 or nearest distance from the sun1 must be much swifter than when they are in their ,aphelia1 or farthest distance from him2 which is the reason why the ,comets make so short a stay in our system2 and when they disappear1 are so long in returning4 ,the figures of the ,comets are observed to be very different2 some of them send forth small beams1 like hair1 every way round them2 others are seen with a long fiery tail1 which is always opposite to the ,sun4 ,their magnitudes are also very different1 but in what proportion they exceed each other1 it is as yet uncertain4 ,nor is it probable1 that their numbers are yet known1 for they have not been observed with due care1 nor their theories discovered1 but of late years4 ,the ancients were divided in their opinions concerning them2 some imagined that they were only a kind of ,meteors kindled in our atmosphere1 and were there again dissipated2 others took them to be some ominous prodigies3 ,but modern discoveries prove1 that they are ,worlds subject to the same laws of motion as the ,planets are2 and they must be very hard and durable bodies1 else they could not bear the vast heat that some of them1 when they are in their ,perihelia1 receive from the ,sun1 without being utterly consumed4 ,the great ,comet which appeared in the year #afhj1 was within _/ part of the ,sun's diameter from his surface2 and therefore its heat must be prodigiously intense beyond imagination4 ,and when it is at its greatest distance from the ,sun1 the cold must be as rigid4 ,illustration ,,sect4 ,,ii4 ,of the ,,fixed ,,stars4 ,sidenote3 ,the fixed ,stars are at immense distance from us4 ,the fixed ,stars are those bright and shining bodies1 which in a clear night appear to us every where dispersed through the boundless regions of space4 ,they are term'd fix'd1 because they are found to keep the same immutable distance one from another in all ages1 without having any of the motions observed in the ,planets4 ,the fixed ,stars are all placed at such immense distances from us1 that the best of telescopes represent them no bigger than points1 without having any apparent diameters4 ,sidenote3 ,the fixed ,stars are luminous bodies like the ,sun4 ,it is evident from hence1 that all the ,stars are luminous bodies1 and shine with their own proper and native light1 else they could not be seen at such a great distance4 ,for the ,satellites of ,jupiter and ,saturn1 tho' they appear under considerable angles through good telescopes1 yet are altogether invisible to the naked eye4 ,sidenote3 ,the distance from us to the ,sun is nothing in comparison of the vast distance of the fixed ,stars4 ,although the distance betwixt us and the ,sun is vastly large1 when compared to the diameter of the ,earth1 yet it is nothing when compared with the prodigious distance of the fixed ,stars2 for the whole diameter of the ,earth's annual orbit1 appears from the nearest fixed ,star no bigger than a point1 and the fixed ,stars are at least #ajj1jjj times farther from us than we are from the ,sun2 as may be demonstrated from the observation of those who have endeavoured to find the ,parallax of the ,earth's annual ,orb1 or the angle under which the ,earth's orbit appears from the fixed ,stars4 ,sidenote3 ,as to appearance1 the ,earth may be consider'd as being the center of the ,heavens4 ,hence it follows1 that tho' we approach nearer to some fixed ,stars at one time of the year than we do at the opposite1 and that by the whole length of the diameter of the ,earth's orbit2 yet this distance being so small in comparison with the distance of the fixed ,stars1 their magnitudes or positions cannot thereby be sensibly altered2 therefore we may always1 without error1 suppose ourselves to be in the same center of the ,heavens1 since we always have the same visible prospect of the ,stars without any alteration4 ,sidenote3 ,the fixed ,stars are ,suns4 ,if a spectator was placed as near to any fixed ,star1 as we are to the ,sun1 he would there observe a body as big1 and every way like1 as the ,sun appears to us3 and our ,sun would appear to him no bigger than a fixed ,star3 and undoubtedly he would reckon the ,sun as one of them in numbering the ,stars4 ,wherefore since the ,sun differeth nothing from a fixed ,star1 the fixed ,stars may be reckoned so many ,suns4 ,sidenote3 ,the fixed ,stars are at vast distance from each other4 ,it is not reasonable to suppose that all the fixed ,stars are placed at the same distance from us2 but it is more probable that they are every where interspersed thro' the vast indefinite space of the universe2 and that there may be as great a distance betwixt any two of them1 as there is betwixt our ,sun and the nearest fixed ,star4 ,hence it follows1 why they appear to us of different magnitudes1 not because they really are so1 but because they are at different distances from us2 those that are nearest excelling in brightness and lustre those that are most remote1 who give a fainter light1 and appear smaller to the eye4 ,illustration3 ,,new and ,,correct ,,globes according to the latest ,observations ,made and ,sold by ,,richard ,,cushee at the ,globe and ,sun between ,st4 ,dunstans ,church ,chancery ,lane and ,tho3,wright ,instrument-maker to ,his ,majesty at the ,orrery and ,globe near ,salisbury ,court ,,fleet ,,street ,,london ,,estates ,survey'd ,,also ,,maps ,,drawn and ,,engrav',d ,sidenote3 ,the distribution of the ,stars into #f classes4 ,sidenote3 ,of ,telescopical ,stars4 ,the astronomers distribute the ,stars into several orders or classes2 those that are nearest to us1 and appear brightest to the eye1 are called ,stars of the first magnitude2 those that are nearest to them in brightness and lustre1 are called ,stars of the second magnitude2 those of the third class1 are stiled ,stars of the third magnitude2 and so on1 until we come to the ,stars of the sixth magnitude1 which are the smallest that can be discerned by the naked eye4 ,there are infinite numbers of smaller ,stars1 that can be seen through telescopes2 but these are not reduced to any of the six orders1 and are only called ,telescopical ,stars4 ,it may be here observed1 that tho' the astronomers have reduced all the ,stars that are visible to the naked eye1 into some one or other of these classes1 yet we are not to conclude from thence that all the ,stars answer exactly to some or other of these orders2 but there may be in reality as many orders of the ,stars1 as they are in number1 few of them appearing exactly of the same bigness and lustre4 ,sidenote3 ,the ,stars digested into constellations ,the ancient astronomers1 that they might distinguish the ,stars1 in regard to their situation and position to each other1 divided the whole starry firmament into ,several ,asterisms1 or systems of ,stars1 consisting of those that are near to one another4 ,these ,asterisms are called ,constellations1 and are digested into the forms of some animals2 as ,men1 ,lyons1 ,bears1 ,serpents1 c4 or to the images of some known things2 as1 of a ,crown1 a ,harp1 a ,triangle1 c4 ,sidenote3 ,zodiac4 ,the starry firmament was divided by the ancients into #dh images1 or constellations2 twelve of which they placed in that part of the ,heavens wherein are the planes of the ,planetary orbits2 which part is called the ,zodiac1 because most of the constellations placed therein resemble some living creature4 ,the two regions of the ,heavens that are on each side of the ,zodiac1 are called the ,north and ,south parts of the ,heavens4 ,sidenote3 ,constellations within the ,zodiac4 ,the constellations within the ,zodiac are1 #a4 ,aries1 the ,ram2 #b4 ,taurus1 the ,bull2 #c4 ,gemini1 the ,twins2 #d4 ,cancer1 the ,crab2 #e4 ,leo1 the ,lion2 #f4 ,virgo1 the ,virgin2 #g4 ,libra1 the ,balance2 #h4 ,scorpio1 the ,scorpion2 #i4 ,sagittarius1 the ,archer2 #aj4 ,capricornus1 the ,goat2 #aa4 ,aquarius1 the ,water-,bearer2 and1 #ab4 ,pisces1 the ,fishes4 ,sidenote3 ,northern constellations4 ,the constellations on the ,north side of the ,zodiac are ,twenty-one1 viz4 the ,little ,bear2 the ,great ,bear2 the ,dragon2 ,cepheus1 a king of ,ethiopia2 ,bootes1 the keeper of the ,bear2 the ,northern ,crown2 ,hercules with his ,club1 watching the ,dragon2 the ,harp2 the ,swan2 ,cassiopeia2 ,persius2 ,andromeda2 the ,triangle2 ,auriga2 ,pegasus1 or the ,flying ,horse2 ,equuleus2 the ,dolphin2 the ,arrow2 the ,eagle2 ,serpentarius2 and the ,serpent4 ,sidenote3 ,southern constellations4 ,the constellations noted by the ancients on the ,south side of the ,zodiac1 were fifteen1 viz4 the ,whale2 the river ,eridanus2 the ,hare2 ,orion2 the ,great ,dog2 ,little ,dog2 the ,ship ,argo2 ,hydra2 the ,centaur2 the ,cup2 the ,crow2 the ,wolf2 the ,altar2 the ,southern ,crown2 and the ,southern ,fish4 ,to these have been lately added the following1 viz4 ,the ,phnix2 the ,crane2 the ,peacock2 the ,indian2 the ,bird of ,paradise2 the ,southern ,triangle2 the ,fly2 ,cameleon2 the ,flying ,fish2 ,toucan1 or the ,american ,goose2 the ,water ,serpent1 and the ,sword ,fish4 ,the ancients placed those particular constellations or figures in the ,heavens1 either to commemorate the deeds of some great man1 or some notable exploit or action2 or else took them from the fables of their religion1 c4 ,and the modern astronomers do still retain them1 to avoid the confusion that would arise by making new ones1 when they compare the modern observations with the old ones4 ,sidenote3 ,unformed ,stars4 ,some of the principal ,stars have particular names given them1 as ,syrius1 ,arcturus1 c4 ,there are also several ,stars that are not reduced into constellations1 and these are called ,unformed ,stars4 ,sidenote3 ,the ,galaxy1 or ,milky ,way4 ,besides the ,stars visible to the naked eye1 there is a very remarkable space in the ,heavens1 called the ,galaxy1 or ,milky ,way4 ,this is a broad circle of a whitish hue1 like milk1 going quite round the whole ,heavens1 and consisting of an infinite number of small ,stars1 visible thro' a telescope1 tho' not discernable by the naked eye1 by reason of their exceeding faintness2 yet with their light they combine to illustrate that part of the ,heavens where they are1 and to cause that shining whiteness4 ,the places of the fixed ,stars1 or their relative situations one from another1 have been carefully observed by astronomers1 and digested into catalogues4 ,the first among the ,greeks1 who reduced the ,stars into a catalogue1 was ,hypparchus1 who1 from his own observations1 and of those who lived before him1 inserted #ajbb ,stars into his catalogue1 about #abj years before the ,christian ra3 ,this catalogue has been since enlarged and improved by several learned men1 to the number of #cjjj1 of which there are a great many telescopical1 and not to be discerned by the naked eye2 and these are all ranked in the catalogue as the ,stars of the seventh magnitude4 ,it may seem strange to some1 that there are no more than this number of ,stars visible to the naked eye2 for sometimes in a clear night they seem to be innumerable3 but this is only a deception of our sight1 arising from their vehement sparkling1 while we look upon them confusedly1 without reducing them into any order2 for there can seldom be seen above #ajjj ,stars in the whole ,heavens with the naked eye at the same time2 and if we should distinctly view them1 we shall not find many but what are inserted upon a good ,celestial ,globe4 ,altho' the number of ,stars that can be discerned by the naked eye are so few1 yet it is probable there are many more which are beyond the reach of our optics1 for through telescopes they appear in vast multitudes1 every where dispersed throughout the whole ,heaven2 and the better our glasses are1 the more of them we still discover4 ,the ingenious ,dr4 ,hook has observed #gh ,stars in the ,pleiades1 of which the naked eye is never able to discern above #g2 and in ,orion1 which has but #hj ,stars in the ,british catalogue 7and some of them telescopical7 there has been numbered #bjjj ,stars4 ,sidenote3 ,an idea of the ,universe4 ,those who think that all these glorious bodies were created for no other purpose than to give us a little dim light1 must entertain a very slender idea of the ,divine ,wisdom2 for we receive more light from the ,moon itself1 than from all the ,stars put together4 ,and since the ,planets are subject to the same laws of motion with our ,earth1 and some of them not only equal1 but vastly exceed it in magnitude1 it is not unreasonable to suppose1 that they are all habitable ,worlds4 ,and since the ,fixed ,stars are no ways behind our ,sun1 either in bigness or lustre1 is it not probable1 that each of them have a system of ,planetary ,worlds turning round them1 as we do round our ,sun8 ,and if we ascend as far as the smallest ,star we can see1 shall we not then discover innumerable more of these glorious bodies1 which now are altogether invisible to us8 ,and so ad infinitum1 thro' the boundless space of the universe4 ,what a magnificient idea must this raise in us of the ,divine ,being6 ,who is every where1 and at all times present1 displaying his ,divine ,power1 ,wisdom and ,goodness1 amongst all his ,creatures6 ,illustration ,the ,,description and ,,use of the ,,celestial and ,,terrestrial ,,globes4 ,sidenote3 ,globe or ,sphere4 ,a ,globe or ,sphere is a round solid body1 having every part of its surface equally distant from a point within it1 called its ,center2 and it may be conceived to be formed by the revolution of a semicircle round its diameter4 ,sidenote3 ,great ,circle4 ,sidenote3 ,hemispheres4 ,any circle passing through the center of the sphere1 thereby dividing into two equal parts or segments1 is called a ,great ,circle2 and the segments of the sphere so divided1 are called ,hemispheres4 ,every great circle has its ,poles and ,axis4 ,sidenote3 ,poles4 ,the ,poles of a great circle are two points on the surface of the sphere1 diametrically opposite to one another1 and every where equally distant from the said circle4 ,sidenote3 ,axis4 ,the ,axis of a circle is a right line passing through the center of the sphere1 and through the ,poles of the said circle1 and is therefore perpendicular to the ,plane3 ,therefore ,sidenote3 ,secundaries4 ,all circles passing through the ,poles of any great circle1 intersect it in two places diametrically opposite1 and also at right angles2 and with respect to the said great circle1 they may be called its ,secundaries4 ,sidenote3 ,parallel or lesser ,circles4 ,all circles dividing the sphere into two unequal parts1 are called lesser or parallel ,circles1 and are usually denominated by that great circle to which they are parallel4 ,sidenote3 ,terrestrial ,globe4 ,the ,earth being globular1 its outward parts1 as the several ,countries1 ,seas1 c4 are best1 and most naturally represented upon the surfaces of a ,globe2 and when such a body has the outward parts of the ,earth and ,sea delineated upon its surface1 and placed in their natural order and situation1 it is called a ,terrestrial ,globe4 ,sidenote3 ,celestial ,globe4 ,the ,celestial ,bodies appear to us as if they were all placed in the same concave sphere1 therefore astronomers place the ,stars according to their respective situations and magnitudes1 and also the images of the constellations1 upon the external surface of a ,globe2 for it answers the same purposes as if they were placed within a concave sphere1 if we suppose the ,globe to be transparent1 and the eye placed in the center4 ,a ,globe having the ,stars placed upon its surface1 as above described1 is called a ,celestial ,globe4 ,these ,globes are both placed in frames1 with other appurtenances1 as shall be described in a proper place4 ,sidenote3 ,the principal use of the ,globes4 ,the principal uses of the ,globes 7besides their serving as ,maps1 to distinguish the outward parts of the ,earth1 and the situations of the fixed ,stars7 is to explain and resolve the phnomena arising from the diurnal motion of the ,earth round its ,axis4 ,sidenote3 ,there will be the same prospect of the fixed ,stars whether the spectator be placed on the ,earth1 or in the ,sun4 ,it has been shewed in the ,introduction1 that the distance of the ,earth from the ,sun1 is no more than a point1 when compared with the immense distance of the fixed ,stars2 therefore let the ,earth be in what point soever of her orbit1 there will be the same prospect of the ,heavens1 as a spectator would observe did he reside in the ,sun3 ,and if several circles be imagined to pass thro' the center of the ,earth1 and others1 parallel to them1 be conceived to pass thro' the center of the ,sun1 these circles in the ,heavens will seem to coincide1 and to pass exactly thro' the same ,stars4 ,wherefore as to the appearances of the fixed ,stars1 it is indifferent whether the ,earth or the ,sun be made the center of the ,universe4 ,but because it is from the ,earth that we always observe the celestial bodies1 and their apparent motions seem to us to be really made in the ,heavens1 it is more natural in explaining the phnomena arising from these motions1 to place the ,earth in the center4 ,and again1 because the semidiameter of the ,earth1 when compared to her distance from the ,sun1 is of no sensible magnitude1 any point1 upon the ,earth's surface1 let her be in what part soever of the orbit1 may be considered as being the center of the ,universe4 ,upon these principles1 the different phnomena arising from the diurnal motion of the ,earth1 and the different situation of a spectator upon its surface1 are very naturally illustrated and explained by the ,globes4 ,as to the alterations of seasons1 c4 arising from the annual motion of the ,earth round the ,sun1 it is indifferent which we suppose to move1 the ,earth or the ,sun1 for in both cases the effect will be the same4 ,wherefore because it is the ,sun that appears to us to move1 we say the ,sun is in such a part of the ecliptic1 without attributing any motion to the ,earth1 any more than if she had actually been at rest4 ,for the same reason we say the ,sun rises1 or the ,sun sets2 by which we mean that he begins to appear or disappear1 without considering in the least how these effects are produced4 ,these things are here mentioned1 to obviate the objections that might be made by beginners1 after they have been told that the ,sun stands still4 ,illustration ,,sect4 ,i4 ,an ,explanation of the ,circles of the ,sphere1 and of some ,astronomical ,terms arising therefrom4 ,sidenote3 ,the ,circles of the ,sphere4 ,in order to determine the relative situations of places upon the ,earth1 as well as the positions of the fixed ,stars1 and other ,celestial phnomena1 the ,globe of the ,earth is supposed to be environed by several imaginary circles1 and these are called the ,circles of the ,sphere4 ,these imaginary circles are either fixed1 and always obtain the same position in the ,heavens1 or moveable1 according to the position of the observer4 ,those circles that are fixed1 owe their origin to the two-fold motion of the ,earth1 and are the ,equator1 and the ,ecliptic1 with their ,secundaries and ,parallels4 ,these fixed circles are usually delineated upon the surface of the ,globes4 ,the moveable circles are only the ,horizon1 its ,secundaries and ,parallels3 ,these are represented by the wooden frame1 and the brass ring1 wherein the ,globe is hung1 and a thin plate of brass to be screwed in a proper place1 upon the said ring1 as occasion requires4 ,i4 ,of the ,equinoctial4 ,sidenote3 ,the ,equator1 or ,equinoctial4 #a4 ,the ,equator1 or the ,equinoctial1 is that great circle in the ,heavens1 in whose plane the ,earth performs her diurnal motion round her axis2 or it is that great circle1 parallel to which the whole ,heavens seem to turn round the ,earth from ,east to ,west in #bd ,hours4 ,note1 ,the ,equator and the ,equinoctial are generally synonymous terms2 but sometimes the ,equator particularly signifies that great circle upon the surface of the ,earth1 which coincides with the ,equinoctial in the ,heavens4 ,this circle is also by ,mariners commonly called the ,line4 ,sidenote3 ,northern and ,southern ,hemispheres4 ,sidenote3 ,the ,axis of the ,world4 ,sidenote3 ,poles of the ,world1 or of the ,equator4 ,the equinoctial divides the globe of the ,earth1 and also the whole ,heavens into two equal parts1 ,north and ,south1 which are called the ,northern and ,southern ,hemispheres4 ,the axis of this circle1 is called the ,axis of the ,world1 or the ,earth's ,axis1 because the ,earth revolves about it 7from ,west to ,east7 in #bd hours4 ,the extreme of this axis are called the ,poles of the ,world1 whereof that which lies in the ,northern ,hemisphere1 is called the ,north ,pole1 and the other is called the ,south ,pole4 ,the equinoctial circle is always delineated upon the surface of each globe1 with its name at length expressed2 the axis of this circle1 or the ,earth's axis1 is only an imaginary line in the ,heavens1 but on the globes it is expressed by the wires about which they really turn4 ,the ,poles of the world1 are the two points upon the surface of the globe through which these wires pass2 the ,north ,pole is that which hath the little brass circle1 with a moveable index placed round it2 and the other opposite to it is the ,south ,pole4 ,the ,northern ,hemisphere is that wherein the ,north ,pole is placed1 and the opposite one is the ,southern ,hemisphere4 ,the astronomers divide all circles into #cfj equal parts1 called ,degrees1 each degree into #fj equal parts1 called ,minutes1 each minute into #fj ,seconds1 c4 ,but besides this division into degrees1 the equinoctial is also divided into #bd equal parts1 or ,hours1 each hour into #fj ,minutes1 each minute into #fj ,seconds1 c4 so that one hour is equal to #ae degrees1 each minute of time is equal to #ae minutes of a degree1 c4 ,sidenote3 ,hour ,circles or ,circles of ,ascension1 also called ,meridians4 #b4 ,all circles conceived to pass through the ,poles of the world1 intersecting the equinoctial at right angles1 are1 with respect to any point in the ,heavens1 called ,hour ,circles2 and the ,circles of ,ascension1 because the ascension of the ,heavenly bodies1 from a certain point1 are by them determined4 ,these circles are also1 with regard to places upon ,earth1 called ,meridians4 ,sidenote3 ,the ,brass ,meridian4 ,the ,meridians are commonly drawn upon the ,terrestrial ,globe thro' every #ae degrees of the equinoctial1 thereby making an ,hour difference betwixt the places through which they pass4 ,on the ,celestial ,globe there are commonly drawn but two of these ,meridians1 crossing the equinoctial in four points equidistant from one another1 thereby dividing it into four quadrants2 but the intermediate ones are here supplied1 and also upon the ,terrestrial ,globe1 by the brass circle on which they are hung1 which1 is therefore called the ,brass ,meridian1 and sometimes only the ,meridian1 it serving for this purpose to all the points upon either ,globe4 ,sidenote3 ,the ,hour ,circle4 ,there is also a little brass circle fixed upon this meridian1 divided into #bd ,hours1 having an index moveable round the axis of the globe1 to be turned to any particular ,hour4 ,the use of this circle is to shew the difference of time betwixt any two meridians1 and is therefore called the ,hour ,circle4 ,sidenote3 ,parallels of ,declination4 #c4 ,all circles parallel to the equinoctial are1 with respect to any point in the ,heavens1 called ,parallels of ,declination4 ,so that1 ,sidenote3 ,declination ,north and ,south4 #d4 ,the ,declination of any ,point in the ,heavens 7as of the ,sun1 a fixed ,star1 or the like7 is an arch of the meridian passing through that point1 and intercepted betwixt it and the equator2 and if the said point be to the 7,northward_/,southward7 of the equator1 it is called 7,north_/,south7 ,declination4 ,sidenote3 ,tropics and ,polar ,circles4 ,of the parallels of declination1 four are eminently distinguished by particular names1 viz4 ,the two ,tropics1 and the two ,polar ,circles4 ,sidenote3 ,tropic of ,cancer2 of ,capricorn4 ,the tropics are on different sides of the equator each #bc degrees and #bi minutes distant from it2 that which lies in the ,northern ,hemisphere1 is called the ,tropic of ,cancer1 and the ,southern one1 the ,tropic of ,capricorn4 ,these circles are the limits of the ,sun's greatest declination1 and are called tropics1 because whenever the ,sun arrives to them1 he seems to return back again towards the equator4 ,sidenote3 ,arctic ,circle4 ,sidenote3 ,arctic ,pole4 ,sidenote3 ,antarctic ,circle4 ,sidenote3 ,antarctic ,pole4 #f4 ,the ,polar ,circles are each of them at the same distance from the ,poles of the world1 that the tropics are from the equator1 viz4 #bc #bi4 ,that which lies near the ,north ,pole1 is called the ,arctic ,circle1 from ,arctos1 a constellation situated in the ,heavens near that ,place2 whence also this ,pole is sometimes called the ,arctic ,pole4 ,the other ,polar circle1 which is situated near the ,south ,pole2 is called the ,antarctic ,circle1 because its position is contrary to the other2 and the ,south ,pole is sometimes called the ,antarctic ,pole4 ,the tropics and the ,polar circles have each their names expressed upon the ,globes4 ,,ii4 ,of the ,ecliptic4 ,sidenote3 ,ecliptic4 ,sidenote3 ,equinoctial4 ,sidenote3 ,solstitial ,points4 ,sidenote3 ,colures4 ,sidenote3 ,equinoctial ,colure4 ,sidenote3 ,solstitial ,colure4 #g4 ,the ,ecliptic is that great circle in whose plane the ,earth performs its annual motion round the ,sun2 or1 in which the ,sun seems to move round the ,earth1 once in a year4 ,this circle makes an angle with the equinoctial of #bc degrees #bi minutes1 and intersects it in two opposite points1 which are called the ,equinoctial ,points2 and the two points in the ecliptic that are at the greatest distance from the equinoctial points1 are called the ,solstitial ,points4 ,the two meridians passing through those points1 are1 by way of eminence1 called ,colures2 whereof that which passeth thro' the equinoctial points1 is called the ,equinoctial ,colure2 and that which is at right angles to it1 passing through the ,solstitial ,points1 is called the ,solstitial ,colure4 ,sidenote3 ,the ,ecliptic divided into signs4 ,the ecliptic is divided into #ab equal parts1 called ,signs1 each sign being #cj degrees1 beginning from one of the equinoctial points1 and numbered from ,west to ,east2 the names and characters of the twelve signs are as follows1 viz4 ,aries1 ,taurus1 ,gemini1 ,cancer1 ,leo1 ,virgo1 #a4 #b4 #c4 #d4 #e4 #f4 ,libra1 ,scorpio1 ,sagittarius1 ,capricornus1 ,aquaries1 #g4 #h4 #i4 #aj4 #aa4 ,pisces4 #ab4 ,sidenote3 ,northern ,signs4 ,the first six of these are called the ,northern ,signs1 and possess that half of the ecliptic which is to the ,northward of the equator2 beginning with the first point of 1 and ending with the last point of 4 ,sidenote3 ,southern ,signs4 ,the latter six are called the ,southern ,signs1 because they possess the ,southern half of the ecliptic2 beginning at the first point of 1 and ending with the last point of 4 ,the division of the ecliptic into signs1 and the names of the colures1 are particularly expressed upon the globes4 ,the signs of the ecliptic took their names from #ab constellations mentioned in the ,introduction to be situated in the ,heavens near those places4 ,it is to be observed1 that the signs are not to be confounded with the constellations of the same name3 ,for the ,sign of ,aries1 is not the same with the ,constellation ,aries2 the latter is a system of ,stars digested into the figure of a ,ram1 but the sign of ,aries is only #cj degrees of the ecliptic1 counted from the equinoctial point 1 7which is reckoned the first point in the ecliptic7 to the beginning of ,taurus3 ,or1 it is sometimes taken for all that space upon the ,celestial ,globe contained between the two circles passing through the first points of and 4 ,what has been here said of ,aries1 is to be noted of all the rest of the signs4 ,the constellations above-mentioned were formerly situated within the signs which now bear their names2 but by a slow motion of the equinoctial points1 being one degree in #gb years1 the constellation ,aries has now got into the sign 1 and so of the rest4 ,so that ,pisces is now got into the ,sign of 2 this slow motion in the ,heavens is called the ,precession of the ,equinoctial ,points4 ,sidenote3 ,poles of the ,ecliptic4 ,the ,poles of the ,ecliptic are both situated in the ,solstitial ,colure1 at #bc degrees1 #bi minutes distance from the ,pole of the world2 and they take their denomination from the ,hemisphere wherein they are placed1 viz4 that which lies in the 7,northern_/,southern7 ,hemisphere1 is called the 7,north_/,south7 ,pole of the ecliptic4 ,the arctic and antarctic circles1 are described by the ,poles of the ecliptic in the diurnal motion of the ,earth round its axis1 whence it seems these two circles are called ,polar4 ,sidenote3 ,circles of ,longitude4 #h4 ,all great circles passing through the ,poles of the ecliptic1 and consequently intersecting it at right angles1 are called ,circles of ,longitude3 ,so that1 ,sidenote3 ,longitude of any ,point in the ,heavens4 ,sidenote3 ,place of a ,star4 #i4 ,the ,longitude of any ,point in the ,heavens 7as a ,star or ,planet1 c47 is an arch of the ecliptic contained between the circle of longitude passing thro' that point1 and the equinoctial point 4 ,and that degree of any sign which lies under the circle of longitude1 passing thro' any ,star or ,planet1 is called the ,place of that ,star or ,planet4 ,note1 ,the ,sun never goes out of the ecliptic1 and it is not usual to say the ,sun's longitude1 but we commonly express it the ,sun's ,place1 which is that sign1 degree1 minute1 c41 of the ecliptic1 which he at any time passes4 #aj4 ,all circles conceived to be drawn parallel to the ecliptic1 are called ,parallels of ,latitude3 ,so that1 ,sidenote3 ,latitude of a ,star1 c4 #aa4 ,the ,latitude of any point in the ,heavens1 7as a fixed ,star1 c47 is an arch of the circle of longitude1 in passing thro' that point1 and intercepted betwixt it1 and the ecliptic2 or1 the latitude is the distance from the ecliptic2 and if the said point be to the ,northward of the ecliptic1 it is called ,north ,latitude2 but if it be to the ,southward1 is called ,south ,latitude4 ,upon the ,terrestrial ,globe1 none of the circles of longitude are described2 and upon the ,celestial1 they are commonly drawn thro' the beginning of every ,sign2 but they are all supplied upon both ,globes1 by fastening a thin plate of brass over one of the ,poles of the ecliptic1 and so as to be moved to any degree thereof at pleasure4 ,the parallels of latitude are also supplied by the graduations upon the said plate1 as shall be shewn in a proper place4 ,we have now done with all those circles that are fixed1 and such as are drawn upon the ,globes themselves2 we next proceed to the moveable circles4 ,,iii4 ,of the ,horizon4 ,sidenote3 ,horizon4 #ab4 ,the ,horizon is that great circle which divides the upper1 or visible ,hemisphere of the world1 from the lower1 or invisible3 ,this circle is distinguished into two sorts1 the ,sensible1 and the ,rational4 ,sidenote3 ,sensible ,horizon4 ,the ,sensible1 or ,apparent ,horizon1 is that circle which limits or determinates our prospect1 whether we are at land or sea1 reaching as far as we can see1 or it is that circle where the ,sky and the ,earth1 or ,water1 seem to meet4 ,when we are on ,terra ,firma1 this circle commonly seems rugged and irregular1 occasioned by the unevenness of the ground terminating our prospect2 but at sea there are no such irregularities2 the semidiameter of this circle varieth according to the height of the eye of the observer2 if a man of six feet high stood upon a large plain1 or the surface of the sea1 he could not see above three miles round4 ,this circle determines the rising and setting of the ,heavenly bodies1 and distinguishes ,day and ,night4 ,sidenote3 ,rational ,horizon4 ,the ,rational1 or true ,horizon1 is a great circle passing thro' the center of the ,earth1 parallel to the sensible ,horizon1 being distant from it by the ,earth's semidiameter1 which is about #cihj miles3 ,this distance is nothing in comparison of the immense distance of the ,sun and the fixed ,stars1 therefore astronomers make no distinction between these two circles1 but consider the apparent ,horizon1 or that wherein the ,sun appears to rise and set1 as passing thro' the center of the ,earth4 ,sidenote3 ,cardinal ,points of the ,horizon4 ,this circle is divided by astronomers into four quadrants1 and each of the quadrants into #ij degrees1 c4 ,the four points quartering this circle are called the ,cardinal ,points1 and are termed the ,east1 ,west1 ,north1 and ,south4 ,the ,east is that point of the ,horizon where the ,sun rises when he is in the equinoctial1 or on that day when he ascends above the ,horizon exactly at six o'clock2 and the ,west is that point of the ,horizon which is directly opposite to the ,east1 or where the ,sun ,sets when he is in the ,equinoctial4 ,the ,south is #ij degrees distant from the ,east and ,west1 and is toward that part of the ,heavens wherein the ,sun always appears to us in ,great-,britain at ,noon2 and the ,north is that part of the ,heavens which is directly opposite to the ,south3 ,or1 the ,north and ,south points of the ,heavens may be found by turning yourself either directly towards the ,east or the ,west3 ,if you look towards the 7,east_/,west7 the 7,south_/,north7 will be to the right ,hand1 and the 7,north_/,south7 to the left4 ,sidenote3 ,points of the ,compass4 ,besides the aforementioned divisions of the ,horizon into degrees4 ,mariners divide it into #cb equal parts1 which they call the ,points of the ,compass2 to each of which points they give a particular name1 compounded of the four ,cardinals1 according to what quarter of the ,compass is intended4 ,sidenote3 ,zenith4 ,sidenote3 ,nadir4 ,the center of the ,horizon is the place of observation1 and the ,poles of it are one exactly over our heads1 called the ,zenith2 and the other exactly under our feet1 called the ,nadir4 ,sidenote3 ,vertical ,circles4 ,sidenote3 ,meridian4 ,sidenote3 ,azimuth4 #ac4 ,all circles conceived to pass thro' the ,zenith and ,nadir1 are called ,vertical ,circles1 or ,azimuths4 ,of these circles1 that which passeth thro' the ,north and ,south points of the ,horizon1 is called the ,meridian2 so that when any object is upon the ,meridian1 it then bears either due ,south1 or due ,north from us2 and the ,azimuth of any object is an arch of the ,horizon intercepted between the vertical circle passing through it1 and either the ,north or ,south part of the ,meridian2 which part is commonly specified4 ,the meridian passes thro' the ,poles of the world1 as well as through the ,zenith and ,nadir1 and therefore is a secundary both of the equinoctial and the horizon3 ,this circle divides the globe into the ,eastern and ,western ,hemispheres1 and the ,poles of it are the ,east and ,west points of the ,horizon4 ,all the heavenly objects are1 during one half of their continuance above the horizon1 in the ,eastern ,hemisphere1 and for the other half in the ,western2 so that whenever the ,sun arrives upon the upper part of the meridian1 it is then ,noon1 or ,mid-day1 which is the reason why this circle is called the meridian2 and when he comes to the lower part1 it is then ,midnight4 ,sidenote3 ,prime ,vertical4 ,the vertical circle passing thro' the ,east and ,west points of the horizon1 is called the ,prime ,vertical1 or ,circle of ,east and ,west1 so that when any object is upon this circle in the ,eastern hemisphere1 it appears due ,east2 and if it be in the ,western hemisphere1 it appears due ,west4 ,sidenote3 ,amplitude4 ,that degree in the horizon wherein any object rises or sets from the ,east or ,west points1 is called the ,amplitude2 which for rising is called ,amplitude ,ortive1 and ,occasive for setting2 which must be also denominated whether it be ,northerly or ,southerly4 ,it may be observed1 that the ,amplitude and ,azimuth are much the same2 the amplitude shewing the bearing of any object when he rises or sets1 from the ,east or ,west points of the horizon2 and the azimuth1 the bearing of any object when it is above the horizon1 either from the ,north or ,south point thereof4 ,as for example1 if an object rises or sets within #aj degrees of the ,east or ,west1 suppose towards the ,south1 we accordingly say1 its ,amplitude is #aj degrees ,southerly2 but if an object1 that is of any height above the horizon1 should be in the vertical circle1 passing thro' the before-mentioned point1 we then say1 its ,azimuth is #hj degrees from the ,south1 or #ajj degrees from the ,north1 both which expressions signify the same4 ,sidenote3 ,almacanthers4 ,sidenote3 ,altitudes4 ,sidenote3 ,meridian ,altitude4 ,sidenote3 ,zenith ,distance4 #ad4 ,all circles drawn parallel to the horizon1 in the upper hemisphere1 are called ,almacanthers1 or ,parallels of ,altitude3 ,so that the ,altitude of any point in the ,heavens is an arch of the vertical circle passing thro' that point1 and intercepted betwixt it and the horizon2 and if the object be upon the meridian1 it is commonly called the ,meridian ,altitude4 ,the complement of the altitude1 or what it wants of #ij degrees1 is called the ,zenith ,distance4 ,the horizon 7by which we mean the rational7 is represented by the upper surface of the ,wooden frame1 wherein the globes are placed2 upon this horizon are described several concentric circles1 the innermost of which is divided into degrees1 which ought to be numbered both ways from the ,east and the ,west1 until they end at #ij degrees in the ,north and ,south points4 ,the use of these divisions is to shew the amplitudes of the ,sun and ,stars1 at their rising and setting3 ,also in some convenient place upon this horizon1 there is commonly noted the points of the ,compass4 ,without the before-mentioned circle there is drawn the ecliptic with its divisions1 into signs1 and degrees1 and a circle of months and days3 ,the use of these two circles is to serve as a kalendar to shew the ,sun's place at any time of the year1 and by that means to find his place in the ,ecliptic1 drawn upon the globe itself4 ,the ,vertical ,circles1 and the ,parallels of ,altitude1 are supplied by a thin plate of brass1 having a nut and screw at one end to fasten it to the brass meridian in the ,zenith point2 which being done1 the lower end of it may be put between the globe it self1 and the inner edge of the horizon1 and so turned round about to any point required4 ,sidenote3 ,quadrant of ,altitude4 ,the fiducial edge thereof representing the ,vertical ,circles1 and the ,degrees upon it1 describing the ,parallels of ,altitude4 ,this thin plate is called the ,quadrant of ,altitude4 ,the center of the horizon being the place of observation1 it is evident that this circle1 and all the others belonging to it1 are continually changed1 which way soever we move2 wherefore we may suppose the horizon1 with its secundaries and parallels1 to invest the globe like a rete or net2 and to be moveable every way round it4 ,this is very naturally illustrated by the globes2 if we move directly ,north1 or directly ,south1 the change made in the horizon1 is represented by moving the brass meridian 7keeping the globe from turning about its axis7 in the notches made in the wooden horizon1 just so much as we travelled4 ,if our course should be due ,east1 or due ,west1 the alterations made thereby are represented by turning the globe accordingly about its axis1 the brass meridian being kept fixed2 and if we steer betwixt the meridian and the ,east or ,west points1 then we are to turn the brass meridian1 and also the globe about its axis accordingly2 the sum of which is1 let the spectator be at what point soever of the ,earth's surface1 he'll there gravitate1 or tend exactly towards its center1 and imagine himself to be on the highest part thereof1 7the unevenness of the ground not being here considered7 wherefore if we turn the globe in such a manner as to bring the several progressive steps of a traveller successively to the ,zenith1 we shall then have the successive alterations made in the horizon1 in every part of his journey4 ,this explication being well considered1 will be of help to young beginners1 to conceive how the ,earth is every where habitable2 and how passengers can travel quite round it2 for since every thing tends toward the center of the ,earth1 we are to conceive that point as being the lowest1 and not to carry our idea of downwards any farther4 ,those that are diametrically opposite to us being as much upon the upper part of the ,earth as we are1 there being no such thing in nature as one place being higher than another1 but as it is at a greater distance from the center of the ,earth1 let it be in what country soever4 ,we have now done with all the circles of the sphere1 and it may be observed1 that the ,equinoctial1 the ,ecliptic1 and the ,horizon1 with their ,secundaries and parallels1 are all alike2 and altering their position1 may be made to serve for one another4 ,thus1 if the ,poles of the ,world be brought into the ,zenith and ,nadir1 the ,equinoctial will coincide with the ,horizon1 the ,meridians will be the same with the ,vertical ,circles1 and the parallels of ,declination will be the parallels of ,altitude4 ,after the same manner1 if shifting the position1 we bring the ,ecliptic to coincide with the ,horizon1 the circles of ,longitude will be the ,vertical ,circles1 and the parallels of ,latitude and ,altitude will coincide4 ,the horizon and the equator may be either parallel1 perpendicular1 or oblique to each other4 ,sidenote3 ,parallel ,sphere4 #ae4 ,a ,parallel ,sphere is that position where the equator coincides with the horizon1 and consequently the poles of the world are in the ,zenith and ,nadir3 ,the inhabitants of this sphere 7if there be any7 are those who live under the poles of the world4 ,sidenote3 ,right ,sphere4 #af4 ,a ,right or ,direct ,sphere is that position where the equator is perpendicular to the horizon1 the inhabitants whereof are those who live under the equinoctial4 ,sidenote3 ,oblique ,sphere4 #ag4 ,an ,oblique ,sphere is when the equinoctial and the horizon make oblique angles with each other1 which every where happens but under the equator and the poles4 ,sidenote3 ,diurnal and ,nocturnal ,arch4 ,the arch of any parallel or declination1 which stands above the horizon is called the ,diurnal ,arch2 and the remaining part of it1 which is below the horizon1 is called the ,nocturnal ,arch4 ,that point of the equinoctial which comes to the 7,eastern_/,western7 part of the horizon with any point of the ,heavens1 is called the 7,ascension_/,descension7 of that point1 counted from the beginning of 2 and if it be in a right sphere1 the ascension or descension is called right2 but if it be an oblique sphere it is called an oblique ascension or descension4 ,so that1 ,sidenote3 ,right ,ascension4 #ah4 ,the ,right ,ascension of the ,sun1 ,moon1 or any ,star1 c4 is an arch of the equator contained betwixt the beginning of 1 and that point of the equinoctial which rises with them in a ,right ,sphere1 or which comes to the meridian with them in an oblique sphere4 ,sidenote3 ,oblique ,ascension4 #ai4 ,oblique ,ascension1 or ,descension1 is an arch of the equinoctial intercepted between the beginning of 1 and that ,point of the ,equator which rises or sets with any point in the ,heavens in an oblique sphere4 ,sidenote3 ,ascensional ,difference4 #bj4 ,ascensional ,difference1 is the difference betwixt the right and oblique ascension or descension1 and shews how long the ,sun rises or sets before or after the hour of six4 ,,iv4 ,of the ,division of ,time4 ,the parts that time is distinguished into1 are ,days1 ,hours1 ,weeks1 ,months1 and ,years4 ,a ,day is either natural or artificial4 ,sidenote3 ,natural and ,artificial ,day4 ,a ,natural ,day is the space of time elapsed while the ,sun goes from any meridian or horary circle1 'till he arrives to the same again2 or1 it is the time contained from noon1 or any particular hour1 to the next noon1 or the same hour again3 ,an ,artificial ,day is the time betwixt the ,sun's rising and setting2 to which is opposed the ,night1 that is1 the time the ,sun is hid under the horizon4 ,sidenote3 ,hours1 c4 ,sidenote3 ,equinoxes4 ,sidenote3 ,vernal and ,autumnal ,equinox4 ,sidenote3 ,solstices4 ,sidenote3 ,summer and ,winter ,solstices4 ,the ,natural ,day is divided into #bd ,hours1 each hour into #fj ,minutes1 each minute into #fj ,seconds1 c4 ,the ,artificial ,days are always unequal to all the inhabitants that are not under the equator1 except when the ,sun is in the equinoctial points and 1 which happens 7according to our way of reckoning7 about the #bast of ,march1 and the #bc;d of ,september2 at those times the ,sun rises at six and sets at six to all the inhabitants of the ,earth4 ,these days are called the ,equinoxes1 or ,equinoctial ,days2 the first of which1 or when the ,sun is in the first point of ,aries1 is called the ,vernal ,equinox1 and the latter is called the ,autumnal ,equinox4 ,in all places where the ,sun descends below the horizon1 excepting under the equator1 the days continually lengthen or shorten1 and that faster or slower1 according as the ,sun is nearer to1 or further from the equinoctial1 until he arrives to either of the ,solstitial ,points or 4 ,at those times the ,sun seems to stand still for a few days1 and then begins to return with a slow motion towards the equinoctial1 still hastening his pace as he comes nearer to it3 ,the ,sun enters the tropics of and 1 about the #bast of ,june1 and the #bb;d of ,december1 which days are sometimes called the ,solstices2 the first of which we call the ,summer ,solstice1 and the latter the ,winter ,solstice4 ,sidenote3 ,the different beginning of the day4 ,all nations do not begin their day1 and reckon their hours alike4 ,in ,great-,britain4 ,france1 and ,spain1 and in most places in ,europe1 the days is reckoned to begin at midnight1 from whence is counted twelve hours 'till noon1 then twelve hours more 'till next midnight1 which makes a compleat day2 yet the ,astronomers 7in these countries7 commonly begin their day at noon1 and so reckon #bd hours 'till next noon1 and not twice twelve1 according to the vulgar computation4 ,sidenote3 ,babylonish ,hours4 ,sidenote3 ,italian ,hours4 ,the ,babylonians began their day at ,sun-rising1 and reckoned #bd hours 'till he rose again6 ,this way of computation we call the ,babylonish ,hours4 ,in several parts of ,germany they count their hours from ,sun-setting1 calling the first hour after the ,sun has set1 the first hour1 c4 'till he sets the next day1 which they call the #bdth hour3 ,these are commonly called the ,italian ,hours4 ,according to both these ways of computation1 their hours are commonly either a little greater or less than the _/ part of a natural day1 in proportion as the ,sun rises or sets sooner or later in the succeeding days4 ,they have also this inconvenience1 that their mid-day and midnight happen on different hours1 according to the seasons of the year4 ,sidenote3 ,jewish ,hours4 ,sidenote3 ,planetary ,hours4 ,the ,jews and the ,romans formerly divided the artificial days and nights each into #ab equal parts2 these are termed the ,jewish ,hours1 and are of different lengths1 according to the seasons of the year2 a ,jewish ,hour in summer being longer than one in winter1 and a night-hour shorter4 ,this method of computation is now in use among the ,turks1 and the hours are stiled the first hour1 second hour1 c4 of the day or night2 so that ,mid-day always falls on the sixth hour of the day4 ,these hours are also called ,planetary ,hours1 because in every hour one of the seven ,planets were suppose to preside over the ,world1 and so take it by turns4 ,the first hour after ,sun-rising on ,sunday was allotted to the ,sun2 the next to ,venus1 the third to ,mercury2 and the rest in order to the ,moon1 ,saturn1 ,jupiter1 and ,mars4 ,by this means on the first hour of the next day1 the ,moon presided1 and so gave the name to that day2 and so seven days by this method had names given them from the ,planets that were supposed to govern on the first hour4 ,sidenote3 ,a ,week4 ,a ,week is a system of seven days1 in which each day is distinguished by a different name4 ,in most countries these days are called after the names of the seven ,planets1 as above noted4 ,all nations that have any notion of religion1 lay apart one day in seven for public worship2 the day solemnized by ,christians is ,sunday1 or the first day of the week1 being that on which our saviour rose from the grave1 on which the apostles afterwards used more particularly to assemble together to perform divine worship4 ,the ,jews observed ,saturday1 or the seventh day of the week1 for their sabbath1 or day of rest1 being that appointed in the fourth commandment under the ,law4 ,the ,turks perform their religious ceremonies on ,friday4 ,sidenote3 ,a ,month4 ,sidenote3 ,periodical and ,synodical ,month4 ,a ,month is properly a certain space of time measured by the ,moon in his course round the ,earth4 ,a ,lunar ,month is either ,periodical or ,synodical4 ,a ,periodical ,month is that space of time the ,moon takes to perform her course from one point in the ecliptic 'till she arrives to the same again1 which is #bg days1 and some odd hours2 and a ,synodical ,month is the time betwixt one new ,moon1 and the next new ,moon1 which is commonly about #bi days4 ,but a ,civil ,month1 is different from these1 and consists of a certain number of days1 fewer or more1 according to the laws and customs of the country where they are observed4 ,sidenote3 ,a ,year ,sydereal and ,tropical4 ,the compleatest period of time is a ,year1 in which all the variety of seasons return1 and afterwards begin anew4 ,a ,year is either ,astronomical or ,civil4 ,an ,astronomical ,year is either a ,sydereal wherein the ,sun departing from a fixed ,star1 returns to it again2 or ,tropical1 which is the space of time the ,sun takes to perform his course from any point of the ecliptic1 'till he returns to it again4 ,a ,tropical ,year consists of #cfe days1 #e hours1 and #di minutes2 this is the time in which all the seasons compleatly returns1 which is a small matter less than a ,sydereal ,year4 ,sidenote3 ,egyptian ,year4 ,the ,civil ,year is the same with the ,political established with the laws of a country2 and is either moveable or immoveable4 ,the moveable year consists of #cfe days1 being less than the tropical year by almost six hours1 and is called the ,egyptian ,year1 because observed in that ,country4 ,the ,romans divided the year into #ab kalendar months1 to which they gave particular names1 and are still retained by most of the ,european nations1 viz4 ,january1 ,february1 ,march1 ,april1 ,may1 ,june1 ,july1 ,august1 ,september1 ,october1 ,november1 and ,december4 ,the number of days in each month may be known by the following verses3 ,thirty ,days hath ,september1 ,april1 ,june1 and ,november2 ,february hath ,twenty-eight alone1 ,and all the rest have ,thirty-one4 ,the year is also divided into four quarters or seasons1 viz4 ,spring1 ,summer1 ,autumn1 and ,winter4 ,these quarters are properly made when the ,sun enters into the equinoctial and solstitial points of the ecliptic2 but in civil uses they are differently reckoned1 according to the customs of several countries4 ,in ,england1 we commonly reckon the first day of ,january to be the first in the year1 which is therefore vulgarly called ,new-,year's-,day2 but in political and ecclesiastical affairs1 the year is reckoned to commence on ,lady-day which is the #beth of ,march2 and from thence to ,midsummer-day1 which is the #bdth of ,june1 is reckoned the first quarter2 from ,midsummer-day to ,michaelmas-day1 which is the #bith of ,september1 is the second quarter2 the third quarter is reckoned from ,michaelmas-day to ,christmas-day1 which is the #beth of ,december2 and from ,christmas-day to ,lady-day1 is reckoned the last quarter in the year4 ,in common affairs1 a quarter is reckoned from a certain day to the same in the fourth month following4 ,sometimes a month is reckoned four weeks1 or #bh days1 and so a quarter #ab weeks4 ,to all the inhabitants in the 7,northern_/,southern7 ,hemisphere1 their ,midsummer is properly when the ,sun is in the tropic of 7,cancer1_/,capricorn17 and their ,midwinter at the opposite time of the year2 but those who live under the equinoctial have two winters1 c4 when the ,sun is in either tropic2 tho' indeed properly1 there is no season that may be called winter in those parts of the world4 ,sidenote3 ,bissextile1 or ,leap-,year4 ,the ,egyptian year of #cfe days being less than the true solar year1 by almost six hours1 it follows1 that four such years are less than four solar years by a whole day2 and therefore in #cfe times four years1 that is1 in #adfj years1 the beginning of the years move through all the seasons4 ,to remedy this inconveniency1 ,julius ,csar 7considering that the six hours1 which remain at the end of every year1 will in four years make a natural day7 ordered that every fourth year should have an intercalary day1 which therefore consists of #cff days2 the day added was put in the month of ,february1 by postponing ,st4 ,matthias's day1 which in common years fall on the #bdth1 to the #beth of the said month1 all the fixed feasts in the year from thenceforwards falling a week-day later than otherwise they would4 ,according to the ,roman way of reckoning1 the #bdth of ,february was the sixth of the kalends of ,march1 and it was ordered that for this year there should be two sixths1 or that the sixth of the kalends of ,march should be twice repeated2 upon which account the year was called ,bissextile1 which we now call the ,leap-,year4 ,to find whether the year of our ,lord be leap-year1 or the first1 second1 or third after2 divide it by four1 and the remainder1 if there be any1 shews how many years it is after leap-year2 but if there be no remainder1 then that year is leap-year3 ,or1 you may omit the hundreds and scores1 and divide the residue by #d1 ,examp4 #ageg1 omitting the hundreds and the twenties1 ,i divide the residue #ag1 by #d1 and the remainder #a1 shews it to be the first after leap-year4 ,sidenote3 ,julian ,account or the ,old ,style4 ,this method of reckoning the year1 viz4 making the common year to consist of #cfe days1 and every fourth year to have #cff days1 is now used in ,great-,britain and ,ireland1 and some of the ,northern parts of ,europe1 and is called the ,julian ,account1 or the ,old ,style4 ,but the time appointed by ,julius ,csar for the length of a solar year is too much2 for the ,sun finishes his course in the ecliptic1 in #cfe days1 #e hours1 and #di minutes1 which is #aa minutes less than the civil year2 and therefore he again begins his circuit #aa minutes before the civil year is ended2 and so much being gained every year1 amounts in #aca years1 to a whole day4 ,so that if the ,sun in any year entered the equinox upon the #bjth of ,march at noon1 after the space of #aca years1 he'll enter the same point on the same hour1 on the #aith of ,march4 ,and therefore the exquinoxes will not always fall on the same day of the month1 but by degrees will move towards the beginning of the year4 ,sidenote3 ,gregorian ,account1 or ,new ,style4 ,at the time of the ,council of ,nice1 when the terms were settled for observing of ,easter1 the ,vernal ,equinox fell upon the #bast of ,march2 but by its falling backwards #aa minutes every year1 it was found that in ,anno #aehb1 when the kalendar was corrected1 the ,sun entered the equinoctial circle on the #aath of ,march1 having departed ten whole days from its former place in the year3 and therefore ,pope ,gregory the ,x,i,i,ith1 designing to place the equinoxes in their situation with respect to the year1 took these ten days out of the kalendar1 and ordered that the #aath of ,march should be reckoned as the twenty-first3 ,and to prevent the seasons of the year from going backwards for the future1 he ordered every hundredth year1 which in ,julian form was to be a ,bissextile1 should be a common year1 and consist only of #cfe days2 but that being too much1 every fourth hundred was to remain ,bissextile4 ,this form of reckoning being established by the authority of ,pope ,gregory ,,xiii4 is called the ,gregorian ,account1 or the ,new ,style2 and is observed in all the countries where the authority of the ,pope is acknowledged1 and likewise by several nations of the reformed religion4 ,there being now above an hundred years past1 since the reformation was made in the kalendar1 the ,gregorian account has accordingly got before the ,julian one day more than it was in the time of its institution1 the difference between these two accounts being now eleven days2 so that the first day of any month1 according to that way of reckoning1 is the #abth of the same month1 according to the ,new ,style4 ,i shall conclude this section with a brief account of the ,atmosphere4 ,sidenote3 ,atmosphere4 ,the ,atmosphere is that thin body of air which surrounds the ,earth1 in which the clouds hover1 and by which in their descent they are broke into drops of rain2 which sometimes1 according to the warmth or coldness of air1 are froze into ,snow1 or ,hailstones4 ,thunder and ,lightning are also made in the ,atmosphere1 and wind is nothing else but a percussion of the air1 occasioned by its different density in different places4 ,the benefits we receive from the atmosphere are innumerable2 without air no earthly creature could live1 as is plainly proved by experiments made by the ,air-,pump2 and the wholsomeness of a climate chiefly depends upon that of its air3 ,if there was no atmosphere to reflect the rays of the ,sun1 no part of the heavens would be lucid and bright1 but that wherein the ,sun was placed2 and if a spectator should turn his back towards the ,sun1 he would immediately perceive it to be quite dark1 and the least ,stars would be seen shining as they do in the clearest night2 and the ,sun immediately before his setting would shine as brisk as at noon1 but in a moment1 as soon as he got below the horizon1 the whole hemisphere of the ,earth would be involved in as great a darkness as if it were midnight4 ,but by means of the atmosphere it happens1 that while the ,sun is above the horizon1 the whole face of the heavens is strongly illuminated by its rays1 so as to obscure the faint light of the ,stars1 and render them invisible2 and after ,sun-setting1 though we receive no direct light from him1 yet we enjoy its reflected light for some time3 ,for the atmosphere being higher than we are1 is a longer time before it is withdrawn from the ,sun 7as if a man was to run to the top of a steeple1 he might see the ,sun after it had been set to those at the bottom47 ,the rays which the atmosphere receives from the ,sun1 after he is withdrawn from our sight1 are by refraction faintly transmitted to us2 until the ,sun having got about #ah degrees below the horizon1 he no longer enlightens our atmosphere1 and then all that part thereof which is over us becomes dark4 ,after the same manner in the morning1 when the ,sun comes within #ah degrees of our horizon1 he again begins to enlighten the atmosphere1 and so more and more by degrees1 until he rises and makes full day4 ,sidenote3 ,twilight1 or ,crepusculum4 ,this small illumination of the atmosphere1 and the state of the ,heavens between day and night1 is called the ,twilight1 or the ,crepusculum4 ,the duration of twilight is different in different climates1 and in the same place at different times of the year4 ,the beginning or ending of twilight being accurately given1 we may from thence easily find the height of the atmosphere1 which is not always the same4 ,the mean height of the atmosphere is computed to be about #dj miles2 but it is probable1 the air may extend itself a great deal further1 there being properly no other limits to it1 as we can conceive1 but as it continually decreases in density the farther remote it is from the ,earth1 in a certain ratio2 which at last1 as to our conception1 must in a manner terminate4 ,illustration ,,sect4 ,,ii4 ,geographical ,definitions4 ,of the ,situations of ,places upon the ,earth2 of the different ,situations of its ,inhabitants2 of ,zones and ,climates4 ,the situations of places upon the ,earth1 are determined by their ,latitude and ,longitude4 ,sidenote3 ,latitude4 #a4 ,the ,latitude of any place 7upon the ,earth7 is its nearest distance1 either ,north or ,south from the ,equator2 and if the place be in the 7,northern_/,southern7 hemisphere1 it is accordingly called 7,north_/,south7 ,latitude2 and is measured by an arch of the meridian intercepted betwixt the zenith of the said place1 and the equator4 ,and all places that lie on the same side1 and at the same distance from the equator1 are said to be in the same parallel of latitude3 the parallels in ,geography1 being the same with the parallels of declination in ,astronomy4 ,from this definition arise the following ,corollaries4 7#a47 ,that no place can have above #ij degrees of latitude1 either ,north or ,south4 7#b47 ,those places that lie under the equinoctial 7or thro' which the equator passes7 have no latitude1 it being from thence that the calculation of latitudes is counted2 and those places that lie under the ,poles have the greatest latitude1 those points being at the greatest distance from the equator4 7#c47 ,the latitude of any place is always equal to the elevation of the ,pole in the same place above the horizon2 and is therefore often expressed by the ,pole's height1 or elevation of the ,pole2 the reason of which is1 because from the equator to the ,pole there is always the distance of #ij degrees1 and from the zenith to the horizon the same number of degrees1 each of these including the distance from the zenith to the ,pole3 ,that distance therefore being taken away from both1 will leave the distance from the zenith to the equator1 7which is the latitude7 equal to the distance of the ,pole to the horizon4 7#d47 ,the elevation of the equator in any place is always equal to the complement of the latitude of the same place4 7#e47 ,a ship sailed directly 7towards_/from7 the equator 7lessens_/augments7 her latitude1 7or 7depresses_/raises7 the ,pole7 just so much as is her distance sailed4 ,sidenote3 ,difference of ,latitude4 #b4 ,difference of latitude is the nearest distance betwixt any two parallels of latitude1 shewing how far the one is to the ,northward or ,southward of the other1 which can never exceed #ahj degrees4 ,and when the two places are in the same hemisphere 7or on the same side of the equator7 the lesser latitude subtracted from the greater1 and when they are on different sides of the equator1 the two latitudes added1 gives the difference of latitude4 ,sidenote3 ,longitude4 #c4 ,the ,longitude of any place 7upon the ,earth7 is an arch of the equator1 contained betwixt the meridian of the given place1 and some fixed or known meridian2 or1 it is equal to the angle formed by the two meridians1 which properly can never exceed #ahj degrees1 tho' sometimes the ,longitude is counted ,easterly quite round the globe4 ,since the meridians are all moveable1 and not one that can be fixed in the heavens1 7as the equinoctial circle is fixed1 from whence the latitudes of all places are determined to be so much either ,north or ,south7 the longitudes of places cannot so well be fixed from any other meridian1 but every ,geographer is at his liberty to make which he pleases his first meridian1 from whence to calculate the longitudes of other places4 ,hence it is that geographers of different nations reckon their longitudes from different meridians1 commonly choosing the meridian passing through the metropolis of their own country for their first3 ,thus1 the ,english geographers generally make the meridian of ,london to be their first1 the ,french that of ,paris1 and the ,dutch that of ,amsterdam1 c4 and mariners generally reckon the longitude from the last known land they saw4 ,this arbitrary way of reckoning the longitude from different places1 makes it necessary1 whenever we express the longitude of any place1 that the place from whence it is counted be also expressed4 ,from the preceding definitions arise the following corollaries3 #a4 ,if a body should steer directly ,north1 or directly ,south1 quite round the globe1 he'll continually change his latitude2 and pass through the two ,poles of the world1 without deviating the least from the meridian of the place he departed from2 and consequently on his return will not differ in his account of time from the people residing in the said place4 #b4 ,if a body should steer round the globe either due ,east1 or due ,west1 he'll continually change his longitude1 but will go quite round without altering his latitude2 and if his course should be due ,east1 he'll gain a day compleatly in his reckoning1 or reckon one day more than the inhabitants of the place from whence he departed2 or if his course had been ,west1 he would have lost one day1 or reckon one less4 ,the reason of which is evident2 for admitting our traveller steers due ,east2 so many miles in one day as to make his difference of longitude equivalent to a quarter of an hour of time1 it is evident that the next day the ,sun will rise to him a quarter of an hour sooner than to the inhabitants of the place from whence he departed2 and so daily1 in proportion to the rate he travels1 which in going quite round1 will make up one natural day4 ,in like manner1 if he steers due ,west after the same rate1 he'll lengthen each day a quarter of an hour1 and consequently the ,sun will rise to him so much later every day2 by which means1 in going quite round1 he'll lose one day compleat in his reckoning4 ,from whence it follows1 #c4 ,if two bodies should set out from the same place1 one steering ,east1 and the other ,west1 and so continue their courses quite round1 until they arrive at the place from whence they set out1 they'll differ two days in their reckoning at the time of their return4 #d4 ,if a body should steer upon an oblique course 7or any where betwixt the meridian and the ,east or ,west points7 he'll continually change both latitude and longitude1 and that more or less1 according to the course he steers2 and if he should go quite round the globe1 he'll differ in his account of time1 as by the second ,corol4 #e4 ,the people residing in the ,easternmost of any two places1 will reckon their time so much the sooner than those who live in the other place1 according to the difference of longitude betwixt the two places1 allowing one hour for every #ae degrees1 c4 and the contrary4 ,,ii4 ,of ,zones and ,climates1 c4 ,sidenote3 ,zones1 ,torrid1 ,temperate1 and ,frigid4 #d4 ,zones are large tracts of the surface of the ,earth1 distinguished by the tropics and polar circles1 being five in number2 viz4 one ,torrid1 two ,temperate and two ,frigid4 ,the ,torrid1 or ,burning ,zone1 is all the space comprehended between the two tropics2 the ancients imagined this tract of the ,earth to be uninhabitable1 because of the excessive heat1 it being so near the ,sun4 ,all the inhabitants of the torrid zone have the ,sun in their zenith1 or exactly over their heads twice in every year2 excepting those who live exactly under the two tropics1 where the ,sun comes to their zenith only once in a year4 ,the two ,temperate ,zones lie on either side of the globe1 between the tropics and the polar circles4 ,the two ,frigid ,zones are those spaces upon the globe that are included between the two polar circles4 ,sidenote3 ,amphiscians4 ,sidenote3 ,ascians4 ,the inhabitants of the ,earth are also distinguished by the diversity of their ,shadows4 ,those who live in the torrid zone1 are called ,amphiscians1 because their noon-shadow is cast different ways1 according as the ,sun is to the northward or southward of their zenith2 but when the ,sun is in their zenith1 they are called ,ascians4 ,sidenote3 ,heteroscians4 ,sidenote3 ,ascians ,heteroscians4 ,sidenote3 ,periscians4 ,the inhabitants of the temperate zones1 are called ,heteroscians1 because their noon-shadow is always cast the same way3 ,but those who live under the tropics are called ,ascians ,heteroscians2 those who live in the frigid zones are called ,periscians1 because sometimes their shadow is cast round about them4 ,these hard names are only ,greek words1 importing how the ,sun casts the shadow of the several inhabitants of the ,earth2 which would be a too trifling distinction to be made here1 was it not for the sake of complying with custom4 ,the inhabitants of the ,earth are also distinguished into three sorts1 in respect to their relative situation to one another1 and these are called the ,perici1 ,antci1 and ,antipodes4 ,sidenote3 ,perici4 #e4 ,the ,perici are those who live under opposite points of the same parallel of latitude4 ,they have their seasons of the year at the same time1 and their days and nights always of the same length with one another1 but the one's ,noon is the other's ,midnight2 and when the ,sun is in the equinoctial1 he rises with the one1 when he sets with the other4 ,those who live under the ,poles have no ,perici4 ,sidenote3 ,antci4 #f4 ,the ,antci live under the same meridian1 and in the same latitude1 but on different sides of the equator2 their ,seasons of the year are contrary1 and the days of the one are equal to the nights of the other1 but the hour of the day and night is the same with both2 and when the ,sun is in the equinoctial1 he rises and sets to both exactly at the same time4 ,those who live under the equator have no ,antci4 ,sidenote3 ,antipodes4 #g4 ,the ,antipodes are those who live diametrically opposite to one another1 standing1 as it were1 exactly feet to feet3 ,their days and nights1 summer and winter1 are at direct contrary times4 ,the surface of the ,earth is by some distinguished into ,climates4 ,sidenote3 ,climates4 #h4 ,a ,climate is a tract of the surface of the ,earth1 included between two such parallels of latitude1 that the length of the longest day in the one exceeds that in the other by half an hour4 ,the whole surface of the ,earth is considered1 as being divided into #fj climates1 viz4 from the equator to each of the polar circles #bd1 arising from the difference of hour in the length of their longest days2 and from the polar circles to the ,poles themselves1 are six1 arising from the difference of an entire month1 the ,sun being seen in the first of these a whole month without setting2 in the second two2 and in the third1 three months1 c4 ,these climates continually decrease in breadth1 the farther they are from the equator4 ,how they are framed1 viz4 the parallel of latitude in which they end 7that being likewise the beginning of the next7 with the respective breadth of each of them1 is shewed in the following table3 ,a ,,table of the ,,climates4 ,,climates between the ,equator and the ,polar ,circles4 ---------------------------------------- ----- ,climates ,longest ,latitude4 ,breadth ,day4 ,d4 ,m4 ,d4 ,m4 ---------------------------------------- ----- #a #ab #h #be #h #be #b #ac #af #be #h #jj #c #ac #bc #ej #g #be #d #ad #cj #be #f #cj ---------------------------------------- ----- #e #ad #cf #bh #f #h #f #ae #da #bb #d #ed #g #ae #de #bi #d #g #h #af #di #a #c #cb ---------------------------------------- ----- #i #af #ea #eh #b #eg #aj #ag #ed #bg #b #bi #aa #ag #ef #cg #b #aj #ab #ah #eh #bi #a #eb ---------------------------------------- ----- #ac #ah #ei #eh #a #bi #ad #ai #fa #ah #a #bj #ae #ai #fb #be #a #g #af #bj #fc #bb #j #eg ---------------------------------------- ----- #ag #bj #fd #f #j #dd #ah #ba #fd #di #j #dc #ai #ba #fe #ba #j #cb #bj #bb #fe #dg #j #bf ---------------------------------------- ----- #ba #bb #ff #f #j #ai #bb #bc #ff #bj #j #ad #bc #bc #ff #bh #j #h #bd #bd #ff #ca #j #c ---------------------------------------- ----- ,,climates between the ,polar ,circles and the ,poles4 -------------------------------- ,length of ,days4 ,latitude4 -------------------------------- ,months4 ,d4 ,m4 #a #fg #ba #b #fi #dh #c #gc #cg #d #gh #cj #e #hd #e #f #jj #jj -------------------------------- ,,iii4 ,of the ,poetical rising and setting of the ,stars4 ,sidenote3 ,cosmical1 ,acronical1 and ,heliacal rising and setting4 ,the ancient ,poets make frequent mention of the ,stars rising and setting1 either ,cosmically1 ,acronically1 or ,heliacally2 whence these distinctions are called ,poetical4 ,a ,star is said to rise or set ,cosmically1 when it rises or sets at ,sun-rising2 and when it rises or sets at ,sun-setting1 it is said to rise or set ,acronically4 ,a ,star rises ,heliacally1 when first it becomes visible1 after it had been so near the ,sun as to be hid by the splendor of his rays3 ,and a ,star is said to set ,heliacally1 when it is first immersed1 or hid by the ,sun's rays4 ,the ,fixed ,stars1 and the three superior ,planets1 ,mars1 ,jupiter1 and ,saturn1 rise ,heliacally in the morning2 but the ,moon rises ,heliacally in the evening1 because the ,sun is swifter than the superior ,planets1 and slower than the ,moon4 ,,iv4 ,of the surface of the ,earth1 considered as it is composed of ,land and ,water4 ,the ,earth consists naturally of two parts1 ,land and ,water1 and therefore it is called the ,terraqueous ,globe4 ,each of these elements is subdivided into various forms and parts1 which accordingly are distinguished by different names4 ,i4 ,of the ,land4 ,the land is distinguished into ,continents1 ,islands1 ,peninsula's1 ,isthmus's1 ,promontories1 ,mountains1 or ,coasts4 ,sidenote3 ,continent4 ,sidenote3 ,main ,land4 #i4 ,a ,continent is a large quantity of land1 in which many great countries are joined together1 without being separated from each other by the sea3 such are ,europe1 ,asia1 ,africa1 and the vast continent of ,america2 which four are the principal divisions of the ,earth4 ,a continent is sometimes called the ,main ,land4 ,sidenote3 ,island4 #aj4 ,an ,island is a country1 or portion of land1 environed round with water3 such are ,great-,britain and ,ireland2 ,sardinia1 ,sicily1 c4 in the ,mediterranean ,sea2 the ,isles of ,wight1 ,anglesey1 c4 near ,england4 ,also a small part of dry land1 in the midst of a river1 is called an island1 when compared to a lesser1 is called the continent2 as if we compare the ,isle of ,wight to ,england1 the latter may be properly called the continent4 ,sidenote3 ,peninsula4 #aa4 ,a ,peninsula is a part of land almost environed with water1 save one narrow neck adjoining it to the continent2 or which is almost an island3 such is ,denmark joining to ,germany2 also ,africa is properly a large peninsula joining to ,asia4 ,sidenote3 ,isthmus4 #ab4 ,an ,isthmus is a narrow neck of land joining a peninsula to the continent2 as the ,isthmus of ,sues1 which joins ,africa to ,asia1 that of ,panama1 joining ,north and ,south ,america1 c4 ,sidenote3 ,promontory4 ,sidenote3 ,mountain4 #ac4 ,a ,promontory is a high part of land stretching out into the sea1 and is often called a ,cape or ,headland3 such is the ,cape of ,good ,hope in the ,south of ,africa2 ,cape ,finistre on the ,west of ,spain2 also the ,lizard ,point1 and the ,land's ,end1 are two ,capes or ,headlands on the ,west of ,england4 ,a ,mountain is a high part of land in the midst of a country1 over topping the adjacent parts4 ,sidenote3 ,a ,coast or ,shore4 ,sidenote3 ,inland4 #ad4 ,a ,coast or ,shore is that part of land which borders upon the sea1 whether it be in islands or a continent3 ,and that part of the land which is far distant from the sea1 is called the ,inland ,country4 ,these are the usual distinctions of the land4 ,the ,water is distinguished into ,oceans1 ,seas1 ,lakes1 ,gulfs1 ,straits1 and ,rivers4 ,sidenote3 ,the ,ocean1 or ,main ,sea4 #ae4 ,the ,ocean1 or ,main ,sea1 is a vast spreading collection of water1 not divided or separated by lands running between2 such is the ,atlantic or ,western ,ocean2 between ,europe and ,america2 the ,pacific ,ocean1 or ,south ,sea1 c4 ,note1 ,those parts of the ocean which border upon the land1 are called by various names1 according to those of the adjacent countries2 as1 the ,british ,sea1 the ,irish ,sea1 the ,french and ,spanish ,sea4 ,sidenote3 ,a ,lake4 #af4 ,a ,lake is a collection of deep standing water1 inclosed all round with land1 and not having any visible and open communication with the sea3 ,but when this lake is very large1 it is commonly called a sea2 as the ,caspian ,sea in ,asia1 c4 ,sidenote3 ,a ,gulf4 ,sidenote3 ,creek or ,haven4 #ag4 ,a ,gulf is a part of the sea almost encompassed with land1 or that which runs up a great way into the land2 as1 the ,gulf of ,venice1 c4 ,but if it be very large1 'tis rather called an ,inland ,sea2 as the ,baltic ,sea1 the ,mediterranean ,sea1 the ,red ,sea1 or the ,arabian ,gulf1 c4 ,and a small part of sea thus environed with land is usually called a ,bay4 ,if it be but a very small ,part1 or1 as it were1 a small arm of the sea1 that runs but a few miles between the land1 it is called a ,creek or ,haven4 ,sidenote3 ,a ,strait4 #ah4 ,a ,strait is a narrow passage lying between two shores1 whereby two seas are joined together2 as1 the ,straits of ,dover1 between the ,british ,channel and the ,german ,sea2 the ,straits of ,gibralter1 between the ,atlantic and the ,mediterranean ,sea4 ,the ,mediterranean itself is also sometimes called the ,straits4 ,these are all the necessary terms commonly used in ,geography4 ,the names of the several countries and seas1 and all the principal divisions of the ,earth1 the reader will find expressed upon the ,terrestrial ,globes4 ,to give a tolerable account of the produce of each country1 the genius of the people1 their political institutions1 c4 is properly a particular subject of itself1 and quite foreign to our design4 ,we shall next proceed to the use of the ,globes2 but first it may not be amiss to take a short review of their appurtenances4 ,those circles of the sphere that are fixed1 are 7as has been already said7 drawn upon the ,globes themselves2 those that are moveable1 are supplied by the ,brass ,meridian1 the ,wooden ,horizon1 and the ,quadrant of ,altitude4 ,sidenote3 ,brass ,meridian4 #a4 ,that side of the ,brazen ,meridian1 which is divided into degrees1 represents the true ,meridian2 this side is commonly turned towards the ,east1 and 'tis usual to place the globe so before you1 that the ,north be to the right hand1 and the ,south to the left4 ,the meridian is divided into #d quadrants1 each being #ij degrees1 two of which are numbered from that part of the equinoctial1 which is above the horizon1 towards each of the ,poles2 the other two quadrants are numbered from the ,poles towards the equator4 ,the reason why two quadrants of the meridian are numbered from the equator1 and the other two from the ,poles1 is because the former of these two serve to shew the distance of any point on the globe from the equator1 and the other to elevate the globe to the latitude of the place4 ,sidenote3 ,wooden ,horizon4 #b4 ,the upper side of the wooden frame called the ,wooden ,horizon2 represents the true horizon2 the circles drawn upon this plane have been already described2 we may observe1 that the first point of is the ,east1 and the opposite being the first point of is the ,west1 the meridian passing through the ,north and ,south points4 ,sidenote3 ,quadrant of ,altitude4 #c4 ,the ,quadrant of ,altitude is a flexible plate of thin brass1 having a nut and screw at one end1 to be fastened to the meridian of either globe1 as occasion requires4 ,the edge of this quadrant which has the graduations upon it1 called the fiducial edge1 is that which is always meant whenever we make mention of the quadrant of altitude4 ,sidenote3 ,hour ,circle4 #d4 ,the ,horary or ,hour ,circle1 is divided into twice twelve hours1 the two ,,xii's coinciding with the meridian2 the uppermost ,,xii is that at ,noon1 and the lowermost towards the horizon is ,,xii at ,night4 ,the hours on the ,east side of the meridian are the ,morning ,hours1 and those on the ,west side the ,hours after ,noon4 ,the axis of the globe carries round the ,hand or ,index which points the hour1 and passes through the center of the hour circle4 ,the things above described are common to both globes2 but there are some others which are peculiar or proper to one sort of globe4 ,the two ,colures1 and the ,circles of ,latitude from the ecliptic1 belong only to the ,celestial ,globes2 also the ecliptic itself does properly belong only to this globe1 tho' it is always drawn on the ,terrestrial1 for the sake of those that might not have the other globe by them4 ,the equinoctial on the celestial globe is always numbered into #cfj degrees1 beginning at the equinoctial point 2 but on the terrestrial1 it is arbitrary1 where these numbers commence1 according to the meridian of what place you intend for your first2 and the degrees may be counted either quite round to #cfj1 or both ways1 'till they meet in the opposite part of the meridian1 at #ahj4 ,illustration ,,sect4 ,,iii4 ,the ,,use of the ,,globes4 ,,problem ,i4 ,to find the ,latitude and ,longitude of any given ,place upon the ,globe2 and on the contrary1 the ,latitude and ,longitude being given1 to find the ,place4 #a4 ,turn the globe round its axis1 'till the given place lies exactly under the 7,eastern side of the brass7 meridian1 then that degree upon the meridian1 which is directly over it1 is the ,latitude2 which is accordingly ,north or ,south1 as it lies in the ,northern or ,southern hemisphere1 the globe remaining in the same position4 ,that degree upon the equator which is cut by the brazen meridian1 is the ,longitude required from the first meridian upon the globe4 ,if the longitude is counted both ways from the first meridian upon the globe1 then we are to consider1 whether the given place lies ,easterly or ,westerly from the first meridian1 and the longitude must be expressed accordingly4 ,the ,latitudes of the following places3 and upon a globe where the longitude is reckoned both ways from the meridian of ,london1 their longitudes will be found as follow3 ,latitude4 ,longitude4 ,deg4 ,deg4 ,rome #da ,north4 #ac ,east4 ,paris #dh ,n4 #b ,e4 ,mexico #bj ,n4 #ajb ,w4 ,cape ,horn #eh ,s4 #hj ,w4 #b4 ,the ,latitude and ,longitude being given to find the ,place4 ,seek for the given longitude in the equator1 and bring that point to the meridian2 then count from the equator on the meridian the degree of latitude given1 towards the arctic and antarctic ,pole1 according as the latitude is ,northerly or ,southerly1 and under that degree of latitude lies the ,place required4 ,,prob4 ,,ii4 ,to find the ,difference of ,latitude betwixt any two given ,places4 ,bring each of the places proposed successively to the meridian1 and observe where they intersect it1 then the number of degrees upon the meridian1 contained between the two intersections1 will be the ,difference of ,latitude required4 ,or1 if the places proposed are on the same side of the equator1 having first found their latitudes1 subtract the lesser from the greater2 but if they are on contrary sides of the equator1 add them both together1 and the difference in the first case1 and the sum in the latter1 will be the difference of latitude required4 ,thus the difference of latitude betwixt ,london and ,rome will be found to be #i degrees2 betwixt ,paris and ,cape ,bona ,esperance #hc degrees4 ,,prob4 ,,iii4 ,to find the ,difference of ,longitude betwixt any two given ,places4 ,bring each of the given places successively to the meridian1 and see where the meridian cuts the equator each time2 the number of degrees contained betwixt those two points1 if it be less than #ahj degrees1 otherwise the remainder to #cfj degrees1 will be the difference of longitude required4 ,or1 ,having brought one of the given places to the meridian1 bring the index of the hour circle to #ab o'clock2 then having brought the other place to the meridian1 the number of hours contained between the place the index was first set at1 and the place where it now points1 is the difference of longitude in time betwixt the two places4 ,thus the difference of longitude betwixt ,rome and ,constantinople will be found to be #ai degrees1 or #a hour and a quarter2 betwixt ,mexico and ,pekin in ,china1 #bdj degrees1 or #i hours4 ,,prob4 ,,iv4 ,any ,place being given to find all those ,places that are in the same ,latitude with the same ,place4 ,the latitude of any given place being marked upon the meridian1 turn the globe round its axis1 and all those places that pass under the same mark are in the same latitude with the given place1 and have their days and nights of equal lengths4 ,and when any place is brought to the meridian1 all the inhabitants that lie under the upper semicircle of it1 have their ,noon or mid-day at the same point of absolute time exactly4 ,,prob4 ,v4 ,the day of the ,month being given2 to find the ,sun's ,place in the ,ecliptic1 and his ,declination4 #a4 ,to find the ,sun's ,place3 ,look for the day of the month given in the kalendar of months upon the horizon1 and right against it you'll find that sign and degree of the ecliptic which the ,sun is in4 ,the ,sun's place being thus found1 look for the same in the ecliptic line which is drawn upon the globe1 and bring that point to the meridian1 then that degree of the meridian1 which is directly over the ,sun's place1 is the ,declination required2 which is accordingly either ,north or ,south1 as the ,sun is in the ,northern or ,southern signs4 ,thus1 ,sun's ,place4 ,declination4 ,deg4 ,min4 ,deg4 ,min4 ,april #bc #c #jj #ab #cb ,n4 ,july #ca #g #ea #ah #bj ,n4 ,october #bf #b #di #ab #bh ,s4 ,january #bj #j #di #bj #jg ,s4 ,,prob4 ,,vi4 ,to rectify the ,globe for the ,latitude1 ,zenith1 and the ,sun's ,place4 #a4 ,for the ,latitude3 ,if the place be in the ,northern hemisphere1 raise the arctic ,pole above the horizon2 but for the ,south latitude you must raise the antarctic2 then move the meridian up and down in the notches1 until the degrees of the latitude counted upon the meridian below the ,pole1 cuts the horizon1 and the globe is adjusted to the latitude4 #b4 ,to rectify the ,globe for the ,zenith3 ,having elevated the globe according to the latitude1 count the degrees thereof upon the meridian from the equator1 towards the elevated ,pole1 and that point will be the zenith or the vertex of the place2 to this point of the meridian fasten the quadrant of altitude1 so that the graduated edge thereof may be joined to the said point4 #c4 ,bring the ,sun's place in the ecliptic to the meridian1 and then set the hour index to ,,xii at ,noon1 and the globe will be rectified to the ,sun's ,place4 ,if you have a little mariner's compass1 the meridian of the globe may be easily set to the meridian of the place4 ,,prob4 ,,vii4 ,to find the ,distance between any two given places upon the ,globe1 and to find all those places upon the globe that are at the same distance from a given place4 ,lay the quadrant of altitude over both the places1 and the number of degrees intercepted between them being reduced into miles1 will be the distance required3 ,or1 you may take the distance betwixt the two places with a pair of compasses1 and applying that extent to the equator1 you'll have the degrees of distance as before4 ,note1 ,a geographical mile is the _/th part of a degree2 whereof if you multiply the number of degrees by #fj1 the product will be the number of geographical miles of distance sought2 but to reduce the same into ,english miles1 you must multiply by #gj1 because about #gj ,english miles make a degree of a great circle upon the superficies of the ,earth4 ,thus1 the distance betwixt ,london and ,rome will be found to be about #ac degrees1 which is #ghj geographical miles4 ,if you rectify the globe for the latitude and zenith of any given place1 and bring the said place to the meridian2 then turning the quadrant of altitude about1 all those places that are cut by the same point of it1 are at the same distance from the given place4 ,,prob4 ,,viii4 ,to find the angle of position of ,places1 or the angle formed by the meridian of one ,place1 and a great circle passing through both the ,places4 ,having rectified the globe for the latitude and zenith of one of the given places1 bring the said place to the meridian1 then turn the quadrant of altitude about1 until the fiducial edge thereof cuts the other place1 and the number of degrees upon the horizon1 contained between the said edge and the meridian1 will be the angle of position sought4 ,thus1 the angle of position at the ,lizard1 between the meridian of the ,lizard and the great circle1 passing from thence to ,barbadoes is #fi degrees ,south-,westerly2 but the angle of position between the same places at ,barbadoes1 is but #ch degrees ,north-,easterly4 ,,scholium ,the angle of position between two places is a different thing from what is meant by the bearings of places2 the ,bearings of two places is determined by a sort of spiral line1 called a ,rhumb ,line1 passing between them in such a manner1 as to make the same or equal angles with all the meridians through which it passeth2 but the angle or position is the very same thing with what we call the azimuth in astronomy1 both being formed by the meridian and a great circle passing thro' the zenith of a given place in the heavens1 then called the azimuth1 or upon the ,earth1 then called the angle of position4 ,from hence may be shewed the error of that geographical paradox1 viz4 ,if a place ,a bears from another ,b due ,west1 ,b shall not bear from ,a due ,east4 ,i find this paradox vindicated by an author1 who at the same time gives a true definition of a rhumb line3 ,but his arguments are ungeometrical2 for if it be admitted that the ,east and ,west lines make the same angles with all the meridians through which they pass1 it will follow that these lines are the parallels of latitude3 ,for any parallel of latitude is the continuation of the surface of a ,cone1 whose sides are the radii of the sphere1 and circumference of its base the said parallel2 and it is evident1 that all the meridians cut the said surface at right 7and therefore at equal7 angles2 whence it follows1 that the rhumbs of ,east and ,west are the parallels of latitude1 though the case may seem different1 when we draw inclining lines 7like meridians7 upon paper1 without carrying our ideas any farther4 ,,prob4 ,,ix4 ,to find the ,antci1 ,perici1 and ,antipodes to any given place4 ,bring the given place to the meridian2 and having found its latitude1 count the same number of degrees on the meridian from the equator towards the contrary ,pole1 and that will give the place of the ,antci4 ,the globe being still in the same position1 set the hour index to ,,xii at noon1 then turn the globe about 'till the index points to the lower ,,xii2 the place which then lies under the meridian1 having the same latitude with the given place1 is the ,perici required4 ,as the globe now stands1 the ,antipodes of the given place are under the same point of the meridian1 that its ,antci stood before3 ,or1 if you reckon #ahj degrees upon the meridian from the given place1 that point will be the ,antipodes4 ,let the given place be ,london1 in the latitude of #ea degrees ,north1 that place which lies under the same meridian and the latitude #ea degrees ,south1 is the ,antci2 that which lies in the same parallel with ,london1 and #ahj degrees of longitude from it1 is the ,perici1 and the ,antipodes is the place whose longitude from ,london is #ahj degrees1 and latitude #ea degrees ,south4 ,,prob4 ,x4 ,the ,hour of the ,day at one place being given2 to find the correspondent ,hour 7or what o',clock it is at that time7 in any other place4 ,the difference of time betwixt two places is the same with their difference of longitude2 wherefore having found their difference of longitude1 reduced into time 7by allowing one hour for every #ae degrees1 c47 and if the place where the hour is required lies 7,easterly_/,westerly7 from the place where the hour is given1 7add_/subtract7 the difference of longitude reduced into time 7to_/from7 the hour given2 and the sum or remainder will accordingly be the hour required4 ,or1 ,having brought the place at which the hour is given to the meridian1 set the hour index to the given hour2 then turn the globe about until the place where the hour is required comes to the meridian1 and the index will point out the hour at the said place4 ,thus when it is ,noon at ,london1 it is ,h4 ,m4 ,rome #j #eb ,p4 ,m4 ,at ,constantinople #b #jg ,p4 ,m4 ,vera-,cruz #e #cj ,a4 ,m4 ,pekin in ,china #g #ej ,p4 ,m4 ,,prob4 ,,xi4 ,the ,day of the ,month being given1 to find those places on the globe where the ,sun will be ,vertical1 or in the ,zenith1 that day4 ,having found the ,sun's place in the ecliptic1 bring the same to the meridian1 and note the degree over it2 then turning the globe round1 all places that pass under that degree will have the ,sun vertical that day4 ,,prob4 ,,xii4 ,a place being given in the ,torrid ,zone1 to find those two ,days in which the ,sun shall be ,vertical to the same4 ,bring the given place to the meridian1 and mark what degree of latitude is exactly over it2 then turning the globe about its axis1 those two points of the ecliptic1 which pass exactly under the said mark1 are the ,sun's place2 against which1 upon the wooden horizon1 you'll have the days required4 ,,prob4 ,,xiii4 ,to find where the ,sun is ,vertical at any given time assigned2 or the ,day of the ,month and the ,hour at any ,place 7suppose ,london7 being given1 to find in what place the ,sun is ,vertical at that very time4 ,having found the ,sun's declination1 and brought the first place 7,london7 to the meridian1 set the index to the given hour1 then turn the globe about until the index points to ,,xii at noon2 which being done1 that place upon the globe which stands under the point of the ,sun's declination upon the meridian1 has the ,sun that moment in the ,zenith4 ,,prob4 ,,xiv4 ,the ,day1 and the ,hour of the ,day at one place1 being given2 to find all those places upon the ,earth1 where the ,sun is then ,rising1 ,setting1 ,culminating 7or on the meridian7 also where it is ,day-light1 ,twilight1 ,dark ,night1 ,midnight2 where the ,twilight then begins1 and where it ends2 the height of the ,sun in any part of the illuminated hemisphere2 also his depression in the obscure hemisphere4 ,having found the place where the ,sun is vertical at the given hour1 rectify the globe for that latitude1 and bring the said place to the meridian4 ,then all those places that are in the ,western semicircle of the horizon1 have the ,sun rising at that time4 ,those in the ,eastern semicircle have it setting4 ,to those who live under the upper semicircle of the meridian1 it is #ab o'clock at noon4 ,and1 ,those who live under the lower semicircle of the meridian1 have it at midnight4 ,all those places that are above the horizon1 have the ,sun above them1 just so much as the places themselves are distant from the horizon2 which height may be known by fixing the quadrant of altitude in the zenith1 and laying it over any particular place4 ,in all those places that are #ah degrees below the ,western side of the horizon1 the twilight is just beginning in the morning1 or the day breaks4 ,and in all those places that are #ah degrees below the ,eastern side of the horizon1 the twilight is ending1 and the total darkness beginning4 ,the twilight is in all those places whose depression below the horizon does not exceed #ah degrees4 ,and1 ,all those places that are lower than #ah degrees1 have dark night4 ,the depression of any place below the horizon is equal to the altitude of its ,antipodes1 which may be easily found by the quadrant of altitude4 ,,prob4 ,,xv4 ,the ,day of the ,month being given2 to show1 at one view1 the length of ,days and ,nights in all places upon the ,earth at that time2 and to explain how the vicissitudes of ,day and ,night are really made by the motion of the ,earth round her axis in #bd hours1 the ,sun standing still4 ,the ,sun always illuminates one half of the globe1 or that hemisphere which is next towards him1 while the other remains in darkness3 ,and if 7as by the last problem7 we elevate the globe according to the ,sun's place in the ecliptic1 it is evident1 that the ,sun 7he being at an immense distance from the ,earth7 illuminates all that hemisphere1 which is above the horizon2 the wooden horizon itself1 will be the circle terminating light and darkness2 and all those places that are below it1 are wholly deprived of the solar light4 ,the globe standing in this position1 those arches of the parallels of latitude which stand above the horizon1 are the ,diurnal ,arches1 or the length of the day in all those latitudes at that time of the year2 and the remaining parts of those parallels1 which are below the horizon1 are the ,nocturnal ,arches1 or the length of the night in those places4 ,the length of the diurnal arches may be found by counting how many hours are contained between the two meridians1 cutting any parallel of latitude1 in the ,eastern and ,western parts of the horizon4 ,in all those places that are in the ,western semicircle of the horizon1 the ,sun appears rising3 ,for the ,sun1 standing still in the vertex 7or above the brass meridian7 appears ,easterly1 and #ij degrees distant from all those places that are in the ,western semicircle of the horizon2 and therefore in those places he is then rising4 ,now1 if we pitch upon any particular place upon the globe1 and bring it to the meridian1 and then bring the hour index to the lower #ab1 which in this case1 we'll suppose to be #ab at noon2 7because otherwise the numbers upon the hour circle will not answer our purpose7 and afterwards turn the globe about1 until the aforesaid place be brought to the ,western side of the horizon2 the index will then shew the time of the ,sun rising in that place4 ,then turn the globe gradually about from ,west to ,east1 and minding the hour index1 we shall see the progress made in the day every hour1 in all latitudes upon the globe1 by the real motion of the ,earth round its axis2 until1 by their continual approach to the brass meridian 7over which the ,sun stands still all the while7 they at last have noon day1 and the ,sun appears at the highest2 and then by degrees1 as they move ,easterly the ,sun seems to decline ,westward1 until1 as the places successively arrive in the ,eastern part of the horizon1 the ,sun appears to set in the ,western3 ,for the places that are in the horizon1 are #ij degrees distant from the ,sun4 ,we may observe1 that all places upon the ,earth1 that differ in latitude1 have their days of different length 7except when the ,sun is in the equinoctial7 being longer or shorter1 in proportion to what part of the parallels stands above the horizon4 ,those that are in the same latitude1 have their days of the same length2 but have them commence sooner or later1 according as the places differ in longitude4 ,,prob4 ,,xvi4 ,to explain in general the alteration of ,seasons1 or length of the ,days and ,nights made in all places of the ,world1 by the ,sun's 7or the ,earth's7 annual motion in the ,ecliptic4 ,it has been shewed in the last problem1 how to place the globe in such a position as to exhibit the length of the diurnal and nocturnal arches in all places of the ,earth1 at a particular time3 ,if the globe be continually rectified1 according as the ,sun alters his declination1 7which may be known by bringing each degree of the ecliptic successively to the meridian7 you'll see the gradual increase or decrease made in the days1 in all places of the ,world1 according as a greater or lesser portion of the parallels of latitude1 stands above the horizon4 ,we shall illustrate this problem by examples taken at different times of the year4 #a4 ,let the ,sun be in the first point of 7which happens on the #bast of ,june7 that point being brought to the meridian1 will shew the ,sun's declination to be #bc degrees ,north2 then the globe must be rectified to the latitude of #bc degrees2 and for the better illustration of the problem1 let the first meridian upon the globe be brought under the brass meridian4 ,the globe being in this position1 you'll see at one view the length of the days in all latitudes1 by counting the number of hours contained between the two extreme meridians1 cutting any particular parallel you pitch upon1 in the ,eastern and ,western part of the horizon4 ,and you may observe that the lower part of the arctic circle just touches the horizon1 and consequently all the people who live in that latitude have the ,sun above their horizon for the space of #bd hours1 without setting2 only when he is in the lower part of the meridian 7which they would call #ab at night7 he just touches the horizon4 ,to all those who live between the arctic circle and the ,pole1 the ,sun does not set1 and its height above the horizon1 when he is in the lower part of the meridian1 is equal to their distance from the arctic circle3 ,for example1 ,those who live in the #hc;d parallel have the ,sun when he is lowest at this time #ac degrees high4 ,if we cast our eye ,southward1 towards the equator1 we shall find1 that the diurnal arches1 or the length of days in the several latitudes1 gradually lessen3 ,the diurnal arch of the parallel of ,london at this time is #af hours2 that of the ,equator 7is always7 #ab hours2 and so continually less1 'till we come to the ,antarctic ,circle1 the upper part of which just touches the horizon2 just those who live in this latitude have just one sight of the ,sun1 peeping as it were in the horizon3 ,and all that space between the antarctic circle and the ,south ,pole1 lies in total darkness4 ,if from this position we gradually move the meridian of the globe according to the progressive alterations made in the ,sun's declination1 by his motion in the ecliptic1 we shall find the diurnal arches of all those parallels1 that are on the ,northern side of the equator1 continually decrease2 and those on the ,southern side continually increase1 in the same manner as the days in those places shorten and lengthen4 ,let us again observe the globe when the ,sun has got within #aj degrees of the equinoctial2 now the lower part of the #hjth parallel of ,north latitude just touches the horizon1 and all the space betwixt this and the pole1 falls in the illuminated hemisphere3 but all those parallels that lie betwixt this and the arctic circle1 which before were wholly above the horizon1 do now intersect it1 and the ,sun appears to them to rise and set4 ,from hence to the equator1 we shall find that the days have gradually shortened2 and from the equator ,southward1 they have gradually lengthened1 until we come to the #hjth parallel of the ,south latitude2 the upper part of which just touches the horizon2 and all places betwixt this and the ,south ,pole are in total darkness2 but those parallels betwixt this and the antarctic circle1 which before were wholly upon the horizon1 are now partly above it2 the length of their days being exactly equal to that of the nights in the same latitude in the contrary hemisphere4 ,this also holds universally1 that the length of one day in one latitude ,north1 is exactly equal to the length of the night in the same latitude ,south2 and vice versa4 ,let us again follow the motion of the ,sun1 until he has got into the equinoctial1 and take a view of the globe while it is in this position4 ,now all the parallels of latitude are cut into two equal parts by the horizon1 and consequently the days and nights are of equal lengths1 viz4 #ab hours each1 in all places of the world2 the ,sun rising and setting at six o'clock1 excepting under the two ,poles1 which now lie exactly in the horizon3 ,here the ,sun seems to stand still in the same point of the heavens for some time1 until by degrees1 by his motion in the ecliptic1 he ascends higher to one and disappears to the other1 there being properly no days and nights under the ,poles2 for there the motion of the ,earth round its axis cannot be observed4 ,if we follow the motion of the ,sun towards the ,southern tropic1 we shall see the diurnal arches of the ,northern parallels continually decrease1 and the ,southern ones increase in the same proportion1 according to their respective latitudes2 the ,north ,pole continually descending1 and the ,south ,pole ascending1 above the horizon1 until the ,sun arrives into 1 at which time all the space within the antarctic circle is above the horizon2 while the space between the arctic circle1 and its neighbouring ,pole1 is in total darkness4 ,and we shall now find all other circumstances quite reverse to what they were when the ,sun was in 2 the nights now all over the world being of the same length that the days were of before4 ,we have now got to the extremity of the ,sun's declination2 and if we follow him through the other half of the ecliptic1 and rectify the globe accordingly1 we shall find the seasons return in their order1 until at length we bring the globe into its first position4 ,the two foregoing problems were not1 as ,i know of1 published in any book on this subject before2 and ,i have dwelt the longer upon them1 because they very well illustrate how the vicissitudes of days and nights are made all over the world1 by the motion of the ,earth round her axis2 the horizon of the globe being made the circle1 separating light and darkness1 and so the ,sun to stand still in the vertex4 ,and if we really could move the meridian1 according to the change of the ,sun's declination1 we should see at one view1 the continual change made in the length of days and nights1 in all places on the ,earth2 but as globes are fitted up1 this cannot be done2 neither are they adapted for the common purposes1 in places near the equator1 or any where in the ,southern hemisphere4 ,but this inconvenience is now remedied 7at a small additional expence7 by the hour circle being made to shift to either ,pole2 and some globes are now made with an hour circle fixed to the globe at each ,pole between the globe and meridian1 so as to have none without side to interrupt the meridian from moving quite round the wooden horizon4 ,,prob4 ,,xvii4 ,to shew by the globe1 at one view1 the longest of the ,days and ,nights in any particular places1 at all times of the ,year4 ,because the ,sun1 by his motion in the ecliptic1 alters his declination a small matter every day2 if we suppose all the torrid zone to be filled up with a spiral line1 having so many turnings2 or a screw having so many threads1 as the ,sun is days in going from one tropic to the other3 ,and these threads at the same distance from one another in all places1 as the ,sun alters his declination in one day in all those places respectively3 ,this spiral line or screw will represent the apparent paths described by the ,sun round the ,earth every day2 and by following the thread from one tropic to the other1 and back again1 we shall have the path the ,sun seems to describe round the ,earth in a year4 ,but because the inclinations of these threads to one another are but small1 we may suppose each diurnal path to be one of the parallels of latitude1 drawn1 or supposed to be drawn upon the globe4 ,thus much being premised1 we shall explain this ,problem1 by placing the globe according to some of the most remarkable positions of it1 as before we did for the most remarkable seasons of the year4 ,in the preceding problem1 the globe being rectified according to the ,sun's declination1 the upper parts of the parallels of latitude1 represented the ,diurnal ,arches1 or the length of the days all over the world1 at that particular time3 ,here we are to rectify the globe according to the latitude of the place1 and then the upper parts of the parallels of declination are the diurnal arches2 and the length of the days at all times of the year1 may be here determined by finding the number of hours contained between the two extreme meridians1 which cut any parallel of declination in the ,eastern and ,western points of the horizon2 after the same manner1 as before we found the length of the day in the several latitudes at a particular time of the year4 #a4 ,let the place proposed be under the equinoctial1 and let the globe be accordingly rectified for #jj degrees of latitude1 which is called a direct position of the sphere4 ,here all the parallels of latitude1 which in this case we will call the parallels of declination1 are cut by the horizon into two equal parts2 and consequently those who live under the equinoctial1 have the days and nights of the same length at all times of the year2 and also in this part of the ,earth1 all the ,stars rise and set1 and their continuance above the horizon1 is equal to their stay below it1 viz4 #ab hours4 ,if from this position we gradually move the globe according to the several alterations of latitudes1 which we will suppose to be ,northerly2 the lengths of the ,diurnal ,arches will continually increase1 until we come to a parallel of declination1 as far distant from the equinoctial1 as the place itself is from the ,pole4 ,this parallel will just touch the horizon1 and all the heavenly bodies that are betwixt it and the ,pole never descend below the horizon4 ,in the mean time1 while we are moving the globe1 the lengths of the diurnal arches of the ,southern parallels of declination1 continually diminish in the same proportion that the ,northern ones increased2 until we come to that parallel of declination which is so far distant from the equinoctial ,southerly1 as the place itself is from the ,north ,pole4 ,the upper part of this ,parallel just touches the horizon1 and all the ,stars that are betwixt it and the ,south ,pole never appear above the horizon4 ,and all the nocturnal arches of the ,southern parallels of declination1 are exactly of the same length with the diurnal arches of the correspondent parallels of ,north declination4 #b4 ,let us take a view of the globe when it is rectified for the latitude of ,london1 or #ea degrees ,north4 ,when the ,sun is in the tropic of 1 the day is about #af hours2 as he recedes from this tropic1 the days proportionably shorten1 until1 he arrives into 1 and then the days are at the shortest1 being now of the same length with the night1 when the ,sun was in 1 viz4 #g hours4 ,the lower part of that parallel of declination1 which is #ch degrees from the equinoctial ,northerly1 just touches the horizon2 and the ,stars that are betwixt this parallel and the ,north ,pole1 never set to us at ,london4 ,in like manner the upper part of the ,southern parallel of #ch degrees just touches the horizon1 and the ,stars that lie betwixt this parallel and the ,southern ,pole1 are never visible in this latitude4 ,again1 let us rectify the globe for the latitude of the ,arctic ,circle1 we shall then find1 that when the ,sun is in 1 he touches the horizon on that day without setting1 being #bd hours compleat above the horizon2 and when he is in ,capricorn1 he once appears in the horizon1 but does not rise in the space of #bd hours3 ,when he is in any other point of the ecliptic1 the days are longer or shorter1 according to his distance from the tropics4 ,all the ,stars that lie between the tropic of ,cancer1 and the ,north ,pole1 never set in this latitude2 and those that are between the tropic of ,capricorn1 and the ,south ,pole1 are always hid below the horizon4 ,if we elevate the globe still higher1 the circle of perpetual ,apparition will be nearer the equator1 as will that of perpetual ,occultation on the other side4 ,for example1 ,let us rectify the globe for the latitude of #hj degrees ,north3 when the ,sun's declination is #aj degrees ,north2 he begins to turn above the horizon without setting2 and all the while he is making his progress from this point to the tropic of 1 and back again1 he never sets4 ,after the same manner1 when his declination is #aj degrees ,south1 he is just seen at noon in the horizon2 and all the while he is going ,southward1 and back again1 he disappears1 being hid just so long as before1 at the opposite time of the year he appeared visible4 ,let us now bring the ,north ,pole into the ,zenith1 then will the equinoctial coincide with the horizon2 and consequently all the ,northern parallels are above the horizon1 and all the ,southern ones below it4 ,here is but one day and one night throughout the year1 it being day all the while the ,sun is to the ,northward of the equinoctial1 and night for the other half year4 ,all the ,stars that have ,north declination1 always appear above the horizon1 and at the same height2 and all those that are on the other side1 are never seen4 ,what has been here said of rectifying the globe to ,north latitude1 holds for the same latitude ,south2 only that before the longest days were1 when the ,sun was in 1 the same happening now when the ,sun is in 2 and so of the rest of the parallels1 the seasons being directly opposite to those who live in different hemispheres4 ,i shall again explain some things delivered above in general terms1 by particular problems4 ,but from what has been already said1 we may first make the following observations3 #a4 ,all places of the ,earth do equally enjoy the benefit of the ,sun1 in respect of time1 and are equally deprived of it1 the ,days at one time of the ,year1 being exactly equal to the ,nights at the opposite season4 #b4 ,in all places of the ,earth1 save exactly under the ,poles1 the ,days and ,nights are of equal length 7viz4 #ab hours each7 when the ,sun is in the equinoctial4 #c4 ,those who live under the equinoctial1 have the days and nights of equal lengths at all times of the year4 #d4 ,in all places between the equinoctial and the ,poles1 the days and nights are never equal1 but when the ,sun is in the equinoctial points and 4 #e4 ,the nearer any place is to the equator1 the less is the difference between the length of the artificial days and nights in the said place2 and the more remote the greater4 #f4 ,to all the inhabitants lying under the same parallel of latitudes the days and nights are of equal lengths1 and that at all times of the year4 #g4 ,the ,sun is vertical twice a year to all places between the tropics2 to those under the tropics1 once a year2 but never any where else4 #h4 ,in all places between the ,polar ,circles1 and the ,poles1 the ,sun appears some number of days without setting2 and at the opposite time of the year he is for the same length of time without rising2 and the nearer unto1 or further remote from the ,pole1 those places are1 the longer or shorter is the ,sun's continued presence or absence from the ,pole4 #i4 ,in all places lying exactly under the ,polar ,circles1 the ,sun1 when he is in the nearest tropic1 appears #bd hours without setting2 and when he is in the contrary tropic1 he is for the same length of time1 without rising2 but at all other times of the year1 he rises and sets there1 as in other places4 #aj4 ,in all places lying in the 7,northern_/,southern7 hemisphere1 the longest day and shortest night1 is when the ,sun is in the 7,northern_/,southern7 tropic1 and on the contrary4 ,,prob4 ,,xviii4 ,the ,latitude of any place1 not exceeding #ff degrees1 and the day of the ,month being given2 to find the time of ,sun-rising and setting1 and the length of the ,day and ,night4 ,having rectified the globe according to the latitude1 bring the ,sun's place to the meridian1 and put the hour index to #ab at noon2 then bring the ,sun's place the ,eastern part of the horizon1 and the index will shew the time when the ,sun rises4 ,again1 turn the globe until the ,sun's place be brought to the ,western side of the horizon1 and the index will shew the time of ,sun-setting4 ,the hour of ,sun-setting doubled1 gives the length of the day2 and the hour of ,sun-rising doubled1 gives the length of the night4 ,let it be required to find when the ,sun rises and sets at ,london on the #bjth of ,april4 ,rectify the globe for the latitude of ,london1 and having found the ,sun's place corresponding to ,may the #ast1 viz4 #aj degrees1 bring to #aj degrees to the meridian1 and set the index to #ab at noon2 then turn the globe about 'till #aj degrees be brought to the ,eastern part of the horizon1 and you'll find the index point #d hours1 this being doubled1 gives the length of the night #i hours4 ,again1 bring the ,sun's place to the ,western part of the horizon1 and the index will point #g hours1 which is the time of ,sun-setting2 this being doubled1 gives the length of the day #ad hours4 ,,prob4 ,,xix4 ,to find the length of the longest and shortest ,day and ,night in any given place1 not exceeding #ff degrees of ,latitude4 ,note1 ,the longest day at all places on the 7,north_/,south7 side of the equator1 is when the ,sun is in the first point of 7,cancer_/,capricorn7 ,wherefore having rectified the globe for the latitude1 find the time of ,sun-rising and setting1 and thence the length of the day and night1 as in the last problem1 according to the place of the ,sun3 ,or1 having rectified the globe for the latitude1 bring the solstitial point of that hemisphere1 to the ,east part of the horizon1 and set the index to #ab at noon2 then turning the globe about 'till the said solstitial point touches the ,western side of the horizon1 the number of hours from noon to the place where the index points 7being counted according to the motion of the index7 is the length of the longest day2 the complement whereof to #bd hours1 is the length of the shortest night1 and the reverse gives the shortest day and the longest night4 ,longest ,day4 ,shor4 ,n4 ,deg4 ,hours4 ,hours4 #de #ae #h ,thus in ,lat4 #ea #af #g #fj #ah #e ,if from the length of the longest day1 you subtract #ab hours1 the number of half hours remaining1 will be the ,climate3 ,thus that place where the longest day is #af hours1 lies in the #ith ,climate4 ,and by the reverse1 having the ,climate1 you have thereby the length of the longest day4 ,,prob4 ,,xx4 ,to find in what ,latitude the longest ,day is1 of any given length1 less than #bd hours4 ,bring the solstitial point to the meridian1 and set the index to #ab at noon2 then turn the globe ,westward1 'till the index points at half the number of hours given2 which being done1 keep the globe from turning round its axis1 and slide the meridian up or down in the notches1 'till the solstitial point comes to the horizon1 then that elevation of the ,pole will be the latitude4 ,if the hours given be #af1 the latitude is #di degrees2 if #bj hours1 the latitude is #fc degrees4 ,,prob4 ,,xxi4 ,a place being given in one of the ,frigid ,zones 7suppose the ,northern7 to find what number of ,days 7of #bd hours each7 the ,sun doth constantly shine upon the same1 how long he is absent1 and also the first and last ,day of his appearance4 ,having rectified the globe according to the latitude1 turn it about until some point in the first quadrant of the ecliptic 7because the latitude is ,north7 intersects the meridian in the ,north point of the horizon2 and right against that point of the ecliptic on the horizon1 stands the day of the month when the longest day begins4 ,and if the globe be turned about 'till some point in the second quadrant of the ecliptic cuts the meridian in the same point of the horizon1 it will shew the ,sun's place when the longest day ends1 whence the day of the month may be found1 as before3 ,then the number of natural days contained between the times the longest day begins and ends is the length of the longest day required4 ,again1 turn the globe about1 until some point in the third quadrant of the ecliptic cuts the meridian in the ,south part of the horizon2 that point of the ecliptic will give the time when the longest night begins4 ,lastly1 turn the globe about1 until some point in the fourth quadrant of the ecliptic cuts the meridian in the ,south point of the horizon2 and that point of the ecliptic will be the place of the ,sun when the longest night ends4 ,or1 the time when the longest day or night begins1 being known1 their end may be found by counting the number of days from that time to the succeeding solstice2 then counting the same number of days from the solstitial day1 will give the time when it ends4 ,,prob4 ,,xxii4 ,to find in what ,latitude the longest ,day is1 of any given length less than #ahb ,natural ,days4 ,find a point in the ecliptic half so many degrees distant from the solstitial point1 as there are days given1 and bring that point to the meridian2 then keep the globe from turning round its axis1 and move the meridian up or down until the aforesaid point of the ecliptic comes to the horizon2 that elevation of the ,pole will be the latitude required4 ,if the days given were #gh1 the latitude is #ga degrees4 ,this method is not accurate1 because the degrees in the ecliptic do not correspond to natural days2 and also because the ,sun does not always move in the ecliptic at the same rate2 however1 such problems as these may serve for amusements4 ,,prob4 ,,xxiii4 ,the day of the ,month being given1 to find when the ,morning and ,evening ,twilight begins and ends1 in any place upon the ,globe4 ,in the foregoing problem1 by the length of the day1 we mean the time from ,sun-rising to ,sun-set2 and the night we reckoned from ,sun-set1 'till he rose next morning4 ,but it is found by experience1 that ,total ,darkness does not commence in the evening1 'till the ,sun has got #ah degrees below the horizon2 and when he comes within the same distance of the horizon next morning1 we have the first ,dawn of ,day4 ,this faint light which we have in the morning and evening1 before and after the ,sun's rising and setting1 is what we call the ,twilight4 #d ,having rectified the globe for the latitude1 the zenith1 and the ,sun's place1 turn the globe and the quadrant of altitude until the ,sun's place cuts #ah degrees below the horizon 7if the quadrant reaches so far7 then the index upon the hour circle will shew the beginning or ending of twilight after the same manner as before we found the time of the ,sun-rising and setting1 in ,prob4 #ah4 ,but by reason of the thickness of the wooden horizon1 we can't conveniently see1 or compute when the ,sun's place is brought to the point aforesaid4 ,wherefore the globe being rectified as above directed1 turn the globe1 and also the quadrant of altitude1 ,westward1 until that point in the ecliptic1 which is opposite to the ,sun's place1 cuts the quadrant in the #ahth degree above the horizon2 then the hour index will shew the time when day breaks in the morning4 ,and if you turn the globe and the quadrant of altitude1 until the point opposite to the ,sun's place cuts the quadrant in the ,eastern hemisphere1 the hour hand will shew when twilight ends in the evening4 ,or1 having found the time from midnight when the morning twilight begins1 if you reckon so many hours before midnight1 it will give the time when the evening twilight ends4 ,having found the time when twilight begins in the morning1 find the time of ,sun-rising1 by ,prob4 #ah1 and the difference will be the duration of twilight4 ,thus at ,london on the #abth of ,may twilight begins at three quarters past one o'clock3 ,the ,sun rises at about half an hour past four3 ,whence the duration of twilight now is #b hours1 both in the morning and evening4 ,on the #abth of ,november1 the twilight begins at half an hour past six1 being somewhat above an hour before ,sun-rising4 ,,prob4 ,,xxiv4 ,to find the time when total ,darkness ceases1 or when the ,twilight continues from ,sun-setting to ,sun-setting1 in any given place4 ,let the place be in the ,northern hemisphere2 then if the complement of the latitude be greater than 7the depression7 #ah degrees1 subtract #ah degrees from it1 and the remainder will be the ,sun's declination ,north1 when total darkness ceases4 ,but if the complement of the latitude is less than #ah degrees1 their difference will be the ,sun's declination ,south1 when the twilight begins to continue all night4 ,if the latitude is ,south1 the only difference will be1 that the ,sun's declination will be on the contrary side4 ,thus at ,london1 when the ,sun's declination ,north is greater than #bj degrees1 there is no total darkness1 but constant twilight1 which happens from the #bfth of ,may to the #ahth of ,july1 being near two months4 ,under the ,north ,pole the twilight ceases1 when the ,sun's declination is greater than #ah degrees ,south1 which is from the #acth of ,november1 'till the #bith of ,january3 ,so that notwithstanding the ,sun is absent in this part of the world for half a year together1 yet total darkness does not continue above #aa weeks2 and besides1 the ,moon is above the horizon for a whole fortnight of every month throughout the year4 ,,prob4 ,,xxv4 ,the day of the ,month be given2 to find those places of the ,frigid ,zones1 where the ,sun begins to shine continually without setting2 and also those places where he begins to be totally absent4 ,bring the ,sun's place to the meridian1 and mark the number of degrees contained betwixt that point and the equator2 then count the same number of degrees from the nearest ,pole 7viz4 the ,north ,pole1 if the ,sun's declination is ,northerly1 otherwise the ,south ,pole7 towards the equator1 and note that point upon the meridian2 then turn the globe about1 and all the places which pass under the said point1 are those where the ,sun begins to shine constantly1 without setting on the given day4 ,if you lay the same distance from the opposite ,pole towards the equator1 and turn the globe about1 all the places which pass under that point1 will be those where the longest night begins4 ,the ,latitude of the place being given1 to find the hour of the day when the ,sun shines4 ,if it be in the summer1 elevate the ,pole according to the latitude1 and set the meridian due ,north and ,south2 then the shadow of the axis will cut the hour on the ,dial plate3 ,for the globe being rectified in this manner1 the hour circle is a true ,equinoctial ,dial2 the axis of the globe being the ,gnomon4 ,this holds true in ,theory1 but it might not be very accurate in practice1 because of the difficulty in placing the horizon of the globe truly horizontal1 and its meridian due ,north and ,south4 ,if it be in the winter half year1 elevate the ,south ,pole according to the latitude ,north1 and let the ,north part of the horizon be in the ,south part of the meridian2 then the shade of the axis will show the hour of the day as before3 ,but this cannot be so conveniently performed1 tho' the reason is the same as in the former case4 ,to find the ,sun's altitude1 when it shines1 by the ,globe4 ,having set the frame of the globe truly horizontal or level1 turn the ,north ,pole towards the ,sun1 and move the meridian up or down in the notches1 until the axis casts no shadow2 then the arch of the meridian1 contained betwixt the ,pole and the horizon1 is the ,sun's altitude4 ,note1 ,the best way to find the ,sun's altitude1 is by a little quadrant graduated into degrees1 and having sights and a plummet to it3 ,thus1 hold the quadrant in your hand1 so as the rays of the ,sun may pass through both the sights1 the plummet then hanging freely by the side of the instrument1 will cut in the limb the altitude required4 ,these quadrants are to be had at the instrument-makers1 with lines drawn upon them1 for finding the hour of the day1 and the azimuth2 with several other pretty conclusions1 very entertaining for beginners4 ,the ,latitude and the ,day of the ,month being given1 to find the hour of the day when the ,sun shines4 ,having placed the wooden frame upon a level1 and the meridian due ,north and ,south1 rectify the globe for the latitude1 and fix a needle perpendicularly over the ,sun's place3 ,the ,sun's place being brought to the meridian1 set the hour index at #ab at noon1 then turn the globe about until the needle points exactly to the ,sun1 and casts no shadow1 and then the index will shew the hour of the day4 ,,prob4 ,,xxvi4 ,the ,latitude1 the ,sun's ,place1 and his ,altitude1 being given2 to find the hour of the ,day1 and the ,sun's ,azimuth from the ,meridian4 ,having rectified the globe for the latitude1 the zenith1 and the ,sun's place1 turn the globe and the quadrant of altitude1 so that the ,sun's place may cut the given degree of altitude3 then the index will show the hour1 and the quadrant will cut the azimuth in the horizon4 ,thus1 if at ,london1 on the #bast of ,august1 the ,suns altitude1 be #cf degrees in the forenoon1 the hour of the day will be ,,ix1 and the ,sun's azimuth about #eh degrees from the ,south part of the meridian4 ,the ,sun's ,azimuth being given1 to place the ,meridian of the ,globe due ,north and ,south1 or to find a ,meridian ,line when the ,sun shines4 ,let the ,sun's azimuth be #cj degrees ,south-,easterly1 set the horizon of the globe upon a level1 and bring the ,north ,pole into the zenith2 then turn the horizon about until the shade of the axis cuts as many hours as is equivalent to the azimuth 7allowing #ae degrees to an hour7 in the ,north-,west part of the hour circle1 viz4 ,x at night1 which being done1 the meridian of the globe stands in the true meridian of the place4 ,the globe standing in this position1 if you hang two plummets at the ,north and ,south points of the wooden horizon1 and draw a line betwixt them1 you will have a meridian line2 which if it be on a fixed plane 7as a floor or window7 it will be a guide for placing the globe due ,north and ,south1 at any other time4 ,,prob4 ,,xxvii4 ,the ,latitude1 ,hour of the ,day1 and the ,sun's place being given1 to find the ,sun's ,altitude and ,azimuth4 ,rectify the globe for the latitude1 the zenith1 and the ,sun's place1 then the number of degrees contained betwixt the ,sun's place and the vertex1 is the ,sun's meridional zenith distance2 the complement of which to #ij degrees1 is the ,sun's meridian altitude4 ,if you turn the globe about until the index points to any other given hour1 then bringing the quadrant of altitude to cut the ,sun's place1 you will have the ,sun's altitude at that hour2 and where the quadrant cuts the horizon1 is the ,sun's azimuth at the same time4 ,thus ,may the #ast at ,london1 the ,sun's meridian altitude will be #fa degrees2 and at #aj o'clock in the morning1 the ,sun's altitude will be #eb degrees1 and his azimuth about #ej degrees from the ,south part of the meridian4 ,,prob4 ,,xxviii4 ,the ,latitude of the place1 and the day of the ,month being given2 to find the depression of the ,sun below the ,horizon1 and the ,azimuth at any ,hour of the ,night4 ,having rectified the globe for the latitude1 the zenith1 and the ,sun's place1 take a point in the ecliptic exactly opposite to the ,sun's place1 and find the ,sun's altitude and azimuth1 as by the last problem1 and these will be the depression and the altitude required4 ,thus1 if the time given be the #ast of ,december1 at #aj o'clock at night1 the depression and azimuth will be the same as was found in the last problem4 ,,prob4 ,,xxix4 ,the ,latitude1 the ,sun's ,place1 and his ,azimuth being given1 to find his ,altitude1 and the ,hour4 ,rectify the globe for the latitude1 the zenith1 and the ,sun's place1 then put the quadrant of altitude to the ,sun's azimuth in the horizon1 and turn the globe 'till the ,sun's place meet the edge of the quadrant1 then the said edge will shew the altitude1 and the index point to the hour4 ,thus1 ,may the #bast at ,london when the ,sun is due ,east1 his altitude will be about #bd degrees1 and the hour about ,,vii in the morning2 and when his azimuth is #fj degrees ,south-,westerly1 the altitude will be about #dd degrees1 and the hour about #b in the afternoon4 ,thus1 the latitude and the day being known1 and having besides either the altitude1 the azimuth1 or the hour2 the other two may be easily found4 ,,prob4 ,,xxx4 ,the ,latitude1 the ,sun's ,altitude1 and his ,azimuth being given2 to find his ,place in the ,ecliptic and the ,hour4 ,rectify the globe for the latitude and zenith1 and set the edge of the quadrant to the given azimuth2 then turning the globe about1 that point of the ecliptic which cuts the altitude1 will be the ,sun's place4 ,keep the quadrant of the altitude in the same position1 and having brought the ,sun's place to the meridian1 and the hour index to #ab at noon1 turn the globe about 'till the ,sun's place cuts the quadrant of altitude1 and then the index will point the hour of the day4 ,,prob4 ,,xxxi4 ,the ,declination and ,meridian ,altitude of the ,sun1 or of any ,star being given2 to find the ,latitude of the ,place4 ,mark the point of declination upon the meridian1 according as it is either ,north or ,south from the equator2 then slide the meridian up or down in the notches1 'till the point of declination be so far distant from the horizon1 as is the given meridian altitude2 that elevation of the ,pole will be the latitude4 ,thus1 if the ,sun's1 or any ,star's meridian altitude be #ej degrees1 and its declination #aa degrees ,north1 the latitude will be #ea degrees ,north4 ,,prob4 ,,xxxii4 ,the ,day and ,hour of a ,lunar ,eclipse being known2 to find all those ,places upon the ,globe where the same will be visible4 #e ,find where the ,sun is vertical at the given hour1 and bring that point to the zenith2 then the ,eclipse will be visible in all those places that are under the horizon2 ,or1 if you bring the ,antipodes to the place where the ,sun is vertical1 into the zenith1 you will have the places where the ,eclipse will be visible above the horizon4 ,note1 ,because ,lunar eclipses continue sometimes for a long while together1 they may be seen in more places than one hemisphere of the ,earth2 for by the ,earth's motion round its axis1 during the time of the eclipse1 the ,moon will rise in several places after the eclipse began4 ,note1 ,when an eclipse of the ,sun is central1 if you bring the place where the ,sun is vertical at that time1 into the zenith1 some part of the eclipse will be visible in most places within the upper hemisphere2 but by reason of the short duration of ,solar eclipses1 and the latitude which the ,moon commonly has at that time 7tho' but small7 there is no certainty in determining the places where those eclipses will be visible by the globe2 but recourse must be had to calculations4 ,,prob4 ,,xxxiii4 ,the ,day of the ,month1 and ,hour of the ,day1 according to our way of reckoning in ,england1 being given2 to find thereby the ,babylonic1 ,italic1 and the ,jewish1 or ,judaical ,hour4 #a4 ,to find the ,babylonic ,hour 7which is the number of hours from ,sun-rising47 ,having found the time of ,sun-rising in the given place1 the difference betwixt this and the hour given1 is the ,babylonic ,hour4 #b4 ,to find the ,italic ,hour 7which is the number of hours from ,sun-setting47 ,subtract the hour of ,sun-setting from the given hour1 and the remainder will be the ,italic ,hour required4 #c4 ,to find the ,jewish ,hour 7which is _/ part of an ,artificial ,day47 ,find how many hours the day consists of2 then say1 as the number of hours the day consists of is to #ab hours1 so is the hour since ,sun-rising to the ,judaical hour required4 ,thus1 if the ,sun rises at #d o'clock 7consequently sets at #h7 and the hour given be #e in the evening1 the ,babylonish hour will be the #acth1 the ,italic the #bast and the ,jewish hour will be nine and three quarters4 ,the converse being given1 the hour of the day1 according to our way of reckoning in ,england1 may be easily found4 ,the following ,problems are peculiar to the ,celestial ,globe4 ,,prob4 ,,xxxiv4 ,to find the ,right ,ascension and ,declination of the ,sun1 or any ,fixed ,star4 ,bring the ,sun's place in the ecliptic to the meridian2 then that degree of the equator1 which is cut by the meridian1 will be the ,sun's ,right ,ascension2 and that degree of the meridian1 which is exactly over the ,sun's place1 is the ,sun's ,declination4 ,after the same manner1 bring the place of any ,fixed ,star to the meridian1 and you will find its ,right ,ascension in the equinoctial1 and ,declination of the meridian4 ,thus1 the right ascension and declination is found1 after the same manner as the longitude and latitude of a place upon the ,terrestrial ,globe4 ,note1 ,the right ascension and declination of the ,sun vary every day2 but the right ascension1 c4 of the ,fixed ,stars is the same throughout the year#f4 ,the ,sun's ,right ,ascension4 ,declin4 ,deg4 ,deg4 ,january #ca #cad #ag ,s4 ,april #e #ad #f ,n4 ,thus on ,july #ba #abj #bj ,n4 ,november #bf #bdb #ba ,s4 ,r4 ,asc4 ,dcl4 ,deg4 ,deg4 ,aldebaran #fe #af ,n4 ,spica ,virginis #aig #i ,s4 ,capella #gd #de ,n4 ,syrius1 or the ,dog-,star #ih #af ,s4 ,note1 ,the declination of the ,sun may be found after the same manner by the ,terrestrial ,globe1 and also his right ascension1 when the equinoctial is numbered into #cfj degrees1 commencing at the equinoctial point 3 ,but as the equinoctial is not always numbered so1 and this being properly a ,problem in ,astronomy1 we choose rather to place it here4 ,by the converse of this problem1 having the right ascension and declination of any point given1 that point itself may be easily found upon the globe4 ,,prob4 ,,xxxv4 ,to find the ,longitude and ,latitude of a given ,star4 ,having brought the solstitial colure to the meridian1 fix the quadrant of altitude over the proper ,pole of the ecliptic1 whether it be ,north or ,south2 then turn the quadrant over the given ,star1 and the arch contained betwixt the ,star and the ecliptic1 will be the latitude1 and the degree cut on the ecliptic will be the ,star's longitude4 ,thus the latitude of ,arcturus will be found to be #ca degrees ,north1 and the longitude #bjj degrees from 1 or #bj degrees from 3 ,the latitude of ,fomalhaut in the ,southern ,fish1 #ba degrees ,south1 and longitude #bii degrees1 or #bi degrees4 ,by the converse of this method1 having the latitude and longitude of a ,star given1 it will be easy to find the ,star upon the globe4 ,the distance betwixt two ,stars1 or the number of degrees contained betwixt them1 may be found by laying the quadrant of altitude over each of them1 and counting the number of degrees intercepted2 after the same manner as we found the distance betwixt two places on the ,terrestrial ,globe1 in ,prob4 ,,vii4 ,,prob4 ,,xxxvi4 ,the ,latitude of the ,place1 the ,day of the ,month1 and the ,hour being given2 to find what ,stars are then rising or setting1 what ,stars are culminating1 or on the meridian1 and the ,altitude and ,azimuth of any ,star above the ,horizon2 and also how to distinguish the ,stars in the ,heavens one from the other1 and to know them by their proper ,names4 ,having rectified the globe for the latitude1 the zenith1 and the ,sun's place1 turn the globe about until the index points to the given hour1 the globe being kept in this position4 ,all those ,stars that are in 7,eastern_/,western7 side of the horizon1 are then 7,rising_/,setting74 ,all those ,stars that are under the meridian1 are then culminating4 ,and if the quadrant of altitude be laid over the center of any particular ,star1 it will show that ,star's altitude at that time2 and where it cuts the horizon1 will be the ,star's azimuth from the ,north or ,south part of the meridian4 ,the globe being kept in the same elevation1 and from turning round its axis1 move the wooden frame about until the ,north and ,south points of the horizon lie exactly in the meridian2 then right lines imagined to pass from the center thro' each ,star upon the surface of the globe1 will point out the real ,star in the heavens1 which those on the globe are made to represent4 ,and if you are by the side of some wall whose bearing you know1 lay the quadrant of altitude to that bearing in the horizon1 and it will cut all those ,stars which at that very time are to be seen in the same direction1 or close by the side of the said wall4 ,thus knowing some of the remarkable ,stars in any part of the heavens1 the neighbouring ,stars may be distinguished by observing their situations with respect to those that are already known1 and comparing them with the ,stars drawn upon the globe4 ,thus1 if you turn your face towards the ,north1 you will find the ,north ,pole of the globe points to the ,pole-,star2 then you may observe two ,stars somewhat less bright than the ,pole-,star1 almost in a right line with it1 and four more which form a sort of quadrangle2 these seven ,stars make the constellation called the ,little ,bear2 the ,pole ,star being in the tip of the tail4 ,in this neighbourhood you will observe seven bright ,stars1 which are commonly called ,charles's ,wane2 these are the bright ,stars in the ,great ,bear1 and form much such another figure with those before-mentioned in the little ,bear3 ,the two foremost of the square lie almost in a right line with the ,pole ,star1 and are called the ,pointers1 so that knowing the ,pointers1 you may easily find the ,pole-,star4 ,thus the rest of the ,stars in this constellation1 and all the ,stars in the neighbouring constellations may be easily found1 by observing how the unknown ,stars lie either in quadrangles1 triangles1 or strait lines from those that are already known upon the globe4 ,after the same manner the globe being rectified1 you may distinguish those ,stars that are to the ,southward of you1 and be soon acquainted with all the ,stars that are visible in our hemisphere4 ,,scholium4 ,the globe being rectified to the latitude of any place1 if you turn it round its axis1 all those ,stars that do not go below the horizon during a whole revolution of the globe1 never set in that place2 and those that do not come above the horizon never rise4 ,,prob4 ,,xxxvii4 ,the latitude of the place being given2 to find the ,amplitude1 ,oblique ,ascension and ,descension1 ,ascensional ,difference1 ,semi-diurnal ,arch1 and the time of continuance above the horizon1 of any given point in the heavens4 ,having rectified the globe for the latitude1 and brought the given point to the meridian1 set the index to the hour of #ab2 then turn the globe until the given point be brought to the ,eastern side of the horizon1 and that degree of the equinoctial which is cut by the horizon at that time1 will be the ,oblique ,ascension2 and where the given point cuts the horizon1 is the ,amplitude ,ortive3 ,if the globe be turned about until the given point be brought to the ,western side of the horizon1 it will there show the ,amplitude ,occasive2 and where the horizon cuts the equinoctial at that time1 is the ,oblique ,descension4 ,the time between the index at either of these two positions1 and the hour of #f2 or half the difference between the oblique ascension and descension is the ,ascensional ,difference4 ,if the place be in ,north latitude and the declination of the given point be 7,north_/,south7 the ascensional difference reduced into time1 and 7added to_/subtracted from7 #f o',clock1 gives the ,semi-diurnal ,arch2 the complement whereof to a semicircle1 is the ,semi-nocturnal ,arch4 ,if the place be in ,south latitude1 then the contrary is to be observed with respect to the declination4 ,the semi-7diurnal_/nocturnal7 arch being doubled1 gives the time of continuance 7above_/below7 the horizon4 ,or the time of continuance above the horizon1 may be found by counting the number of hours contained in the upper part of the horary circle1 betwixt the place where the index pointed when the given point was in the ,eastern or ,western parts of the horizon4 ,if the given point was the ,sun's place1 the index pointed the time of his rising and setting1 when the said place was in the ,eastern and ,western parts of the horizon1 as in ,prob4 #ah4 ,or the time of ,sun-rising may be found by adding or subtracting his ascensional difference1 to or from the hour of six1 according as the latitude and declination are either contrary or the same way4 ,thus1 at ,london1 on the #cast of ,may1 the ,sun's ,amplitude is #bd degrees ,northerly4 ,oblique ,ascension1 #bj4 ,oblique ,descension1 #eh4 ,ascensional ,difference1 #ai4 ,semi-diurnal ,arch1 #aji4 ,his continuance above the horizon1 #ad hours4 ,sun rises at three quarters past four4 ,sun sets a quarter past seven4 ,these things for the ,sun vary every day2 but for a ,fixed ,star the day of the month need not be given1 for they are the same all the year round4 ,in the latitude of #ea ,north1 ,syrus's ,amplitude is about #bh degrees ,southerly4 ,oblique ,ascension1 #aba4 ,oblique ,descension1 #ge4 ,ascensional ,difference1 #bc4 ,semi-diurnal ,arch1 #fg4 ,continuance above the horizon1 #i hours4 ,,prob4 ,,xxxviii4 ,the ,latitude and the ,day of the ,month being given2 to find the ,hour when any known ,star will be upon the meridian1 and also the time of its rising and setting4 ,having rectified the globe for the latitude of the ,sun's place1 bring the given ,star to the meridian1 and also to the ,east or ,west side of the horizon1 and the index will shew accordingly when the ,star culminates1 or the time of the rising or setting4 ,thus at ,london1 on the #bast of ,january1 ,syrius will be upon the meridian1 at a quarter past ten in the evening2 rises at #e hours1 and sets at three quarters past two in the morning4 ,by the converse of this problem1 knowing the time when any ,star is upon the meridian1 you may easily find the ,sun's place4 ,thus1 bring the given ,star to the meridian1 and set the index to the given hour2 then turn the globe 'till the index points to #ab at noon1 and the meridian will cut the ,sun's place in the ecliptic4 ,thus when ,syrius comes to the meridian at #aj hours after noon1 the ,sun's place will be deg4 ,,prob4 ,,xxxix4 ,to find at what time of the ,year a given ,star will be upon the ,meridian1 at a given ,hour of the ,night4 ,bring the ,star to the meridian1 and set the index to the given hour1 then turn he globe 'till the index points to #ab at noon1 and the meridian will cut the ecliptic in the ,sun's place2 whence the day of the month may be easily found in the kalendar upon the horizon4 ,,prob4 ,,xl4 ,the ,day of the ,month1 and the ,azimuth of any known ,star being given2 to find the ,hour of the ,night4 ,having rectified the globe for the latitude and the ,sun's place1 if the given ,star be due ,north or ,south1 bring it to the meridian1 and the index will show the hour of the night4 ,if the ,star be in any other direction1 fix the quadrant of altitude in the zenith1 and set it to the ,star's azimuth in the horizon2 then turn the globe about until the quadrant cuts the center of the ,star1 and the index will shew the hour of the night4 ,the bearing of any point in the heavens may be found by the following methods4 ,having a meridian line drawn in two windows1 that are opposite to one another1 you may cross it at right angles with another line representing the ,east and ,west2 from the point of the intersection describe a circle1 and divide each quadrant into #ij degrees2 then get a smooth board1 of about #b feet long1 and foot broad 7more or less1 as you judge convenient7 and on the back part of it fix another small board crossways1 so that it may serve as a foot to support the biggest board upright1 when it is set upon a level1 or an horizontal plane4 ,the board being thus prepared1 set the lower edge of the smooth1 or fore side of it1 close to the center of the circle1 then turn it about to the meridian1 or to any azimuth point required 7keeping the edge of it always close to the center7 and casting your eye along the flat side of it1 you will easily perceive what ,stars are upon the meridian1 or any other bearing that the board is set to4 ,,prob4 ,,xli4 ,two known ,stars having the same ,azimuth1 or the same ,height1 being given2 to find the ,hour of the ,night4 ,rectify the globe for the latitude1 the zenith1 and the ,sun's place4 #a4 ,when the two ,stars are in the same azimuth1 turn the globe1 and also the quadrant about1 until both ,stars coincide with the edge thereof2 then will the index shew the hour of the night2 and where the quadrant cuts the horizon1 is the common azimuth of both ,stars4 #b4 ,if the two ,stars are of the same altitude1 move the globe so that the same degree on the quadrant will cut both ,stars1 then the index will shew the hour4 ,this problem is useful when the quantity of the azimuth of the two ,stars in the first case1 or of their altitude in the latter case1 is not known4 ,if two ,stars were given1 one on the meridian1 and the other in the ,east or ,west part of the horizon2 to find the ,latitude4 ,bring that ,star which was observed on the meridian1 to the meridian of the globe1 and keep the globe from turning round its axis2 then slide the meridian up or down in the notches1 'till the other ,star is brought to the ,east or ,west part of the horizon1 and that elevation of the ,pole will be the ,latitude sought4 ,,prob4 ,,xlii4 ,the ,latitude1 ,day of the ,month1 and the ,altitude of any known ,star being given2 to find the ,hour of the ,night4 ,rectify the globe for the latitude1 zenith1 and ,sun's place3 ,turn the globe1 and the quadrant of altitude1 backward or forward1 'till the center of that ,star meets the quadrant in the degree of altitude given2 then the index will point the true hour of the night2 and also where the quadrant cuts the horizon1 will be the azimuth of the ,star at that time4 ,if the ,latitude1 the ,sun's ,altitude1 and his ,declination 7instead of his ,place in the ,ecliptic7 are given2 to find the ,hour of the ,day and ,azimuth4 ,rectify the globe for the latitude and zenith1 and having brought the equinoctial colure to the meridian1 set the index to #ab at noon2 which being done1 turn the globe and the quadrant1 until the given declination in the equinoctial colure1 cuts the altitude on the quadrant2 then the index will shew the ,hour of the day1 and the quadrant cut the ,azimuth in the horizon4 ,if the ,altitude of two ,stars on the same ,azimuth were given2 to find the ,latitude of the ,place4 ,set the quadrant over both ,stars at the observed degrees of altitude1 and keep it fast upon the globe with your fingers2 then slide the meridian up or down in the notches1 'till the quadrant cuts the given azimuth in the horizon2 that elevation of the ,pole will be the latitude required4 ,,prob4 ,,xliii4 ,having the ,latitude of the place1 to find the degree of the ,ecliptic1 which rises or sets with a given ,star2 and from thence to determine the time of its ,cosmical and ,achronical rising and setting4 ,having rectified the globe for the latitude1 bring the given ,star to the ,eastern side of the horizon1 and mark what degree of the ecliptic rises with it3 ,look for that degree in the wooden horizon1 and right against it1 in the kalendar1 you will find the month and day when the ,star rises ,cosmically4 ,if you bring the ,star to the ,western side of the horizon1 that degree of the ecliptic which rises at that time1 will give the day of the month when the said ,star sets ,cosmically4 ,so likewise against the degree which sets with the ,star1 you will find the day of the month of the ,achronical setting2 and if you bring it to the ,eastern part of the horizon1 that degree which sets at that time will be the ,sun's place when the ,star rises ,achronically4 ,thus1 in the latitude of ,london1 ,syrius1 or the ,dog-,star1 rises ,cosmically the #ajth of ,august1 and sets ,cosmically the #ajth of ,october4 ,aldebaran1 or the ,bull's ,eye1 rises ,achronically on the #bb;d of ,may1 and sets ,achronically on the #aith of ,december4 ,,prob4 ,,xliv4 ,having the ,latitude of the place1 to find the time when a ,star rises and sets ,heliacally4 ,having rectified the globe for the latitude1 bring the ,star to the ,eastern side of the horizon1 and turn the quadrant round to the ,western side1 'till it cuts the ecliptic in #ab degrees of altitude above the horizon1 if the ,star be of the first magnitude2 then that point of the ecliptic which is cut by the quadrant1 is #ab degrees high above the ,western part of the horizon1 when the ,star rises2 but at the same time the opposite point in the ecliptic is #ab degrees below the ,eastern part of the horizon1 which is the depression of a ,star of the first magnitude1 when she rises ,heliacally2 or has got so far from the ,sun's beams1 that she may be seen in the morning before ,sun-rising4 ,wherefore look for the said point of the ecliptic on the horizon1 and right against it will be the day of the month when the ,star rises ,heliacally4 ,to find the ,heliacal setting1 bring the ,star to the ,west side of the horizon1 and turn the quadrant about to the ,eastern side1 'till the #abth degree of it above the horizon1 cuts the ecliptic2 then that degree of the ecliptic which is opposite to this point1 is the ,sun's place when the ,star sets ,heliacally4 ,thus you will find that ,arcturus rises ,heliacally the #bhth of ,september1 and sets ,heliacally ,december the #b;d4 ,,prob4 ,,xlv4 ,to find the place of any ,planet upon the globe2 and so by that means1 to find its place in the ,heavens3 ,also to find at what ,hour any ,planet will rise or set1 or be on the meridian at any one ,day in the ,year4 ,you must first seek in an ,ephemeris 7,white's ,ephemeris will do well enough7 for the place of the ,planet proposed on that day2 then mark that point of the ecliptic1 either with chalk1 or by sticking on a little black patch2 and then for that night you may perform any problem1 as before1 by a ,fixed ,star4 ,let it be required to find the situation of ,jupiter among the ,fixed ,stars in the heavens1 and also what time he rises and sets1 and comes to the meridian on the #aith of ,may1 #ageg1 ,n4 ,s4 at ,london4 ,looking for the #aith of ,may1 #ageg1 in ,white's ,ephemeris1 ,i find that ,jupiter's place at that time is in about #ab degrees of 2 latitude about #a degree ,north4 ,then looking for that point upon the ,celestial globe1 ,i find that is then nearly in conjunction with the bright ,star in the ,southern ,balance1 and about #a degree ,north of it4 ,to find when he rises and sets1 and comes to the meridian3 ,having put a little black patch on the place of ,jupiter1 elevate the globe according to the latitude1 and having brought the ,sun's place to the meridian1 set the hour index to #ab at noon2 then turn the mark which was made for ,jupiter1 to the ,eastern part of the horizon1 ,i find will rise somewhat more than half an hour after three in the afternoon2 and turning the globe about1 ,i find it comes to the meridian a little before eleven at night2 and sets almost a quarter past six next morning4 ,this example being understood1 it will be easy to find when either of the other two superior ,planets1 viz4 ,mars and ,saturn1 rise1 set1 and come to the meridian4 ,i shall conclude this subject about the ,globes with the following problems4 ,,prob4 ,,xlvi4 ,to find all that space upon the ,earth1 where an ,eclipse of one of the ,satellites of ,jupiter will be visible4 ,having found that place upon the ,earth1 in which the ,sun is vertical at the time of the eclipse1 by ,prob4 #ac1 elevate the globe according to the latitude of the said place2 then bring the place to the meridian1 and set the hour index to #ab at noon4 ,if ,jupiter be in consequence of the ,sun1 draw a line with black lead1 or the like1 along the ,eastern side of the horizon1 which line1 will pass over all those places where the ,sun is setting at that time2 then count the difference betwixt the right ascension of the ,sun1 and that of ,jupiter1 and turn the globe ,westward1 'till the hour index points to this difference2 then keep the globe from turning round its axis1 and elevate the meridian1 according to the declination of ,jupiter4 ,the globe being in this position1 draw a line along the ,eastern side of the horizon2 then the space between this line1 and the line before drawn1 will comprehend all those places of the ,earth where ,jupiter will be visible1 from the setting of the ,sun1 to the setting of ,jupiter4 ,but if ,jupiter be in antecedence of the ,sun 7i4 e4 rises before him7 having brought the place where the ,sun is vertical1 to the zenith1 and put the hour index to #ab at noon1 draw a line on the ,western side of the horizon2 then elevate the globe according to the declination of ,jupiter1 and turn it about ,eastward1 until the index points to so many hours distant from noon1 as is the difference of right ascension of the ,sun and ,jupiter4 ,the globe being in this position1 draw a line along the ,western side of the horizon2 then the space contained between this line1 and the other last drawn1 will comprehend all those places upon the ,earth where the ,eclipse is visible1 between the rising of the ,sun1 and that of ,jupiter4 ,illustration ,the ,,description of the ,great ,,orrery1 lately made by ,mr4 ,,thomas ,,wright1 ,mathematical ,instrument-,maker to his late ,,majesty1 and now by ,,benjamin ,,cole1 his ,successor4 ,the ,,orrery is an ,astronomical ,machine1 made to represent the motions of the ,planets4 ,these machines are made of various sizes1 some having more ,planets than others2 but ,i shall here confine myself to the description of that above-mentioned4 ,in the ,introduction we gave a short account of the ,order1 ,periods1 ,distances1 and ,magnitudes of the ,primary ,planets2 and of the ,distances and ,periodical ,resolutions of the ,secondary ,planets round their respective ,primaries4 ,we shall here explain their ,stations1 ,regradations1 ,eclipses1 ,phases1 c4 but first let us take a general view of the ,orrery4 ,sidenote3 ,the ,description of the ,orrery4 ,sidenote3 ,vide ,frontispiece4 ,the frame which contains the wheel-work1 c4 that regulates the whole ,machine1 is made of fine ebony1 and is near four feet in diameter2 the outside thereof is adorned with twelve pilasters1 curiously wrought and gilt3 ,between these pilasters the twelve ,signs of the ,zodiac are neatly painted1 with gilded frames4 ,above the frame is a broad ring1 supported with twelve pillars3 ,this ring represents the ,plane of the ,ecliptic1 upon which there are two scales of degrees1 and between those the names and characters of the twelve ,signs4 ,near the outside is a scale of months and days1 exactly corresponding to the ,sun's place at noon1 each day throughout the year4 ,above the ecliptic stands some of the principal circles of the sphere1 according to their respective situations in the heavens1 viz4 ,n #aj1 are the two ,colures1 divided into degrees1 and half degrees2 ,n #aa1 is one half of the ,equinoctial ,circle1 making an angle with the ecliptic of #bc degrees4 ,the ,tropic of ,cancer1 and the ,arctic ,circle1 are each fixed parallel1 and at their proper distance from the equinoctial4 ,on the ,northern half of the ecliptic is a brass semicircle1 moveable upon two points fixed in and 3 ,this semicircle serves as a moveable horizon1 to be put to any degree of latitude upon the ,north part of the meridian4 ,the whole machine is also so contrived1 as to be set to any latitude1 without in the least affecting any of the inside motions3 ,for this purpose there are two strong hinges 7,n #ac17 fixed to the bottom frame1 upon which the instrument moves1 and a strong brass arch1 having holes at every degree1 thro' which a strong pin is to be put1 according to the elevation4 ,this arch and the two hinges1 support the whole machine1 when it is lifted up according to any latitude2 and the arch at other times lies conveniently under the bottom frame4 ,when the machine is set to any latitude 7which is easily done by two men1 each taking hold of two handles1 conveniently fixed for that purpose7 set the moveable horizon to the same degree upon the meridian1 and you may form an idea of the respective altitude1 or depressions of the ,planets1 above or below the horizon1 according to their respective positions1 with regard to the meridian4 ,within the ecliptic1 and nearly in the same place thereof1 stands the ,sun1 and all the ,planets1 both ,primary and ,secondary4 ,the ,sun 7,n #a47 stands in the middle of the whole system1 upon a wire1 making an angle with the plane of the ecliptic1 of about #hb degrees2 which is the inclination of the ,sun's axis1 to the axis of the ecliptic4 ,next to the ,sun is a ,small ball 7,n #b47 representing ,mercury3 ,next to ,mercury is ,venus 7,n #c47 represented by a larger ball 7and both these stand upon wires17 so that the balls themselves may be more visibly perceived by the eye4 ,the ,earth is represented 7,n #d47 by an ivory ball1 having some of the principal meridians and parallels1 and a little sketch of a map described upon it4 ,the wire which supports the ,earth1 makes an angle with the plane of the ecliptic #ff degrees1 which is the inclination of the ,earth's axis to that of the ecliptic4 ,near the bottom of the ,earth's axis is a ,dial ,plate 7,n #i47 having an index pointing to the hours of the day1 as the ,earth turns round its axis4 ,round the ,earth is a ring1 supported by two small pillars1 which ring represents the ,orbit of the ,moon1 and the division upon it answers to the ,moon's latitude2 the motion of this ring represents the motion of the ,moon's ,orbit1 according to that of the ,nodes4 ,within this ring is the ,moon 7,n #e47 having a black cap or case1 which by its motion1 represents the ,phases of the ,moon according to her age4 ,without the ,orbits of the ,earth and ,moon is ,mars 7,n #f47 ,the next in order to ,mars is ,jupiter1 and his four ,moons 7,n #g72 each of these moons is supported by a crooked wire fixed in a socket1 which turns about the pillar that supports ,jupiter4 ,these satellites may be turned by the hand to any position2 and yet when the machine is put in motion1 they will all move in their proper times4 ,the outermost of all is ,saturn1 and his five ,moons 7,n #h47 ,these moons are supported and contrived after the same manner with those of ,jupiter4 ,the whole machine is put into motion by turning a small winch 7like the key of a clock1 ,n #ad47 and all the inside work is so truly wrought1 that it requires but very small strength to put the whole motion4 ,above the handle there is a cylindrical pin1 which may be drawn a little out1 or pushed in1 at pleasure3 when it is pushed in1 all the ,planets1 both primary and ,secondary1 will move according to their respective periods1 by turning the handle3 ,when it is drawn out1 the motions of the ,satellites of ,jupiter and ,saturn will be stopped1 while all the rest move without interruption4 ,this is a very good contrivance to preserve the instrument from being clogged by the swift motions of the wheels belonging to the ,satellites of ,jupiter and ,saturn1 when the motions of the rest of the ,planets are only considered4 ,there is also a brass lamp having two convex glasses1 to be put in the room of the ,sun2 and also a smaller ,earth and ,moon1 made somewhat in proportion to their distance from each other1 which may be put on at pleasure4 ,the lamp turns round in the same time with the ,earth1 and by means of the glasses cast a strong light upon her2 and when the smaller ,earth and ,moon are placed on1 it will be easy to shew when either of them may be eclipsed4 ,having thus given a brief description of the outward part of this machine1 ,i shall next give an account of the phnomena explained by it1 when it is put into motion4 ,of the ,motions of the ,planets in general4 ,having put on the handle1 push in the pin which is just above it1 and place a small black patch 7or bit of wafer7 upon the middle of the ,sun 7for instance7 right against the first degree of 2 you may also place patches upon ,venus1 ,mars1 and ,jupiter1 right against some noted point in the ecliptic4 ,if you lay a thread from the ,sun to the first degree of 1 you may set a mark where it intersects the orbit of each ,planet1 and that will be a help to note the time of their revolutions4 ,one entire turn of the handle answers to the diurnal motion of the ,earth round her axis1 as may be seen by the motion of the hour index1 which is placed at the foot of the wire on which the terella is fixed4 ,when the index has moved the space of ten hours1 you may observe that ,jupiter has made one revolution compleat round its axis2 the handle being turned until the hour index has passed over #bd days1 #h hours1 will bring the patch upon ,venus to its former situation with respect to the ecliptic1 which shews that has made one entire revolution round her axis4 ,mars makes one compleat revolution round its axis in #bd hours and about #dj minutes4 ,when the handle is turned #be times round1 the spot upon the ,sun will point to the same degree of the ecliptic1 as it did when the instrument was first put into motion4 ,by observing the motions of the spots upon the surface of the ,sun1 and of the ,planets in the heavens1 their diurnal motion was discovered2 after the same manner as we do here observe the motions of their representatives1 by that of the marks placed upon them4 ,if while you turn the handle you observe the ,planets1 you will see them perform their motions in the same relative times as they really do in the heavens1 each making its period in the times mentioned in the ,tables1 ,page1 #bh1 #bg turns of the handle will bring the ,moon round the ,earth1 which is called a ,periodic ,month2 and all the while she keeps the same face towards the ,earth2 for the ,moon's annual and diurnal motion are performed both in the same time nearly1 so that we always see the same face or side of the ,moon4 ,if before the instrument is put into motion1 the satellites of ,jupiter and ,saturn be brought into the same right line from their respective primaries1 you will see them1 as you turn the handle1 immediately dispersed from one another1 according to their different celerities4 ,thus one turn of the handle will bring the first of ,jupiter's ,moons about _/ part round ,jupiter1 while the second has described but _/ part1 the third but above _/1 and the fourth not quite _/ part1 each of its respective orbits4 ,if you turn the handle until the hour index has moved #ah hours more1 the first satellite will then be brought into its former position1 and so has made one entire revolution2 the second at the same time will be almost diametrically opposite to the first1 and so has made a little more than half of one revolution2 the others will be in different aspects1 according to the length of their periods1 as will be plainly exhibited by the instrument4 ,the same observations may be made with respect to the satellites of ,saturn4 ,the machine is so contrived1 that the handle may be turned either way2 and1 if before you put it into motion1 you observe the aspect 7or situation with respect to each other7 of the ,planets1 and then turn the handle round any number of times2 the same number of revolutions being made backwards1 will bring all the ,planets to their former situations4 ,i shall next proceed to particulars4 ,of the ,stations and ,retrogradations of the ,planets4 ,sidenote3 ,retrograde ,motion of the ,planets4 ,the primary ,planets1 as they all turn round the ,sun1 at different distances1 and in different times1 appear to us from the ,earth to have different motions2 as sometimes they appear to move from ,west to ,east1 according to the order of the signs1 which is called their ,direct ,motion2 then by degrees they slacken their pace1 until at last they lose all their motion1 and become ,stationary1 or not to move at all2 that is1 they appear in the same place with respect to the fixed ,stars for some time together2 after which they again begin to move1 but with a contrary direction1 as from ,east to ,west1 which is called their ,retrograde ,motion2 then again they become stationary1 and afterwards reassume their direct motion4 ,the reason of all these appearances is very evidently shewn by the ,orrery4 ,of the ,stations1 c4 of the ,inferior ,planets4 ,we shall instance in the ,planet ,mercury1 because his motion round the ,sun differs more from the ,earth's than that of ,venus does4 ,when ,mercury is in his superior conjunction 7or when he is in a direct line from the ,earth beyond the ,sun7 fasten a string about the axis of the ,earth1 and extend it over ,mercury to the ecliptic2 then turning the handle1 keep the thread all the while extended over 1 and you will find it move with a direct motion in the ecliptic1 but continually slower1 until ,mercury has the greatest elongation from the ,earth4 ,near this position1 the thread for some time will lay over ,mercury without being moved in the ecliptic1 tho' the ,earth and ,mercury both continue their progressive motion in their respective orbits4 ,when ,mercury has got a little past this place1 you will find the thread must be moved backward in the ecliptic1 beginning first with a slow motion1 and then faster by degrees1 until ,mercury is in his inferior conjunction1 or directly between the ,earth and the ,sun4 ,next this position of 1 his retrograde motion will be the swiftest2 but he still moves the same way1 tho' continually slower1 'till he has again come to his greatest elongation1 where he will appear the second time to be stationary2 after which he begins to move forward1 and that faster by degrees1 until he is come to the same position with respect to the ,earth1 that he was in at first4 ,the same observations may be made relating to the motions of ,venus4 ,in like manner the different motions observed in the superior ,planets may be also explained by the ,orrery4 ,if you extend the thread over ,jupiter1 and proceed after the same manner as before we did in regard to ,mercury1 you will find that from the time ,jupiter is in conjunction with the ,sun1 his motion is direct1 but continually slower1 until the ,earth is nearly in a quadrate aspect with ,jupiter1 near which position ,jupiter seems to be stationary3 ,after which he begins to move1 and continually mends his pace1 until he comes in opposition to the ,sun1 at which time his retrograde motion is swiftest4 ,he still seems to go backward1 but with a slower pace1 'till the ,earth and he are again in a quadrate aspect1 where ,jupiter seems to have lost all his motion2 after which he again resumes his direct motion1 and so proceeds faster by degrees1 'till the ,earth and he are again in opposition to each another4 ,sidenote3 ,plate #c4 ,fig4 #a4 ,these different motions observed in the ,planets1 are easily illustrated1 as followeth3 ,the lesser circle round the ,sun is the orbit of ,mercury1 in which he performs his revolution round the ,sun1 in about three months1 or while the ,earth is going thro' part of her orbit1 or from ,a to ,n4 ,the numbers #a1 #b1 #c1 c4 in the orbit of ,mercury1 show the spaces he describes in a week nearly1 and the distance ,,ab1 ,,bc1 ,,dc1 c4 in the ,earth's orbit1 do likewise show her motion in the same time4 ,the letters ,a1 ,b1 ,c1 c4 in the great orb1 are the motions of ,mercury in the ,heavens1 as they appear from the ,earth4 ,now if the ,earth be supposed in ,a1 and ,mercury in #ab1 near his superior conjunction with the ,sun2 a spectator on the ,earth will see 1 as if he were in the point of the ,heavens ,a1 and while is moving from #ab to #a1 and from #a to #b1 c4 the ,earth in the same time also moves from ,a to ,b1 and from ,b to ,c1 c4 ,all which time appears in the ,heavens to move in a direct motion from ,a to ,b1 and from ,b to ,c1 c4 but gradually slower1 until he arrives near the point ,g2 near this place he appears stationary1 or to stand still2 and afterwards 7tho' he still continues to move uniformly in his own orbit1 with a progressive motion7 yet in the sphere of the fixed ,stars he will appear to be retrograde1 or to go backwards1 as from ,g to ,h1 from ,h to ,i1 c4 until he has arrived near the point ,l1 where again he will appear to be stationary2 and afterwards to move in a direct motion from ,l to ,m1 and from ,m to ,n1 c4 ,what has been here shewed concerning the motions of ,mercury1 is also to be understood of the motions of ,venus2 but the conjunctions of ,venus with the ,sun do not happen so often as in ,mercury2 for ,venus moving in a larger orbit1 and much slower than ,mercury1 does not so often overtake the ,earth4 ,but the retrogradations are much greater in ,venus than they are in ,mercury1 for the same reasons4 ,sidenote3 ,fig4 #b4 ,the innermost circle represents the ,earth's orbit1 divided into #ab parts1 answering to her monthly motion2 the greatest circle is in the orbit of ,jupiter1 which he describes in about #ab years2 and therefore the _/ thereof1 from ,a to ,n1 defines his motion1 in one of our years nearly2 and the intermediate divisions1 ,a1 ,b1 ,c1 c4 his monthly motion4 ,let us suppose the ,earth to be in the point of her orbit #ab1 and ,jupiter in ,a1 in his conjunction with the ,sun2 it is evident that from the ,earth ,jupiter will be seen in the great orb1 or in the point of the ,heavens ,a1 and while the ,earth is moving from #ab to #a1 #b1 c4 also moves from ,a to ,b1 c4 all which time he appears in the ,heavens to move with a direct motion from ,a to ,b1 ,c1 c41 until he comes in opposition to the ,earth near the point of the ,heavens ,e1 where he appears to be stationary2 after which again begins to move 7tho' at first with a slow pace7 from ,e through ,f1 ,h1 ,i to ,k1 where again he appears to stand still1 but afterwards he reassumes his direct motion from ,i thro' ,k1 to ,m1 c4 ,from the construction of the preceding figure it appears1 that when the superior ,planets are in conjunction with the ,sun1 their direct motion is much quicker than at other times2 and that because they really move from ,west to ,east1 while the ,earth in the opposite part of the ,heavens is carried the same way1 and round the same center4 ,this motion afterwards continually slackens until the ,planet comes almost in opposition to the ,sun1 when the line joining the ,earth and ,planet1 will continue for some time nearly parallel to itself1 and so the ,planet seems from the ,earth to stand still2 after which1 it begins to move with a slow motion backward1 until it comes into a quartile aspect with the ,sun1 when again it will appear to be stationary1 for the above reasons2 after that it will resume its direct motion1 until it comes into a conjunction with the ,sun1 then it will proceed as above explained4 ,hence it also appears1 that the retrogradations of the superior ,planets are much slower than their direct motions1 and their continuance much shorter2 for the ,planet1 from its last quarter1 until it comes in opposition to the ,sun1 appears to move the same way with the ,earth1 by whom it is then overtaken3 ,after which it begins to go backwards1 but with a slow motion1 because the ,earth being in the same part of the ,heavens1 and moving the same way that the ,planet really does1 the apparent motion of the ,planet backwards1 must thereby be lessened4 ,what has been here said concerning the motions of ,jupiter1 is also to be understood of ,mars and ,saturn4 ,but the retrogradations of ,saturn do oftener happen than those of ,jupiter1 because the ,earth oftener overtakes ,saturn2 and for the same reason1 the regressions of ,jupiter do oftener happen than those of ,mars4 ,but the retrogradations of ,mars are much greater than those of ,jupiter1 whose are also much greater than those of ,saturn4 ,in either of the satellites of ,jupiter or ,saturn1 these different appearances in the neighbouring ,worlds are much oftener seen than they are by us in the primary ,planets4 ,we never observe these different motions in the ,moon1 because she turns round the ,earth as her center2 neither do we observe them in the ,sun1 because he is the center of the ,earth's motion2 whence the apparent motion of the ,sun always appears the same way round the ,earth4 ,of the ,annual and ,diurnal ,motion of the ,earth1 and of the increase and decrease of ,days and ,nights4 ,the ,earth in her annual motion round the ,sun1 has her axis always in the same direction1 or parallel to itself2 that is1 if a line be drawn parallel to the axis1 while the ,earth is in any point of her orbit1 the axis in all other positions of the ,earth will be parallel to the said line4 ,this parallelism of the axis1 and the simple motion of the ,earth in the ecliptic1 solves all the phnomena of different seasons4 ,these things are very well illustrated by the ,orrery4 ,illustration3 ,plate #c4 ,if you put on the lamp in the place of the ,sun1 you will see how one half of our globe is always illuminated by the ,sun1 while the other hemisphere remains in darkness2 how ,day and ,night are formed by the revolution of the ,earth round her axis2 for as she turns from ,west to ,east1 the ,sun appears to move from ,east to ,west4 ,and while the ,earth turns in her orbit1 you may observe that her axis always points the same way1 and the several seasons of the year continually change4 ,to make these things plainer1 we will take a view of the ,earth in different parts of her orbit4 ,when the ,earth is in the first point of ,libra 7which is found by extending a thread from the ,sun1 and over the ,earth1 to the ecliptic7 we have the ,vernal ,equinox1 and the ,sun at that time appears in the first point of 4 ,in this position of the ,earth1 two ,poles of the world are in the line separating light and darkness2 and as the ,earth turns round her axis1 just one half of the equator1 and all its parallels1 will be in the light1 and the other half in the dark2 and therefore the days and nights must be every where equal4 ,as the ,earth moves along in her orbit1 you will perceive the ,north ,pole advances by degrees into the illuminated hemisphere1 and at the same time the ,south ,pole recedes into darkness2 and in all places to the ,northward of the equator1 the days continually lengthen1 while the contrary happens in the ,southern parts1 until at length the ,earth is arrived in ,capricorn4 ,in this position of the ,earth all the space included within the arctic circle falls wholly within the light1 and all the opposite part lying within the antarctic circle1 is quite involved in darkness4 ,in all places between the equator and the arctic circle1 the days are now at the longest1 and are gradually longer1 as the place are more remote from the equator4 ,in the ,southern hemisphere there is a contrary effect4 ,all the while the ,earth is travelling from ,capricorn towards ,aries1 the ,north ,pole gradually recedes from the light1 and the ,south ,pole approaches nearer to it2 the days in the ,northern hemisphere gradually decrease1 and in the ,southern hemisphere they increase in the same proportion1 until the ,earth be arrived in 2 then the two ,poles of the world lie exactly in the line separating light and darkness1 and the days are equal to the nights in all places of the world4 ,as the ,earth advances towards ,cancer1 the ,north ,pole gradually recedes from the light1 while the ,southern one advances into it1 at the same rate4 ,in the ,northern hemisphere the days decrease1 and in the ,southern one they gradually lengthen1 until the ,earth being arrived in ,cancer1 the ,north frigid ,zone is all involved in darkness1 and the ,south frigid ,zone falls intirely within the light2 the days every where in the ,northern hemisphere are now at the shortest1 and to the ,southward they are at the longest4 ,as the ,earth moves from hence towards ,libra1 the ,north ,pole gradually approaches the light1 and the other recedes from it2 and in all places to the ,northward of the equator1 the days now lengthen1 while in the opposite hemisphere they gradually shorten1 until the ,earth has gotten into 2 in which position the days and nights will again be of equal length in all parts of the world4 ,you might have observed that in all positions of the ,earth1 one half of the equator was in the light1 and the other half in darkness2 whence under the equator1 the days and nights are always of the same length3 ,and all the while the ,earth was going from towards 1 the ,north ,pole was constantly illuminated1 and the ,south ,pole all the while in darkness2 and for the other half year1 the contrary4 ,sometimes there is a semicircle exactly facing the ,sun1 fixed over the middle of the ,earth1 which may be called the horizon of the disk3 ,this will do instead of the lamp1 if that half of the ,earth which is next the ,sun be considered1 as being the illuminated hemisphere1 and the other half1 to be that which lies in darkness4 ,sidenote3 ,plate #d4 ,the great circle 1 1 c4 represent the ,earth's annual orbit2 and the four lesser circles ,,esqc1 the ecliptic1 upon the surface of the ,earth1 coinciding with the great ecliptic in the ,heavens4 ,these four lesser figures represent the ,earth in the four cardinal points of the ecliptic1 ,p being the ,north ,pole of the equator1 and p the ,north ,pole of the ecliptic2 ,,spc1 the solstitial colure which is always parallel to the great solstitial colure in the ,heavens2 ,,epq the equinoctial colure4 ,the other circles passing thro' ,p1 are meridians at two hours distance from one another2 the semicircle ,e,q is the ,northern half of the equator2 the parallel circle touching the ecliptic in ,s1 is the tropic of ,cancer2 the dotted circle1 the parallel of ,london1 and the small circle1 touching the ,pole of the ecliptic1 is the ,arctic ,circle4 ,the shaded part1 which is always opposite to the ,sun1 is the obscure hemisphere1 or that which lies in darkness2 and that which is next the ,sun1 is the illuminated hemisphere4 ,if we suppose the ,earth in 1 she will then see the ,sun in 7which makes our vernal equinox7 and in this position the circle bounding light and darkness1 which here is ,,sc1 passes thro' the ,poles of the ,world1 and bisects all the parallels of the equator2 and therefore the diurnal and nocturnal arches1 or the length of the days and nights1 are equal in all places of the world4 ,but while the ,earth in her annual course1 moves through 1 1 to 1 the line ,,sc1 keeping still parallel to itself1 or to the place where it was at first1 the ,pole ,p will1 by this motion1 gradually advance into the illuminated hemisphere2 and also the diurnal arches of the parallels gradually increase1 and consequently the nocturnal ones decrease in the same proportion1 until the ,earth has arrived into 2 in which position the ,pole ,p1 and all the space within the arctic circle1 fall wholly within the illuminated hemisphere1 and the diurnal arches of all the parallels that are without this circle1 will exceed the nocturnal arches more or less1 as the places are nearer to1 or farther off from it1 until the distance from the ,pole is as far as the equator1 where both these arches are always equal4 ,again1 while the ,earth is moving from through 1 1 to 1 the ,pole ,p begins to incline to the line1 distinguishing light and darkness1 in the same proportion that before it receded from it2 and consequently the diurnal arches gradually lessen1 until the ,earth has arrived into where the ,pole ,p will again fall on the horizon1 and so cause the days and nights to be every where equal4 ,but when the ,earth has passed 1 while she is going thro' 1 and 1 c4 the ,pole ,p will begin to fall in the obscure hemisphere1 and so recede gradually from the light1 until the ,earth is arrived in 2 in which position not only the ,pole1 but all the space within the arctic circle1 are involved in darkness1 and the diurnal arches of all the parallels1 without the arctic circle1 are equal to the nocturnal arches of the same parallels1 when the ,earth was in the opposite point 2 and it is evident that the days are now at the shortest1 and the nights the longest4 ,but when the ,earth has past this point1 while she is going through and 1 the ,pole ,p will again gradually approach the light1 and so the diurnal arches of the parallels gradually lengthen1 until the ,earth is arrived in 2 at which time the days and nights will again be equal in all places of the ,world1 and the ,pole itself just see the ,sun4 ,illustration3 ,plate #d4 ,here we only considered the phnomena belonging to the ,northern parallels2 but if the ,pole ,p be made the ,south ,pole1 then all the parallels of latitude will be parallels of ,south latitude1 and the days1 every where1 in any position of the ,earth1 will be equal to the nights of those who lived in the opposite hemisphere1 under the same parallels4 ,of the ,phases of the ,moon1 and of her ,motion in her ,orbit4 ,sidenote3 ,nodes4 ,sidenote3 ,dragon's ,head4 ,sidenote3 ,dragon's ,tail4 ,sidenote3 ,retrograde ,motion of the ,nodes4 ,the orbit of the ,moon makes an angle with the plane of the ecliptic1 of above #e degrees1 and cuts it into two points1 diametrically opposite 7after the same manner as the equator and the ecliptic cut each other upon the globe1 in and 7 which points are called the ,nodes2 and a right line joining these points1 and passing through the center of the ,earth1 is called the ,line of the ,nodes4 ,that node where the ,moon begins to ascend ,northward above the plane of the ecliptic1 is called the ,ascending ,node1 and the ,head of the ,dragon1 and is thus commonly marked ,symbol4 ,the other node from whence the ,moon1 descends to the ,southward of the ecliptic1 is called the ,descending ,node1 and the ,dragon's ,tail1 and is thus marked ,symbol4 ,the line of nodes continually shifts itself from ,east to ,west1 contrary to the order of the signs2 and with this retrograde motion1 makes one revolution round the ,earth1 in the space of about #ai years4 ,sidenote3 ,periodical ,month4 ,sidenote3 ,synodical ,month4 ,the ,moon describes its orbit round the ,earth in the ,space of #bg days and #g hours1 which space of time is called a ,periodical ,month2 yet from one conjunction to the next1 the ,moon spends #bi days and a half1 which is called a ,synodical ,month2 because while the ,moon in her proper ,orbit finishes her course1 the ,earth advances near a whole sign in the ecliptic2 which space the ,moon has still to describe1 before she will be seen in conjunction with the ,sun4 ,when the ,moon is in conjunction with the ,sun1 note her place in the ecliptic2 then turning the handle1 you will find that #bg days and #g hours will bring the ,moon to the same place2 and after you have made #b revolutions more1 the ,moon will be exactly betwixt the ,sun and the ,earth4 ,sidenote3 ,phases of the ,moon4 ,the ,moon all the while keeps in her orbit1 and so the wire that ,supports her continually rises or falls in a socket1 as she changes her latitude2 the black cap shifts itself1 and so shews the phases of the ,moon1 according to her age1 or how much of her enlightened part is seen from the ,earth4 ,in one synodical month1 the line of the nodes moves about #a degree from ,west to ,east1 and so makes one entire revolution in #ai years4 ,let ,,ab be an arch of the ,earth's orbit1 and when the ,earth is in ,t1 let the ,moon be in ,n1 in conjunction with the ,sun in ,s1 while the ,moon is describing her orbit ,,nafd1 the ,earth will describe the arch of her orbit ,t t2 and when the ,earth has got into the point t1 the ,moon will be in the point of her orbit n1 having made one compleat revolution round the ,earth4 ,but the ,moon1 before she comes in conjunction with the ,sun1 must again describe the arch n o2 which arch is similar to ,t t1 because the lines ,,fn1 f n1 are parallel2 and because1 while the ,moon describes the arch n o1 the ,earth advances forward in the ecliptic2 the arch described by the ,moon1 after she has finished her periodical month1 before she makes a synodical month1 must be somewhat greater than n o4 ,to determine the mean length of a synodical month1 find the diurnal motion of the ,moon 7or the space she describes round the ,earth in one day7 and likewise the diurnal motion of the ,earth2 then the difference betwixt the two motions1 is the apparent motion of the ,moon round the ,earth in one day2 then it will be1 as this differential arch is to a whole circle2 so is one day to that space of time wherein the ,moon appears to describe a compleat circle round the ,earth1 which is about #bi days4 ,but this is not always a true ,lunation1 for the motion of the ,moon is sometimes faster1 and sometimes slower1 according to the position of the ,earth in her orbit4 ,in one synodical month the ,moon has all manner of aspects with the ,sun and ,earth1 and because she is opaque1 that face of hers will only appear bright which is towards the ,sun1 while the opposite remains in darkness4 ,but the inhabitants of the ,earth can only see that face of the ,moon which is turned towards the ,earth2 and therefore1 according to the various positions of the ,moon1 in respect of the ,sun and ,earth1 we observe different portions of her illuminated face1 and so a continual change in her#g,phases4 ,let ,s be the ,sun1 ,,rtv an arch of the ,earth's orbit1 ,t the ,earth1 and the circle ,,abcd1 c4 the ,moon's orbit1 in which she turns round the ,earth in the space of a month2 and let ,a1 ,b1 ,c1 c4 be the centers of the ,moon in different parts of her orbit4 ,now if with the lines ,s ,a1 ,s ,b1 c4 we join the centers of the ,sun and ,moon1 and at right angles to these draw the lines ,h ,o2 the said lines ,h ,o will be the circles that separate the illuminated part of the ,moon from the dark and obscure4 ,again1 if we conceive another line ,i ,l to be drawn at right angles to the lines ,,ta1 ,,tb1 c4 passing from the center of the ,earth to the ,moon1 the said line ,i ,l will divide the visible hemisphere of the ,moon1 or that which is turned towards us1 from the invisible1 or that which is turned from us2 and this circle may be called the ,circle of ,vision4 ,sidenote3 ,full ,moon4 ,sidenote3 ,half ,moon4 ,sidenote3 ,new ,moon4 ,now it is manifest1 that whenever the ,moon is in the position ,a1 or in that point of her orbit which is opposite to the ,sun1 the circle of vision1 and the circle bounding light and darkness1 do coincide1 and all the illuminated face of the ,moon is turned towards the ,earth1 and is visible to us2 and in this position the ,moon is said to be full4 ,but when the ,moon arrives to ,b1 all her illuminated face is then not towards the ,earth1 there being a part of it1 ,,hbi1 not to be seen by us2 and then her visible face is deficient from a circle1 and appears of a gibbous form1 as in ,b4 ,fig4 #c4 ,again when she arrives to ,c1 the two forementioned circles cut each other at right angles1 and then we observe a half ,moon1 as in ,c1 ,fig4 #c4 ,and again the illuminated face of the ,moon is more and more turned from the ,earth1 until she comes to the ,point ,e1 where the circle of vision1 and that bounding light and darkness1 do again coincide4 ,here the ,moon disappears1 the illuminated part being wholly turned from the ,earth2 and she is now said to be in ,conjunction with the ,sun1 because she is in the same direction from the ,earth that the ,sun is in1 which position we call a ,new ,moon4 ,when the ,moon is arrived to ,f1 she again assumes a horned figure1 but her horns 7which before the change were turned ,westward7 have now changed their position1 and look ,eastward4 ,when she has arrived to a quadrate aspect at ,g1 she will appear bissected1 like a half ,moon1 afterwards she will still grow bigger1 until at last she comes to ,a1 where again she will appear in her full splendor4 ,the same appearances which we observe in the ,moon are likewise observed by the ,lunarians in the ,earth1 our ,earth seeing a ,moon to them1 as their ,moon is to us2 and we are observed by them to be carried round in the space of time that they are really carried round the ,earth4 ,but the same phases of the ,earth and ,moon happen when they are in contrary position2 for when the ,moon is in conjunction to us1 the ,earth is then in opposition to the ,moon1 and the ,lunarians have then a full ,earth1 as we in a similar position have a full ,moon4 ,when the ,moon comes in opposition to the ,sun1 the ,earth1 seen from the ,moon1 will appear in conjunction with her1 and in that position the ,earth will disappear2 afterwards she will assume a horned figure1 and so shew the same phases to the inhabitants of the ,moon as she does to us4 ,of the ,eclipses of the ,sun and ,moon4 ,sidenote3 ,eclipse4 ,an ,eclipse is that deprivation of light in a ,planet1 when another is interposed betwixt it and the ,sun4 ,thus1 an eclipse of the ,sun is made by the interposition of the ,moon at her conjunction1 and an eclipse of the ,moon is occasioned by the shadow of the ,earth falling upon the ,moon1 when she is in opposition to the ,sun4 ,sidenote3 ,fig4 #d4 ,sidenote3 ,lunar ,eclipse4 ,let ,s be the ,sun1 ,t the ,earth1 and ,,abc its shadow2 now if the ,moon1 when she is in opposition to the ,sun1 should come into the conical space ,,abc1 she will then be deprived of the solar light1 and so undergo an eclipse4 ,sidenote3 ,solar ,eclipse4 ,sidenote3 ,fig4 #e4 ,in the same manner1 when the shadow of the ,moon falls upon the ,earth 7which can never happen but when the ,moon is in conjunction with the ,sun7 that part upon which the shadow falls will be involved in darkness1 and the ,sun eclipsed4 ,but because the ,moon is much less than the ,earth1 the shadow of the cannot cover the whole ,earth1 but only a part of it4 ,let ,s be the ,sun1 ,t the ,earth1 ,,abc the ,moon's orbit1 and ,l the ,moon in conjunction with the ,sun3 ,here the shadow of the ,moon falls only upon the part ,,de of the ,earth's surface1 and there only the ,sun is intirely hid3 but there are other parts ,,ef1 ,,dg1 on each side of the shadow1 where the inhabitants are deprived of part of the ,solar rays1 and that more or less1 according to their distance from the shadow4 ,those who live at ,h and ,i will see half of the ,sun eclipsed1 but in the spaces ,,fm1 ,,gn1 all the ,sun's body will be visible1 without any eclipse4 ,from the preceding figure it appears1 that an eclipse of the ,sun does not reach a great way upon the superficies of the ,earth2 but the whole body of the ,moon may sometimes be involved in the ,earth's shadow4 ,sidenote3 ,fig4 #f4 ,although the ,moon seen from the ,earth1 and the ,earth seen from the ,moon1 are each alternately1 once a month1 in conjunction with the ,sun2 yet1 by reason of the inclination of the ,moon's orbit to the ecliptic1 the ,sun is not eclipsed every new ,moon1 nor the ,moon at every full4 ,let ,t be the ,earth1 ,,dte an arch of the ecliptic1 ,,albf1 the ,moon's orbit1 having the ,earth ,t1 in its center2 and let ,,agbg be another circle coinciding with the ecliptic1 and ,a1 ,b1 the nodes1 or the two points where the ,moon's orbit and the ecliptic cut each other4 ,a the ascending node1 and ,b the descending node4 ,the angle ,,gal equal to ,,gbl is the inclination of the ,moon's orbit to the ecliptic1 being about #e degrees4 ,now a spectator from the ,earth at ,t1 will observe the ,sun to move in the circle ,,agbc1 and the ,moon in her orbit ,,albf2 whence it is evident1 that the ,sun and ,moon can never be seen in a direct line1 from the center of the ,earth1 but when the ,moon is in one of the nodes ,a or ,b2 and then only will the ,sun appear centrally eclipsed4 ,but if the conjunction of the ,moon happens when she is any where within the distance ,a c of the nodes1 either ,north or ,south1 the ,sun will then be eclipsed1 more or less1 according to the distance from the node ,a1 or ,b4 ,if the conjunction happens when the ,moon is in b1 the ,sun will be then one half eclipsed2 and if it happens when she is in c1 the ,moon's limb will just touch the ,sun's disk1 without hiding any part of it4 ,the shadow of the ,earth at the place where the ,moon's orbit intersects it1 is three times as large as the ,moon's diameter1 as in ,fig4 #d4 and therefore it often happens that eclipses of the ,moon are total1 when they are not central3 ,and for the same reason the ,moon may sometimes be totally eclipsed for three hours together2 whereas total eclipses of the ,sun can scarcely ever exceed four minutes4 ,the eclipses of the ,sun and ,moon are very well explained by the ,orrery3 ,thus having put the lamp in the place of the ,sun1 and the little ,earth and the little ,moon in their proper places1 instead of the larger ones1 let the room wherein the instrument stands be darkened2 then turning the handle about1 you will see when the conjunction of the ,moon happens4 ,when she is in or near one of the nodes1 her shadow will fall upon the ,earth1 and so deprive that part upon which it falls of the light of the ,sun3 ,if the conjunction happens when the ,moon is not near one of the nodes1 the light of the lamp will fall upon the ,earth1 either above or below the ,moon1 according to her latitude at that time4 ,in like manner1 when the full ,moon happens near one of the nodes1 the shadow of the ,earth will fall upon the ,moon2 and if the ,moon's latitude be but small1 her whole face will be involved in darkness4 ,at other times1 when the full ,moon happens when she is not near one of her nodes1 the shadow of the ,earth will pass either above or below the ,moon1 and so by that means the ,moon will escape being eclipsed4 ,of the ,eclipses of the ,satellites of ,jupiter4 ,the apparent diameters of the inferior ,planets are so small1 that when they pass betwixt us and the ,sun1 they only appear like small spots upon the ,sun's surface1 without depriving us of any sensible quantity of his light4 ,the shadow of the ,earth likewise terminates before it reaches any of the superior ,planets1 so that they are never eclipsed by us2 and the ,earth when she is in conjunction with the ,sun1 only appears like a black spot upon his surface4 ,but ,jupiter and his ,moons mutually eclipse each other1 as our ,earth and ,moon do2 as also doth ,saturn and his ,moons4 ,the satellites of ,jupiter become twice hid from us1 in one circulation round 2 viz4 once behind the body of ,jupiter1 i4 e4 when they are in the right line joining the centers of the ,earth and 2 and again they become invisible when they enter the shadow of ,jupiter1 which happens when they are at their ,full1 as seen from 1 at which times they also suffer eclipses2 which eclipses happen to them after the same manner as they do to our ,moon1 by the interposition of the ,earth betwixt her and the ,sun4 ,sidenote3 ,fig4 #g4 ,let ,s be the ,sun1 ,,abt the ,earth's orbit2 and ,c ,d1 an arch of ,jupiter's orbit1 in which let ,jupiter be in the point 2 and let ,,cfdh be the orbit of one of ,jupiter's satellites1 which we will here suppose to be the farthest from him4 ,these satellites1 while they move thro' the inferior parts of their orbs1 viz4 from ,d thro' ,h1 ,i1 to ,c1 seem from the ,earth and the ,sun to have a retrograde motion2 but when they are in the superior part of their orbit1 they are then seen to move from ,west to ,east1 according to their true motion4 ,now while they describe the superior part of their orbits1 they will be twice hid from the ,earth1 once in the shadow of 1 and once behind his body4 ,if ,jupiter be more ,westerly than the ,sun1 that is1 when the ,earth is in ,a1 they will be first hid in the shadow ,f1 and afterwards behind the body of in ,g3 ,but when the ,earth is in ,b1 then they are first hid behind 's body in ,e1 and afterwards fall into the shadow ,f4 ,while the satellites describe the inferior parts of their orbit1 they only once disappear1 which may be either in ,i or ,h1 according to the position of the ,earth1 in which places they cannot be distinguished from the body of ,jupiter4 ,illustration3 ,plate #e ,fig4 ,i ,fig4 ,,ii ,fig4 ,,iii ,fig4 ,,iv ,fig4 ,v ,fig4 ,,vi ,fig4 ,,vii ,when the satellites seen from are in conjunction with the ,sun1 their shadows will then fall upon 1 and some part of his body be involved in darkness1 to which part the ,sun will be totally eclipsed4 ,by observing the eclipses of ,jupiter's satellites1 it was first discovered that light is not propogated instantaneously1 though it moves with an incredible swiftness3 ,for if light came to us in an instant1 an observer in ,t will see an eclipse of one of the satellites1 at the same time that another in ,k would4 ,but it has been found by observations1 that when the ,earth is in ,k1 at her nearest distance from ,jupiter1 these eclipses happen much sooner than when she is in ,t4 ,now having the difference of time betwixt these appearances in ,k and ,t1 we may find the length of time the light takes in passing from ,k to ,t1 which space is equal to the diameter of the ,earth's annual orb4 ,by these kinds of observations it has been found1 that light reaches from the ,sun to us in the space of eleven minutes of time1 which is at least at the rate of #ajj1jjj miles in a second4 ,,finis4 ,illustration ,,an ,,index ,,of ,,the ,,astronomical ,,terms ,made ,use of in this ,,book4 ,acronical ,rising and ,setting of the ,stars ,page #if ,almacanthers #fc ,altitudes ib4 ------ ,meridian ,altitude #fc ,amplitude #fb ,amphiscians #ia ,annual ,motion #g ,antci #ib ,antarctic ,circle #ec ------ ,pole ib4 ,antipodes #ic ,arctic ,circle #eb ,arctic ,pole #ec ,ascension #fh ------ ,right ib4 ------ ,oblique #fi ,ascensional ,difference ib4 ,ascians #ia ------ ,heteroscians ib4 ,asterisms #cf ,atmosphere #ha ,axis #dc ------ of the ,world #di ,azimuth #fa ,babylonish ,hours #ga ,bissextile #gh ,circle #db ------ ,great ,circles ib4 ------ ,parallel1 or lesser ,circles #dc ------ ,secondary ,circles ib4 ,circles of the ,sphere #dg ,climates #ic ,colures #ec ------ ,equinoctial ,colure ib4 ------ ,solstitial ,colure #ed ,comets #bi ,conjunction #aa1 #bjg ,constellations #cf ,cosmical rising and setting of the ,stars #if ,crepusculum #hc ,day1 ,natural and ,artificial #fi ,declination #eb ,diurnal ,motion #g ,diurnal ,arch #fh ,eclipses #bjh ------ ,solar ib4 ------ ,lunar ib4 ,eclipses of ,jupiter's ,satellites #bab ,ecliptic #ec ,egyptian ,year #ge ,elongation #ah ,equator1 or ,equinoctial #dh ,equinoctial ,points #ec ------ ,precession of #ee ------ ,vernal and ,autumnal #gj ,excentricity #d ,galaxy1 or ,milky ,way #ch ,geocentric ,place #ai ,globe #db ------ ,terrestrial #dc ------ ,celestial #dd ,gregorian ,account #hj ,heliacal rising and setting of the ,stars #if ,heliocentric ,place #ai ,hemisphere #db ------ ,northern and ,southern #di ,heteroscians #ia ,horizon #eh ------ ,sensible ib4 ------ ,rational #ei ,hour ,circles #ej ,italian ,hours #gb ,jewish ,hours ib4 ,julian ,account #gi ,latitude1 in ,astronomy #ef ------ in ,geography #hd ,longitude in ,astronomy #ef ------ in ,geography #hg ,meridian #ej1 #fa ,nadir #fa ,nodes #c1 #bjb ,nocturnal ,arch #fh ,orbit #c ,parallel of the ,earth's ,semidiameter #bc ------ of the ,earth's ,annual ,orb #bj ,perici #ib ,periscians #ia ,periodical ,month #gd1 #bjb ,phases of the ,moon #bja ,planets #a ------ ,inferior and ,superior #ad ,planetary ,hours #gb ,poles #db ------ of the ,world #di ------ of the ,ecliptic #ef ,polar ,circles #eb ,points of the ,compass #fj ------ ,cardinal ,points #ei ,primary ,planets #e ,retrograde ,motion of the ,planets #ahg ------ of the ,nodes #bjb ,secondary ,planets #e ,sidereal ,year #gd ,signs of the ,zodiac #ed ------ ,northern and ,southern ib4 ,solstices #ga ------ ,summer and ,winter ,solstices ib4 ,solstitial ,points #ec ,sphere #db ------ ,parallel and ,right #fg ------ ,oblique #fh ,stationary #ahf ,style ,old #gi ------ ,new ,style #hj ,synodical ,month #gd1 #bjb ,tropics 7of ,cancer and ,capricorn7 #eb ,twilights #hc ,vertical ,circles #fa ------ ,prime ,vertical #fb ,zenith #fa ,zenith ,distance #fc ,zones1 ,torrid1 ,temperate1 and ,frigid #ij ,,the ,,end ,directions to the ,binder4 ,the great ,,orrery to face the ,title4 ,plate ,i4 ,page #b ,plate ,,ii4 #bh ,the ,globes #ce ,plate ,,iii4 #aid ,plate ,,iv4 #bjj ,plate ,v4 #bad ,a ,,catalogue ,of ,mathematical1 ,philosophical1 and ,optical ,instruments1 ,,made and ,,sold by ,,benjamin ,,cole1 ,at his ,shop1 the ,sign of the ,orrery1 ,no4 #acf1 in ,fleet street1 ,london4 l4 s4 d4 ,variety of pocket cases of ,drawing ,instruments1 in ,silver1 from #cl4 #cs4 to #bj #j #j ,ditto1 in ,brass1 from #es4 to #e #e #j ,magazine ,cases1 in ,silver1 from #abl4 to #aej #j #j ,ditto1 in ,brass1 from #el4 to #ej #j #j ,circular ,compasses to describe a ,circle as small as a pin's head1 from #cs4 to #j #g #f ,long ,hand ,drawing-pens1 from #as4 to #j #e #j ,compasses in ,brass1 with shifting points1 as the ,ink and ,black ,lead points1 from #bs4 #f;d4 to #a #a #j ,plain ,compasses1 from #f;d4 to #j #e #j ,beam ,compasses1 for drawing large circles1 from #ab4 to #c #j #j ,proportionable ,compasses1 from #al4 #as4 to #e #e #j ,triangular ,compasses1 from #ads4 to #j #ah #j ,elliptical ,compasses1 for ,ovals1 from #al4 #aas4 #f;d4 to #e #e #j ,hair ,compasses #j #g #f ,bows for drawing curved lines1 from #ds4 to #j #aj #f ,sets of ,feather-edge ,scales1 in ,brass1 ,ivory1 or ,wood1 from #abs4 to #a #af #j ,plain ditto1 or ,plotting ditto1 in ditto1 from #h;d4 to #j #ah #j ,gunter's #b feet1 and #a foot ,scales1 in ,brass or ,wood1 from #bs4 to #b #b #j ,protractors of all sorts1 from #as4 #f;d4 to #a #af #j ,parallel ,rules1 from #f to #cf inches1 from #bs4 #f;d4 to #a #af #j ,cross-bar ditto1 in ,brass1 ,ivory1 or ,wood1 from #d inches1 to #c feet1 from #ajs4 #f;d4 to #c #j #j ,sectors1 in ditto1 from #bs4 #f;d4 to #d #ad #f ,theodolites1 from #cl4 #cs4 to #f #f #j ,ditto1 with ,vertical arch1 ,spirit ,levels1 ,telescope1 c4 from #ajl4 #ajs4 to #ba #j #j ,plain ,tables1 from #cl4 #cs4 to #e #e #j ,circumferentors1 the principal ,instrument for ,surveying in the ,west-,indies1 from #al4 #afs4 to #c #ac #f ,gunter's four pole chains1 from #fs4 to #j #ab #j ,spirit ,levels of all sorts1 from #es4 to #ab #ab #j ,pentographia1 for the ready and exact reduction or copying of ,schemes1 ,drawings1 ,prints1 c4 #d #ad #f ,measuring ,wheels for ,surveying1 from #dl4 #ads4 #f;d4 to #f #f #j ,hadley's ,quadrants1 with ,diagonal ,divisions #a #ad #j ,ditto1 with a ,nonius1 from #bl4 #bs4 to #c #ac #f ,ditto1 all in ,brass1 from #cl4 #acs4 #f;d4 to #f #f #j ,davies's ,quadrant1 from #abs4 to #a #a #j ,cole's ditto1 from #ahs4 to #a #e #j ,sutton's ditto #j #f #j ,gunter's ditto1 from #cs4 #f;d4 to #a #a #j ,horizontal ,sun ,dials1 for all ,latitudes1 from #es4 to #aj #j #j ,ring ,dials1 from #ajs4 #f;d4 to #ba #j #j ,azimuth ,compasses1 from #el4 #es4 to #aj #j #j ,amplitude ditto1 from #al4 #gs4 to #e #e #j ,mariner's ,compasses1 either for the ,cabin1 or ,binacle1 from #gs4 #f;d4 to #c #ac #j ,pocket ,compasses1 from #as4 to #a #aa #f ,large ,orreries1 from #ejl4 to #bej #j #j ,armillary ,spheres1 from #abl4 to #ej #j #j ,seventeen inch ,globes #f #f #j ,fifteen inch ditto #e #e #j ,twelve inch ditto #c #c #j ,nine inch ditto #b #b #j ,six inch ditto #a #af #j ,three inch ditto1 in a case1 from #hs4 to #j #aj #j ,large double ,barrell'd standing air pumps #be #j #j ,apparatus to ditto1 from #cl4 #cs4 to #ab #ab #j ,double ,barrell'd table air pumps1 with their apparatus1 from #el4 #aes4 #f;d4 to #bj #j #j ,single ,barrell'd ditto #b #ab #f ,apparatus to ditto #b #b #j ,electrical ,machines1 in ,brass1 with apparatus1 box1 c4 from #el4 #es4 to #ac #ac #j ,barometers1 from #al4 #as4 to #a #af #j ,ditto ,thermometer1 in one frame1 from #a4 #aas4 #f;d4 to #b #ab #f ,barometer1 ,thermometer1 and ,hydrometer1 all in one frame1 from #bl #abs4 #f;d4 to #c #ac #f ,farenheit's ,thermometers1 in mahogany cases1 from #al4 #es4 to #a #aa #f ,pocket ditto1 in black cases1 from #abs4 to #a #a #j ,spirit ,thermometers1 on box scales1 for hot-houses #j #aj #f ,hydrometers1 in ,ivory1 from #ds4 to #j #e #f ,ditto1 in copper1 with weights1 c4 for proving ,spirits1 from #al4 #as4 to #a #e #j ,hydrostatic ,balance1 with apparatus1 c4 #a #ae #j ,speaking ,trumpets1 from #ajs4 to #a #aa #f ,hearing ditto1 from #gs4 #f;d4 to #a #a #j ,reflecting ,telescopes1 from #al4 #afs4 to #ej #j #j ,refracting ditto1 of various lengths1 with four or six glasses1 from #gs4 #f;d4 to #f #f #j ,double reflecting ,microscopes1 from #cl4 #acs4 #f;d4 to #g #g #j ,solar ditto1 in ,brass1 from #dl4 #ds4 to #f #f #j ,wilson's pocket ditto1 from #al4 #es4 to #b #ab #f ,opake ditto1 from #bl4 #abs4 #f;d4 to #c #ac #f ,cloth ditto1 from #cs4 #f;d4 to #j #g #f ,flower ditto1 from #cs4 #f;d4 to #j #e #j ,diagonal ,machines for viewing prints1 from #afs4 to #a #aa #f ,large ,book ,camera ,obscura1 from #dl4 #ds4 to #e #e #j ,box ,camera ,obscura1 from #ajs4 #f;d4 to #b #b #j ,scioptric ,ball and ,socket1 in ,wood #j #g #f ,opera ,glasses1 from #es4 to #b #ab #f ,prospect ditto1 from #h;d4 to #j #aj #f ,magic ,lanthorn1 without objects1 from #al4 #as4 to #a #g #j ,magic ,lanthorn sliders1 with objects1 from #es4 to #j #aj #f ,mirrors1 convex or concave1 of all sizes1 in black frames1 from #ajs4 #f;d4 to #af #af #j ,prisms1 from #fs4 to #a #a #j ,reading ,glasses set in a variety of curious frames1 from #bs4 #f;d4 to #b #ab #f ,watchmaker's ,glasses1 in frames1 from #as4 to #j #aj #f ,concave ditto1 for short sighted persons1 from #as4#f;d4 to #b #b #j ,spectacles ground on brass tools1 and set in silver1 tortoise shell1 horn1 c4 from #as4 to #a #g #j ,achromatic1 ,opera1 and ,prospect glasses1 from #al4 #as4 to #a #af #j ,achromatic ,telescopes of any length1 at #al4 #as4 each foot4 ,gauging ,rules1 ,carpenter's ,rules1 and all other kind of ,rules1 at the usual ,prices4 ,the ,eleventh ,edition of ,,harris on the ,globes1 with the ,description and ,use of the ,orrery1 #cs4 #f;d4 ,the ,use of the ,sector and plain ,scale explained1 #as4 ,the ,use of ,,hadley's ,quadrant explained1 #f;d4 ,a fine ,print of the ,orrery1 on imperial paper1 #bs4 ,a smaller ditto1 #f;d4 ,variety of other ,instruments too tedious to mention1 are made and sold at the above place3 ,where any ,gentleman1 by ,letter1 or other ,directions1 may depend on being as faithfully served as if present4 ,and as ,i have been long in the ,wholesale part of the ,business1 ,merchants1 c4 may be sure of being supplied on the ,best ,terms4 ,as also by ,m4 ,,allison1 at ,falmouth4 ,illustration ,,footnotes3 #a ,by the ,orbit of a ,planet is commonly understood the ,tract or ,ring1 described by its ,center round the ,sun1 but by the ,plane of the ,orbit is meant a flat ,surface extended every way thro' the ,orbit infinitely4 #b ,n4 ,b4 ,according to ,biachini's ,observations1 ,venus's axis inclines #ge degrees from the perpendicular to the plane of the ,ecliptic 7which is #ea deg4 more than the axis of our ,earth7 her ,tropics are only #ae deg4 from her ,poles1 and her ,polar ,circles at the same distance from her ,equator2 so that the ,sun's greatest ,declination on each side of her ,equator is #ge deg4 by which she must undergo a much greater variety of seasons than we do on our ,earth4 #c ,is a mark commonly used for conjunction2 thus with the 1 is to be read conjunction with the ,sun4 #d ,prob4 ,,vi4 #e ,prob4 ,,xiii4 #f ,the insensible change in the ,longitude1 ,right ,ascension1 and ,declination of the ,fixed ,stars1 made by their slow motion1 parallel to the ecliptic 7being but #a degree in #gb years7 is not worth notice in this place4 #g ,phases of the ,moon are those different appearances we observe in her1 according to her position in respect to the ,sun and ,earth4