,illustration3 ,plate ,i4 ,the ,,copernican or ,,solar ,,system4 ,the comparative ,distances of the ,planets from the ,sun ,t4 ,conder ,sculpt4 ,,the ,,study ,,of ,,astronomy1 ,,adapted ,,to ,,the ,,capacities ,,of ,,youth3 ,,in ,,twelve ,,familiar ,,dialogues1 ,,between ,a ,,tutor ,,and ,,his ,,pupil3 ,explaining the ,general ,,ph,,nomena of the ,,heavenly ,,bodies1 the ,,theory of the ,,tides1 c4 ,,illustrated ,,with ,,copper-,,plates4 ,,by ,,john ,,stedman4 ,,london3 ,,printed ,,for ,c4 ,,dilly1 ,,in ,,the ,,poultry4 ,m4,,dcc4,,xcvi4 ---------------------------------------- -------------------------------- ,,errata4 ,page #bj4 line #h4 for he read the4 ---- #bb4 -- #f4 ---- #bc4 -- #b4 -- disk -- disc4 ---- #db4 -- last ---- #gi4 -- #e4 ---- #gd4 -- #f4 -- it axis -- its axis4 ---- #gh4 -- #ai4 dele ,mercury4 ---------------------------------------- -------------------------------- ,,preface4 ,it has long been a matter of surprize to those who are interested in the education of youth1 that1 among the numerous publications intended for their improvement1 so few attempts have been made to facilitate the study of ,astronomy4 ,many excellent treatises have been written on this important and useful science2 but if it be considered that they abound with technical terms1 unintelligible to juvenile minds1 it cannot be expected that they should derive any great advantage from the perusal of them4 ,to remove these difficulties1 the ,author has endeavoured1 whenever he had occasion to use them1 to give such illustrations as to leave no doubt on the young student's mind respecting their true meaning4 ,the subject appeared to him to be best calculated for dialogues1 which are certainly more agreeable as well as more perspicuous to young persons1 than the discouraging formality of a treatise4 ,and it is presumed the language will be found natural and easy4 ,in the order he has chosen1 he has been careful not to introduce any thing new1 till the former part1 on which it depends1 has been clearly explained4 ,on the whole1 it has been his aim to render it as concise and plain as the nature of the subject will admit2 and he flatters himself1 that at a time when the sciences are so universally studied1 the introduction now offered to the public will not be unacceptable4 ---------------------------------------- -------------------------------- ,,contents4 ,,dialogue ,i4 p4 #a4 ,introduction4 ,definition4 ,the sun and planets4 ,a globe defined4 ,sun's distance and magnitude4 ,planets1 what2 their names1 periods1 and distances from the sun2 their magnitudes1 compared with the earth2 called inferior and superior1 why4 ,comets2 derivation of the name4 ,solar system2 why so called4 ,,dialogue ,,ii4 p4 #aj4 ,different systems explained4 ,planets appear like stars2 they shine by reflection2 how known from stars2 they never twinkle1 why4 ,stars shine with their own native light2 their inconceivable distance2 are suns1 the centers of other systems4 ,plurality of worlds4 ,,dialogue ,,iii4 p4 #bj4 ,the earth has the appearance of a star to ,venus4 ,remote objects appear at equal distances from us4 ,our earth is a moon to the moon4 ,the orb of the moon visible soon after the change2 her disc and bulk compared with the earth2 her mean distance4 ,sun's disc compared with hers4 ,our sun a star1 if seen from a planet of another system4 ,stars as far from each other as the nearest is to us4 ,stars distinguished by their apparent magnitude4 ,the ,milky ,way innumerable stars4 ,number of stars visible at one time to the naked eye4 ,,dialogue ,,iv4 p4 #bi4 ,stars divided into constellations2 necessary for ascertaining the situation of the planets1 and of the stars with each other4 ,planets motion regular if seen from the sun2 irregular as seen from the earth1 the motion being sometimes direct1 sometimes retrograde2 at others they appear stationary4 ,superior and inferior conjunction1 and opposition1 what4 ,venus has the different phases of the moon4 ,planets1 how distinguished from each other4 ,,dialogue ,v4 p4 #ci4 ,ecliptic1 what4 ,inclination of the orbits of the planets4 ,nodes of the planets1 what4 ,a plane1 what4 ,planets move in unbounded space4 ,mercury and ,venus seen on the sun's disc4 ,number of signs in the zodiac4 ,zodiac1 what4 ,a degree1 what4 ,names of the signs4 ,number of degrees in each sign4 ,sun's place in the ecliptic4 ,table of signs1 their characters1 c4 ,to find the sun's place in the ecliptic for any day in the year4 ,,dialogue ,,vi4 p4 #ej4 ,the orbits of the planets are not true circles1 but somewhat elliptical4 ,perihelion1 aphelion1 and mean distance1 what4 ,attraction1 what4 ,laws of attraction4 ,attraction of gravitation1 its effects4 ,simple motion rectilineal4 ,attractive or centripetal1 and projectile or centrifugal forces1 what4 ,,dialogue ,,vii4 p4 #fa4 ,bodies moving in circles have a tendency to fly off4 ,planets kept in their orbits by the joint action of the centripetal and centrifugal forces2 they describe equal areas in equal times4 ,orbits of the comets very elliptical4 ,the earth in its perihelion in ,december4 ,equation of time4 ,center of gravity1 what2 sun and planets move round it4 ,sun the center of the system4 ,,dialogue ,,viii4 p4 #gc4 ,the earth revolves on its axis4 ,cause of day and night4 ,the motion of the earth so uniform as not to be perceived4 ,the apparent motion of the sun caused by the earth's motion on its axis4 ,an objection to the earth's motion answered4 ,the sun and some of the planets revolve on their axes4 ,atmosphere1 what2 cause of twilight4 ,horizon1 what2 the sun and moon appear largest near the horizon1 why2 they appear above the horizon when below it2 caused by refraction2 proved by experiment4 ,,dialogue ,,ix4 p4 #hg4 ,inclination of the earth's axis4 ,an angle1 what4 ,the poles1 what4 ,equinoctial1 what4 ,earth's parallelism described4 ,the axis of the earth points to the same parts of the heavens4 ,equator1 ecliptic1 polar circles1 and meridians1 explained4 ,difference of time between places lying under different meridians4 ,longitude1 what4 ,how to reduce longitude to time1 and time to longitude4 ,latitude1 what4 ,,dialogue ,x4 p4 #aja4 ,the seasons4 ,vernal and autumnal equinoxes4 ,days and nights always equal1 if the axis of the earth were perpendicular to the plane of its orbit4 ,seasons occasioned by the inclination of the earth's axis4 ,seasons continued4 ,days and nights equal at all times under the equator4 ,the sun above the horizon of the poles six months2 and six months below them alternately1 so that they have but one day and one night in the year2 the longest day under the polar circles is twenty-four hours4 ,the sun rises on different points of the compass at different seasons of the year4 ,twilight in the polar regions of long duration4 ,we are nearest the sun in winter1 yet it is our coldest season1 why4 ,the earth divided into zones2 proved to be globular1 but is not a true sphere4 ,,dialogue ,,xi4 p4 #abj4 ,the moon4 ,her diameter1 synodical and periodical revolutions4 ,her phases4 ,has always the same side to the earth1 and makes a revolution on her axis every lunation4 ,has mountains and valleys1 but no seas nor atmosphere2 yet may be inhabited4 ,her real and apparent motion described4 ,eclipses4 ,of the sun2 total and partial eclipses4 ,digit1 what4 ,eclipse of the moon4 ,penumbra1 what4 ,central and total eclipse4 ,why we have not an eclipse at every full and change of the moon4 ,she does not always rise with the sun at change2 nor when he sets at full4 ,she is visible when totally eclipsed4 ,,dialogue ,,xii4 p4 #acf4 ,tides4 ,occasioned by the attraction of the sun and moon1 and their centrifugal forces2 exemplified by an experiment4 ,spring and neap tides4 ,tides not highest directly under and opposite the moon1 but after she has passed the meridian4 ,they are later and later every day4 ,rule for finding the proportional magnitudes of the planets compared with the earth2 or the proportion that one globe bears to another4 ,a cube number1 what4 ,table of roots1 squares1 and cubes2 an example4 ,rule for finding the mean distances of the planets from the sun4 ,dr4 ,turner's rule for extracting the cube root2 an example to explain the rule4 ,example to find the mean distance of ,mercury from the sun4 ,table of diameters1 c4 ,conclusion4 ---------------------------------------- -------------------------------- ,,dialogue ,i4 ,,tutor4 ,well1 ,sir6 ,i suppose this early visit is in consequence of my promise1 and your anxiety to become an astronomer4 ,,pupil4 ,it is1 ,sir4--,and as astronomy is a science of which ,i have a very imperfect idea1 ,i must beg of you to explain it to me4 ,,tutor4 ,that ,i shall do with pleasure4 ,but you surely cannot wholly forget what ,i have formerly told you4 ,however1 as ,i mean to treat the subject as if you had no previous knowledge of it1 you will have an opportunity from what you can recollect1 to make such remarks1 and ask such questions1 as may appear most material to you4 ,,pupil4 ,i thank you1 ,sir1 it is just what ,i wish4 ,,tutor4 ,by astronomy then is meant a knowledge of the heavenly bodies1 the sun1 moon1 planets1 comets1 and stars1 respecting their nature1 magnitudes1 distances1 motions1 c4 ,,pupil4 ,i fear ,i shall find it a difficult study4 ,,tutor4 ,have patience4---- 8,the wise and prudent conquer difficulties1 8,by daring to attempt them4 ,sloth and folly 8,shiver and shrink at sight of toil and danger1 8,and make the impossibility they fear40 ,,pupil4 ,this gives me encouragement1 and1 if you will have patience with me1 ,i will endeavour to profit by your instructions4----,pray1 ,sir1 what is the sun8 ,,tutor4 ,the sun1 the source of light and heat1 has been considered a globe of fire1 round which seven other spherical bodies revolve at different distances from him1 and in different periods of time1 from west by south to east4 ,these are the planets#a4 ,footnote #a3 ,from ,planeta1 roving or wandering4 ,,pupil4 ,any round ball is a globe1 is it not8 ,,tutor4 ,a sphere or globe is defined a round solid body1 every part of whose surface is equally distant from a point within called its center2 and a line drawn from one side through the center to the opposite side1 is called its diameter4 ,,pupil4 ,you say the sun has been considered a globe of fire4 ,is he not now thought to be so8 ,,tutor4 #b;,doctor ,herschell1 from some late observations1 is of a different opinion4--,but what think you of his magnitude8 ,footnote #b3 ,see his letter read at the ,royal ,society1 ,december #ahth1 #agid4 ,,pupil4 ,i really cannot conjecture4--,this ,i know1 that when ,i saw him through the fog the other day1 he appeared about the size of a common plate4 ,,tutor4 ,you must not always judge by appearances4 ,you will find that there is a material difference between his real and apparent magnitude1 which ,i think you will be convinced of when ,i tell you1 that he is no less than #ie millions of miles from our earth4 ,,pupil4 ,ninety-five millions of miles6 ,you astonish me4 ,,tutor4 ,you will1 ,i dare say1 be no less surprized at being told1 that he is more than a million of times as large as our earth4 ,,pupil4 ,it is almost incredible6 ,and what are the planets8 ,,tutor4 ,the planets are opaque1 that is dark bodies1 which receive their light from the sun2 and1 as ,i told you1 revolve about him4 ,the first1 or that nearest the sun1 is called ,mercury1 the next ,venus1 then the ,earth1 ,mars1 ,jupiter1 ,saturn1 and ,georgian1 or the ,georgium ,sidus4#c ,these are called primary planets4 ,footnote #c3 ,their characters are1 ,sun1 ,merc4 ,venus1 ,earth1 ,mars1 ,jup4 ,saturn1 ,georgian1 4 ,,pupil4 ,are there then any others8 ,,tutor4 ,yes4 ,there are fourteen others1 which move round their respective primaries as their centers1 and with them round the sun1 and are called secondaries1 satellites or moons4 ,,pupil4 ,have all the primaries secondaries8 ,,tutor4 ,only four of them have moons4 ,the earth1 ,i need not tell you1 has one2 ,jupiter has four2 ,saturn seven1 besides a stupendous ring which surrounds his body2 and ,georgian two4 ,,pupil4 ,in what time1 and at what distances1 from the sun1 do the planets perform their periodical revolutions8 ,,tutor4 ,mercury revolves about the sun in #hh days1 at the distance of #cf millions of miles4 ,venus1 at the distance of #fh millions of miles1 completes her revolution in #bbd days4 ,earth1 on which we live1 at the distance of #ie millions of miles1 performs its period in one year4#d ,footnote #d3 ,the motion of the earth in its orbit is at the rate of #fh thousand miles an hour4 ,mars1 at the distance of #ade millions of miles1 in little less than two of our years4 ,jupiter1 at the distance of #did millions of miles1 in near #ab years4 ,saturn1 at the distance of #ijf millions of miles1 in about #cj years4 ,georgian1 discovered a few years since by ,dr4 ,herschell1 performs its period at the distance of #ahab millions of miles1 in about #hc years4#e ,footnote #e3 ,as the distances of the planets1 when marked in miles1 are a burthen to the memory1 astronomers often express their mean distances in a shorter way1 by supposing the distance of the earth from the sun to be divided into ten parts4 ,mercury may then be estimated at four of such parts from the sun1 ,venus at seven1 the ,earth at ten1 ,mars at fifteen1 ,jupiter at fifty-two such parts1 ,saturn at ninety-five1 and ,georgian #aij parts4 ,see ,plate ,i4 ,fig4 #a4 ,these are calculated by multiplying the respective distances of the planets by #aj1 and dividing by #ie1 the mean distance of the earth from the sun2 and may be set off by any scale of equal parts4 ,,pupil4 ,what proportion does the earth bear in magnitude to the other planets8 ,,tutor4 ,the earth is fourteen times as large as ,mercury1 very little larger than ,venus1 and three times as large as ,mars4 ,but ,jupiter is more than fourteen hundred times as large as the earth2 ,saturn above a thousand times as large1 exclusive of his ring2 and ,georgian eighty-two times as large4 ,,pupil4 ,have you any thing else1 ,sir1 to remark concerning the planets8 ,,tutor4 ,there are several other things ,i intend to make you acquainted with1 namely1 their nature1 appearances1 motions1 c4 ,at present ,i shall only say1 that ,mercury and ,venus are called #f;inferior planets1 their orbits or paths described in going round the sun1 being within that of the earth2 and the other four1 whose orbits are without the earth's orbit1 #gsuperior planets4 ,footnote #f3 ,perhaps with more propriety interior or inward4 ,footnote #g3 ,exterior or outward4 ,,pupil4 ,there is one thing more ,i wish to know1 if---- ,,tutor4 ,i suppose you were going to say if not too much trouble2 that is quite unnecessary1 as you well know that where ,i see a desire to learn1 teaching is to me a pleasure4--,what is it8 ,,pupil4 ,that you will be so kind as to inform me what the comets are1 and if they have any motion8 ,,tutor4 ,the knowledge we have of comets is very imperfect1 as they afford few observations on which to ground conjecture4 ,they are generally supposed to be planetary bodies1 forming a part of our system3 for1 like the planets1 they revolve about the sun1 but in different directions1 and in extremely long elliptic curves1 being sometimes near the sun1 at others staying far beyond the orbit of the outermost planet2 whereas the orbits of the planets are nearly circular4 ,the period of one1 which appeared in #afhj1 is computed to be #ege years4 ,,pupil4 ,whence do they derive their name8 ,,tutor4 ,from ,cometa1 a hairy star1 because they appear with long tails1 somewhat resembling hair3 some1 however1 have been seen without this appendage1 as well defined and round as planets4 ,,pupil4 ,you say our system3 what am ,i to understand by it8 ,,tutor4 ,the word system1 in an astronomical sense1 means a number of bodies moving round one common center or point3 and1 because the planets and comets revolve about the sun1 it is called the ,solar ,system 7,plate ,i4 fig4 #b472 and we say our system1 as the earth is one of the planets4 ,other systems have been invented for solving the appearances and motions of the heavenly bodies1 a description of which ,i shall leave till ,i next see you4 ---------------------------------------- -------------------------------- ,,dialogue ,,ii4 ,,pupil4 ,i am afraid1 ,sir1 ,i am come before you are prepared for me3 but the very great pleasure ,i received yesterday1 induced me to be with you as early as possible4 ,,tutor4 ,i am glad to see you1 and happy to find you are so well pleased with your difficult study4 ,it will1 ,i assure you1 give you more exalted ideas of the ,deity than any that ,i know of4 ,the ,psalmist was undoubtedly of this opinion when he said1 ,the ,heavens declare the glory of ,god1 and the ,firmament sheweth his handy work4 ,,pupil4 ,i will no longer call it a difficult1 but a pleasing study1 and feel myself ashamed at having used the expression4 ,i shall now beg you to explain to me the different systems4 ,,tutor4 ,the system ,i have been describing to you was known and taught by ,pythagoras1 a ,greek philosopher1 who flourished about #ejj years before ,christ1 as he found it impossible1 in any other way1 to give a consistent account of the heavenly motions4 ,this system1 however1 was so extremely opposite to all the prejudices of sense and opinion1 that it never made any great progress1 nor was ever widely spread in the ancient world4 ,ptolemy1 an ,egyptian philosopher1 who flourished #acj years after ,christ1 supposed that the earth was fixed in the center1 and that the sun and the rest of the heavenly bodies moved round it in twenty-four hours1 or one natural day1 as this seemed to correspond with the sensible appearances of the clestial motions4 ,this system was maintained from the time of ,ptolemy to the revival of learning in the sixteenth century4 ,at length1 ,copernicus1 a native of ,poland1 a bold and original genius1 adopted the ,pythagorean system1 and published it to the world in the year #aecj4 ,this doctrine had been so long in obscurity1 that the restorer of it was considered as the inventor4 ,europe1 however1 was still immersed in ignorance2 and the general ideas of the world were not able to keep pace with those of a refined philosophy4 ,this occasioned ,copernicus to have few abettors1 but many opponents4 ,tycho ,brahe1 in particular1 a noble ,dane1 sensible of the defects of the ,ptolemaic system1 but unwilling to acknowledge the motion of the earth1 endeavoured1 about #aehf1 to establish a new system of his own2 but1 as this proved to be still more absurd than that of ,ptolemy1 it was soon exploded1 and gave way to the #h;,copernican or true ,solar ,system4 ,footnote #h3 ,see ,plate ,i4 fig4 #b4 ,,pupil4 ,i confess1 ,i should have thought with ,ptolemy1 that the earth was in the center1 and that the sun moved round it4 ,,tutor4 ,you must at present content yourself with knowing that it is not so2 and it shall be my business to prove it4 ,,pupil4 ,may ,i beg the favour of the information you intended respecting the planets8 ,,tutor4 ,i will grant it with pleasure4 ,the planets are spherical bodies1 which appear like stars1 but are not luminous2 that is1 they have no light in themselves2 though they give us light2 for they shine by reflecting the light of the sun4 ,,pupil4 ,you say1 ,sir1 that they appear like stars2 if so1 how am ,i to know them from stars8 ,,tutor4 ,very easily3 for the stars1 or as they are more properly called fixed stars1 always keep the same situation with respect to each other2 whereas the planets1 as they move round the sun1 must be continually changing their places among the fixed stars1 and with one another4 ,,pupil4 ,is there any other method of distinguishing them besides what you have mentioned8 ,,tutor4 ,yes4 ,the planets never twinkle like the fixed stars1 and are seen earliest in the evening and latest in the morning4 ,,pupil4 ,how is the twinkling of the stars in a clear night accounted for8 ,,tutor4 ,it arises from the continual agitation of the air or atmosphere through which we view them2 the particles of air being always in motion1 will cause a twinkling in any distant luminous body1 which shines with a strong light4 ,,pupil4 ,then1 ,i suppose1 the planets not being luminous1 is the reason why they do not twinkle4 ,,tutor4 ,most certainly4 ,the feeble light with which they shine is not sufficient to cause such an appearance4 ,,pupil4 ,have the stars then light in themselves8 ,,tutor4 ,they undoubtedly shine with their own native light1 or we should not see even the nearest of them3 the distance being so immensely great1 that if a cannon-ball were to travel from it to the sun1 with the same velocity with which it left the cannon1 it would be more than #a million1 #hfh thousand years1 before it reached it4#i ,footnote #i3 ,the distance of ,syrius is #ah1gag1ddb1fij1ebf miles4 ,a cannon-ball going at the rate of #aadc miles an hour1 would only reach the sun in about #a1hfh1cjg years1 #hh days4 ,adams's ,lectures1 vol4 #d4 page #dd4 ,,pupil4 ,this is wonderful indeed6 what then are they supposed to be8 ,,tutor4 ,suns4 ,,pupil4 ,suns6 the fixed stars suns6 ,,tutor4 ,yes1 suns4 8,one sun by day1 by night ten thousand shine40 ,and what will increase your astonishment1 each of them is the center of a system of planets1 which move round him4#aj ,footnote #aj3 ,dr4 ,herschell says1 that in some clusters of stars he has observed1 they appear too close together to admit any planets to revolve about them4 8,observe how system into system runs40 8,what other planets circle other suns40 ,,pupil4 ,i am almost lost4--,i used to think they were designed to give us light4 ,,tutor4 ,this is a vulgar error4--,they were doubtless created for a much nobler purpose1 since thousands of them are invisible to us without the help of a telescope2 and we receive more light from the moon than from all the stars together4 ,,pupil4 ,how do you know they are suns8 ,is their being luminous a proof of their being so8 ,,tutor4 ,no4 ,but we know that the sun shines with his own light on all the planets belonging to our system2 and from what ,i have told you1 have the greatest reason to believe that the stars shine with their own light3 we therefore from analogy conclude1 that they are so many suns conveying light and heat to other worlds#aa4 ,footnote #aa3 ,dr4 ,herschell thinks it probable that the sun and fixed stars may be inhabited4 ,,pupil4 ,are there then other worlds besides this we live in8 ,,tutor4 ,consider4--,has not the earth we inhabit a moon to enlighten it8 ,,pupil4 ,yes1 ,sir4 ,,tutor4 ,and have ,i not told you that ,jupiter1 ,saturn1 and ,georgian1 have also moons8 ,,pupil4 ,this ,i well remember4 ,,tutor4 ,for what purpose then do you suppose those orbs were designed8 ,,pupil4 ,indeed1 ,i cannot tell4 ,,tutor4 ,you surely cannot imagine that they were intended for our use1 since we knew nothing of them till after the invention of telescopes4 ,,pupil4 ,that is what ,i think no one can suppose4 ,,tutor4 ,and do not all the planets enjoy the benefit of the sun in common with us8 ,,pupil4 ,undoubtedly4 ,,tutor4 ,well1 then2 of what use would the light and heat be which is conveyed to them from the sun2 or the light which they receive from their moons if there are no inhabitants8 ,,pupil4 ,i know of none4 ,,tutor4 ,can you then have any doubt about their being inhabited8 ,,pupil4 ,no1 ,sir4--,but you say that the stars are suns1 each of which is the center of a system of planets or worlds4 ,,tutor4 ,if you are satisfied that the planets belonging to our system are inhabited1 and that the fixed stars are suns1 the centers of other systems1 what reasonable objection can you have to all the planets in the universe being so8 ,,pupil4 ,it is what ,i cannot comprehend4 ,,tutor4 ,it may be so4--,but is not the same ,almighty ,power1 who does nothing in vain1 as capable of making ten thousand worlds if he pleased1 as well as one8 ,,pupil4 ,i will not presume to dispute his power2 but are we not told that all mankind descended from ,adam8 ,,tutor4 ,yes2 ,moses wrote concerning this earth1 he has not made us acquainted with the inhabitants of the other planets3 for aught we know they might descend from other ,adams4--,to-morrow evening1 ,i hope to see you again4 ---------------------------------------- -------------------------------- ,,dialogue ,,iii4 ,,pupil4 ,i recollect1 ,sir1 you mentioned last night1 that the planets appear like stars4 ,our earth is a planet2 how can it have the appearance of a star8 ,,tutor4 ,if you were on the planet ,venus1 the earth would have as much the appearance of a star as ,venus has to us4 ,,pupil4 ,but ,venus appears amongst the fixed stars4 ,,tutor4 ,yes4 ,and so would the earth appear from ,venus4 ,,pupil4 ,how can it be8 ,,tutor4 ,because1 in whatever part of the universe we are1 we appear to be in the center of a concave1 that is hollow1 sphere1 where remote objects appear at equal distances from us3 so that1 whether we are on the planet ,venus or on the earth1 in this particular the effect will be the same4 ,,pupil4 ,then the light we receive from the sun is by reflection conveyed to the other planets4 ,,tutor4 ,no doubt of it4 ,and our earth appears as a moon to the inhabitants of the moon1 and undergoes the various changes of that planet4 ,,pupil4 ,have you any proof of this1 ,sir8 ,,tutor4 ,nothing can be clearer2 for1 on a fine evening1 soon after the change of the moon1 when the earth appears nearly as a full moon to the moon1 and we see a faint streak of light1 the whole body of the moon is visible to us4 ,,pupil4 ,i remember to have seen it4 ,,tutor4 ,you do8--,the earth then will appear there thirteen times as large as the moon does to us2 of course it must reflect a strong light on the body of the moon1 and it is by that light we see that part of the moon which is turned from the sun4 ,,pupil4 ,is the earth1 then1 only thirteen times as big as the moon8 ,,tutor4 ,in solidity it is about fifty times as large2 but its disc or face is only thirteen times4 ,,pupil4 ,what is the moon's distance from the earth8 ,,tutor4 #bdj thousand miles1 which is about #djj times less than that of the sun4 ,,pupil4 ,and yet she appears as far distant as the sun4 ,,tutor4 ,you are now1 ,i hope1 convinced of what ,i said relative to distant objects4 ,,pupil4 ,i am1 ,sir3 and ,i suppose the reason of the moon's appearing as large as the sun1 is because she is so much nearer to us4 ,,tutor4 ,it is so4--,for1 at a total eclipse of the sun1 which happens when the moon is in a right line between the sun and the earth1 the sun is obscured from our sight1 although his disc is #afj thousand times as large as that of the moon4 ,in like manner would the moon1 when at full1 be hid by placing your cricket-ball in a line between your eye and her1 yet1 you know1 the ball is not so large as the moon2 but being nearer the eye1 it is apparently so4 ,,pupil4 ,this is very clear4 ,but---- ,,tutor4 ,i conjecture you were going to ask me to explain the nature of eclipses4 ,,pupil4 ,that was certainly my intention1 ,sir4 ,,tutor4 ,there are other things you must be made acquainted with before you will be able to comprehend it1 and which ,i will endeavour to make you understand before we enter on the subject4 ,,pupil4 ,whenever you please1 ,sir4 ,,tutor4 ,you have taken a view of the earth from the planet ,venus4--,suppose ,i transport you to one of the planets belonging to another system2 what description do you think you should give of it8 ,,pupil4 ,i must consider4 ,what ,i now call a star would be a sun4 ,the planets of that system ,i should see as ,i now do those belonging to ours3 our sun would be a star2 and the earth1 with all the other planets1 would be invisible4 ,,tutor4 ,very well1 ,sir4 ,can you then find it difficult to conceive that all the stars are as far from each other in unbounded space as our sun is from the nearest star8 ,,pupil4 ,it is hard to conceive3 but when ,i consider that wherever ,i am1 every remote object appears at an equal distance from me1 the difficulty vanishes4 ,,tutor4 ,that you might form some idea of the immense distance of the fixed stars1 you must recollect1 ,i mentioned the time a cannon-ball would be in reaching the nearest of them4 ,,pupil4 ,i do1 ,sir4 ,more than #a1hfh1jjj years4 ,,tutor4 ,you have an excellent memory4 ,i suppose then you know the distance of the earth from the sun8 ,,pupil4 ,yes1 ,sir4 ,i wrote it down2 and1 it made so strong an impression on my memory1 that ,i believe ,i shall never forget it4--#ie millions of miles4 ,,tutor4 ,now1 suppose the earth to be in that part of its orbit which is nearest to the star1 it would be #ie millions of miles nearer to it than the sun is4 ,,pupil4 ,certainly4 ,,tutor4 ,and1 in the opposite side of its orbit1 as much farther from the star4 ,,pupil4 ,without doubt4 ,,tutor4 ,then you find that the earth is #aij millions of miles nearer to the star at one time of the year than it is at another2 and yet the magnitude of the star does not appear the least altered1 nor is its distance affected by it4 ,,pupil4 ,a proof of its amazing distance4--,i was going to ask a silly question4 ,,tutor4 ,what is it8 perhaps not so simple as you may imagine4 ,,pupil4 ,whether the most conspicuous stars are not supposed to be the nearest to us8 ,,tutor4 ,undoubtedly4--,and are called stars of the first magnitude2 the next in splendor1 stars of the second magnitude2 and so on to the sixth magnitude2 and those beyond1 which are not visible to the naked eye1 are called telescopic stars4 ,,pupil4 ,the distance of the telescopic stars must be great indeed1 beyond all conception4 ,,tutor4 ,you judge rightly2 and their numbers are beyond all computation4 ,doctor ,herschell says1 he has not a doubt but that the broad circle in the heavens1 called the ,milky ,way1 is a most extensive stratum of stars1 he having discovered in it many thousands4 ,besides1 some stars appear to him double1 others treble1 c4 not that they are really so1 but are stars at different distances from us1 which appear nearly in a right line4 8,as in the milky-way a shining white 8,o'erflows the heav'ns with one continued light1 8,that not a single star can shew his rays1 8,whilst jointly all promote the common blaze40 ,,pupil4 ,i have heard of numbering the stars2 but that1 ,i find1 is impossible4 ,,tutor4 ,if you mean that immense host of stars ,i have been describing1 it is impossible2 but1 though in a clear winter's night1 without moonshine1 they seem to be innumerable1 which is owing to their strong sparkling1 and our looking at them in a confused manner2 yet when the whole firmament is divided as it has been done by the ancients1 the number that can be seen at a time1 by the naked eye1 is not above a thousand4 ,,pupil4 ,pray1 ,sir1 how did the ancients divide the firmament8 ,,tutor4 ,i would willingly answer your question2 but1 as ,i find ,i shall not have time to give you that information ,i wish1 ,i shall postpone it till ,i see you to-morrow evening4 ---------------------------------------- -------------------------------- ,,dialogue ,,iv4 ,,tutor4 ,the ancients1 in reducing astronomy to a science1 combined the fixed stars into constellations1 allowing several stars to make one constellation3 and1 for the better distinguishing and observing them1 they reduced the constellations to the forms of animals1 or to the images of some known things1 by which means they were enabled to signify to others any particular star they meant to notice4 ,job mentions two of the constellations1 namely1 ,orion and ,pleiades1 which shews the study of astronomy to be very ancient4 ,,pupil4 ,pray1 ,sir1 how may ,i know them8 ,,tutor4 ,by studying the use of the clestial globe1 on which they are drawn4 ,,pupil4 ,will you be kind enough to instruct me1 ,sir8 ,,tutor4 ,at some future time ,i probably may3 at present you are not prepared for it4 ,,pupil4 ,i am satisfied4--,have you any thing more to remark of the constellations1 ,sir8 ,,tutor4 ,yes4 ,the situation of the planets1 as they are continually changing their places1 could not be pointed out without first dividing the stars into constellations3 hence1 necessity was the mother of invention4 ,,pupil4 ,and ,i think a very ingenious one4--,if ,i may be allowed a comparison1 ,i will suppose the different kingdoms of the world on my dissected map1 to represent so many constellations2 then1 if ,i hear of ,london1 ,i know it is in ,england2 if of ,paris1 in ,france2 of ,lisbon1 in ,portugal2 and so on4 ,these ,i would compare with stars of the first magnitude1 being the chief cities of their respective kingdoms2 inferior cities1 stars of the second magnitude2 principal towns of the third1 c4 ,,tutor4 ,a very apt comparison indeed4 ,now if you hear of a traveller setting off from ,london to ,dover1 thence to ,calais1 ,paris1 ,bern1 and so on to ,rome1 you know that he must go through part of ,england1 ,flanders1 ,france1 ,switzerland1 and ,italy1 passing many towns and villages on his way4 ,,pupil4 ,that is very evident4 ,,tutor4 ,very well1 then2 in like manner would the planets1 if seen from the sun1 be traced from star to star1 from constellation to constellation1 through their whole periods4 ,,pupil4 ,it is not possible to view them from the sun1 surely1 is it8 ,,tutor4 ,no1 certainly4 ,,pupil4 ,why then do you say if seen from the sun8 ,,tutor4 ,because it is there only their motions can appear uniform2 as seen from the earth they apparently move very irregularly4--,suppose you were in the center of a circular course2 and1 whilst a horse was going round1 you kept your eye on him3 cannot you conceive that you should see him run round the course in a regular manner1 moving the whole time the same way8 ,,pupil4 ,it is not at all difficult to conceive4 ,,tutor4 ,again4 ,imagine yourself placed at a considerable distance on the outside of the course1 where you could see the horse the whole time he was going round1 would he appear to move as uniformly as before8 ,,pupil4 ,certainly not3 on the opposite side of the course his motion would be the same as when ,i stood in the center of it2 when he was approaching me1 ,i should scarcely see him move2 in that part of the course next to me he would move in a direction contrary to what he did at first2 and again when going from me1 his motion would be scarcely visible4 ,,tutor4 ,this ,i think will give you a tolerable idea of the irregular motion of the inferior planets1 as seen from the earth4 ,when farthest from us their motion is said to be direct2 when nearest to us retrograde1 because they appear to be moving back again2 and1 when approaching1 or going from us1 we say they are stationary2 because1 if then observed in a line with any particular star1 they will continue so for a considerable time3 now these appearances could not happen if they moved round the earth4 ,,pupil4 ,nothing can be plainer3 for if the earth were in the center we should always see them move the same way4 ,,tutor4 ,when the planet is nearest to us1 that is in a line between us and the sun1 we say it is in its inferior conjunction2 when farthest from us1 and the sun is between us and the planet1 in its superior conjunction4 ,but the superior planets have alternately a conjunction and an opposition4 ,,pupil4 ,a conjunction1 ,i suppose1 when the sun is between the earth and the planet1 and an opposition when the earth is between the sun and the planet2 that is1 when the planet is nearest to us1 and appears to be opposite to the sun8 ,,tutor4 ,you are right4--,therefore1 when in conjunction it rises and sets1 nearly with the sun2 but in opposition1 it rises nearly when the sun sets1 and sets when he rises4 ,,pupil4 ,why do you say nearly1 ,sir8 ,,tutor4 ,because it cannot be exactly1 but when the sun1 earth1 and planet are in a right line1 which seldom happens4 ,,pupil4 ,how do you account for this1 ,sir8 ,,tutor4 ,at present ,i fear you will not be able to comprehend what ,i wish to explain1 as ,i must use a term you are unacquainted with4 ,the reason is1 that the planets are very seldom in or near their nodes at their conjunctions or oppositions4 ,,pupil4 ,i do not indeed understand what you mean by the word nodes4 ,,tutor4 ,it will be explained to you in due time1 and ,i shall conclude this evening with a few more remarks relative to the appearance of the planets4 ,,pupil4 ,any thing you please1 ,sir4 ,,tutor4 ,you know that the planets1 being opaque bodies1 receive their light from the sun2 and that only that part which is turned to the sun can be enlightened by him1 whilst the opposite side must remain in darkness4 ,,pupil4 ,this is self-evident3 if ,i hold my ball to the candle it will have the same effect4 ,,tutor4 ,tell me then how you think they will appear as seen from the earth4 ,,pupil4 ,if1 when you shewed me ,venus1 she had not appeared perfectly round1 ,i should say that1 both before and after her superior conjunction ,i should see her nearly with a full face2 when stationary1 only half enlightened1 like the moon at first quarter2 because1 an equal portion of the dark and bright parts will be turned towards us2 the bright part will be decreasing till her inferior conjunction1 when the dark side will be turned towards us1 and consequently invisible2 the light will then increase2 and1 when she is again stationary1 she will appear like the moon at last quarter4 ,,tutor4 ,when seen through a telescope she has the different appearances you have mentioned2 and when ,i next see you ,i will shew you that both ,venus and ,mercury may sometimes be seen when in their inferior conjunctions2 the superior planets always appear with nearly a full face4 ,,pupil4 ,how are the planets distinguished from each other8 ,,tutor4 ,mercury1 from his vicinity to the sun1 is seldom seen1 being lost in the splendor of the solar brightness4 ,when seen1 he emits a very bright white light4 ,venus1 known by the names of the morning and evening star1 is the brightest1 and to appearance1 the largest of all the planets2 her light is of a white colour1 and so considerable1 that in a dusky place she projects a sensible shade4 ,she is visible only for three or four hours in the morning or evening1 according as she is before or after the sun4 ,mars is the least bright of all the planets4 ,he appears of a dusky reddish hue1 and much larger at some periods than at others1 according as he is nearer to1 or farther from us4 ,jupiter is distinguished by his peculiar magnitude and light4 ,to the naked eye he appears almost as large as ,venus1 but not altogether so bright4 ,saturn shines but with a pale feeble light1 less bright than ,jupiter1 though less ruddy than ,mars4 ,the ,georgium ,sidus cannot be readily perceived without the assistance of a telescope4 ---------------------------------------- -------------------------------- ,,dialogue ,v4 ,,tutor4 ,before ,i proceed to explain what ,i promised you1 it is necessary you should be informed that the earth as seen from the sun1 in its periodical revolutions1 will describe a circle among the stars which astronomers call the ecliptic1 and sometimes the sun's annual path1 because the sun1 as seen from the earth1 always appears in that line4 ,,pupil4 ,do not all the planets move in the ecliptic8 ,,tutor4 ,no4--,on account of the obliquity of their orbits1 they are1 in every revolution1 one half of their periods above the ecliptic1 and the other half below it4 ,,pupil4 ,i think ,i comprehend your meaning2 but shall be obliged to you1 ,sir1 if you can make it clearer to me4 ,,tutor4 ,i have here a little design1 7,plate ,,ii4 ,fig4 #a47 which will answer our purpose3 where ,s represents the sun2 ,,abcd1 the orbit of the earth2 and ,,efgh1 the orbit of one of the inferior planets1 suppose ,venus4 ,illustration3 ,plate ,,ii4 ,t4 ,conder ,sculpt4 ,,pupil4 ,now ,i understand it perfectly3 the half ,,ehg rises above1 and the other half ,,efg sinks below it1 from the points ,,eg1 which ,i perceive are in a line with the orbit of the earth4 ,but pray1 ,sir1 have you any name for that dotted line8 ,,tutor4 ,yes1 it is called the line of the nodes2 and the points ,,eg the nodes of the planet3 the latter is called the ascending node1 because1 when the planet is in ,g1 it is ascending or rising above the orbit of the earth2 or1 which is the same thing1 above the ecliptic3 and when in ,e1 it is descending or sinking below it1 whence it is called the descending node4 ,but you must remember that the orbits of all the planets do not cross or intersect the ecliptic in the same points2 but that their nodes or intersections are at different parts of it4 ,,pupil4 ,how can the orbit of the earth and the ecliptic be the same8 ,,tutor4 ,they are very different2 but being in the same plane1 if the orbit of any planet inclines to one it must incline equally to the other4 ,,pupil4 ,you will1 ,i fear1 ,sir1 think me very stupid3 but ,i must beg of you to inform me what you mean by a plane8 ,,tutor4 ,any flat surface is a plane4 ,you may therefore suppose the edge of a round tea-table to represent the ecliptic1 and a circle within it1 drawn from the center of the table1 the orbit of the earth3 will they not be both in the same plane8 ,,pupil4 ,certainly4 ,,tutor4 ,you must not imagine1 when ,i am speaking to you of the plane of the ecliptic1 or plane of the earth's orbit1 that it is a visible flat surface1 or1 in speaking of the orbits of the planets1 ,i mean solid rings4--,no4 ,the planets perform their revolutions with the utmost regularity1 in unbounded space2 and1 like a bird thro' the air1 leave no track behind them4 ,,pupil4 ,how then are they retained in their orbits8 ,,tutor4 ,the question1 ,i confess1 is natural1 and is what ,i expected2 but ,i must of necessity postpone it to another opportunity2 and shall now fulfil the promise ,i made of shewing you in what manner the inferior planets may be seen when in their inferior conjunctions4 ,cast your eye again on the little design ,i gave you1 and consider1 if ,venus were in her ascending node at ,g1 when the earth is at b2 or1 in her descending node1 at ,e1 when the earth is at a1 what the effect would be4 ,,pupil4 ,she would be in a line with the sun4 ,,tutor4 ,and1 on the sun's disc1 she would appear a dark round spot1 passing over it4 ,these appearances1 which are called transits1 happen very seldom3 because she is very seldom in or near her nodes at her inferior conjunctions4 ,there was one in ,june #agfa1 one in ,june #agfi2 and the next will be in the year #ahgd4 ,and as ,mercury is seen in the same manner1 it is a proof that their orbits must be within that of the earth4 ,,pupil4 ,i thank you1 ,sir1 and shall be obliged to you to inform me how many constellations the earth pastes over in every revolution8 ,,tutor4 ,twelve1 which correspond with the months of the year1 and are called the twelve signs of the zodiac4 ,,pupil4 ,what is the zodiac8 ,,tutor4 ,that part of the heavens which contains the twelve signs1 and which you may conceive to be a zone or belt extending eight degrees on each side the ecliptic1 in which the planets constantly revolve3 so that no planet is ever seen more than eight degrees either north or south1 that is above or below the ecliptic4 ,,pupil4 ,what am ,i to understand by a degree8 ,,tutor4 ,all circles1 whether great or small1 are supposed to be divided into #cfj equal parts1 called degrees1 and each degree into #fj equal parts1 called minutes3 therefore1 if ,i speak of a circle in the heavens1 the circumference of the earth1 or any other circle1 by a degree is meant the #cfjth part of that circle2 and a minute the #fjth part of a degree4 ,,pupil4 ,what are the names of the twelve signs8 ,,tutor4 ,the first is called ,aries1 which you know signifies a ,ram2 ,taurus1 the ,bull2 ,gemini1 the ,twins2 ,cancer1 the ,crab2 ,leo1 the ,lion2 ,virgo1 the ,virgin2 ,libra1 the ,balance2 ,scorpio1 the ,scorpion2 ,sagittarius1 the ,archer2 ,capricorn1 the ,goat2 ,aquarius1 the ,water-bearer2 and ,pisces1 the ,fishes4 ,,pupil4 ,do you wish me to commit these to memory1 ,sir8 ,,tutor4 ,it is very requisite2 but as ,i know you are fond of verse1 you shall hear what ,doctor ,watts says-- ,the ,ram1 the ,bull1 the heav'nly ,twins1 ,and next the ,crab the ,lion shines1 ,the ,virgin1 and the ,scales3 ,the ,scorpion1 ,archer1 and ,sea-goat1 ,the ,man that holds the ,water-pot1 ,and ,fish with glitt'ring tails4 ,,pupil4 ,i like it much1 as it will assist my memory4 ,,tutor4 ,as the twelve signs correspond with the months of the year1 the earth must pass over nearly one degree every day1 one sign every month1 and in twelve months complete a whole circle1 or #cfj degrees2 therefore every sign must contain #cj degrees1 because #cj multiplied by #ab is equal to #cfj4 ,,pupil4 ,it must be so4 ,,tutor4 ,you must remember1 that when the earth is in any sign1 as seen from the sun1 the sun will be in the opposite sign1 as seen from the earth3 for instance1 if the earth be in ,aries1 the sun will be in ,libra2 if in ,taurus1 the sun will be in ,scorpio1 c4 therefore1 as by the earth's annual motion1 the sun appears to move1 we always speak of the sun's1 not the earth's place1 in the ecliptic4--,you do not seem to understand me8 ,,pupil4 ,not perfectly1 ,sir4 ,,tutor4 ,take this orange1 and put it in the middle of the round table before us1 and place an apple on the opposite side next the window3 the orange may represent the sun1 the apple the earth1 and the window the sign ,aries4 ,now go round the table to the apple2 look at the orange1 and tell me to what part of the room the eye will be directed4 ,,pupil4 ,to the part opposite to the window1 ,sir4 ,,tutor4 ,if then you suppose the door1 which is opposite to the window1 to be the sign ,libra1 the sun will be in ,libra when the earth is in ,aries--will it not8 ,,pupil4 ,it is very plain4 ,,tutor4 ,i shall now give you a table of the signs1 their characters1 the corresponding months1 and the days of the month the sun enters each sign1 by means of which1 if you reckon a degree for a day1 you may find the sun's place1 nearly1 for any day in the year4 ,,pupil4 ,this will give me much pleasure1 and ,i shall be happy to have it4 ,,the ,,table4 ,,northern ,,signs4 ,aries1 ,taurus1 ,gemini1 ,cancer1 ,leo1 ,virgo4 ,march1 ,april1 ,may1 ,june1 ,july1 ,aug4 #bj1 #bj1 #ba1 #ba1 #bc1 #bc4 ,,southern ,,signs4 ,libra1 ,scorpio1 ,sagittarius1 ,capricorn1 ,aqua4 ,pisces4 ,sept4 ,october1 ,november1 ,decem4 ,jan4 ,feb4 #bc1 #bc1 #ba1 #ba1 #bj1 #ah4 ,,pupil4 ,why do you write northern and southern signs1 ,sir8 ,,tutor4 ,because they are situated north and south of a circle in the heavens1 called the equinoctial1 which circle crosses the ecliptic in the points ,aries and ,libra1 and extends #bc-a_/b degrees on each side of it2 and which ,i shall have occasion to mention to you another time4 ,,pupil4 ,when you think proper1 ,sir1 ,i shall be glad to have it explained to me4 ,,tutor4 ,look at your table1 and tell me what sign and what degree the sun is in the #cjth of ,march1 and #bjth of ,october4 ,,pupil4 ,the sun enters ,aries the #bjth of ,march1 of course he must be #aj degrees in that sign the #cjth2 and1 as he does not enter ,scorpio till the #bc;d of ,october1 he must want three degrees of completing the sign ,libra2 he must therefore1 on the #bjth of ,october1 be in #bg degrees of ,libra4 ,,tutor4 ,very well4--,do you learn the table1 as you will have a farther use for it4 ---------------------------------------- -------------------------------- ,,dialogue ,,vi4 ,,pupil4 ,since ,i was last with you1 ,sir1 ,i have been thinking of what you then told me1 that the planets perform their revolutions in open space3 ,i have not the least idea how this can be2 if convenient1 ,i shall be happy to have it explained4 ,,tutor4 ,it will be necessary first to inform you1 that the orbits or paths described by the revolution of the planets round the sun1 are not true circles 7as ,plate ,,ii4 fig4 #b47 but somewhat elliptical1 that is1 longer one way than the other1 as fig4 #c4 ,,pupil4 ,this is exceedingly plain4 ,,tutor4 ,in a circle1 the periphery or circumference is equally distant from a point within called its center1 as ,a2 but an ellipsis has two points called the focuses or foci1 as ,b ,c4 ,in one of these1 called its lower focus1 is the sun3 so that you see in every revolution of the planet it must be nearer to the sun in one part of its orbit1 than it is in another4 ,,pupil4 ,i see it clearly4 ,,tutor4 ,now let ,s 7,plate ,,ii4 fig4 #d47 represent the sun1 ,a ,b ,c ,d a planet in different parts of its orbit2 when it is nearest to the sun1 as at ,a it is said to be in its perihelion2 when at ,b its aphelion2 but when at ,c or ,d its middle or mean distance1 because the distance ,s ,c or ,s ,d is the middle between ,a ,s the least and ,b ,s the greatest distance2 and half the distance between the two focuses is called the eccentricity of its orbit1 as ,s ,e or ,e ,f4 ,,pupil4 ,this ,i will endeavour to understand2 but ,i find it will take me some time to be perfected in it4 ,,tutor4 ,you may study it at your leisure1 as it will not prevent our proceeding to the thing proposed1 namely1 the laws which govern the motion of the planets1 or ,,attraction ,,of ,,gravitation4 ,,pupil4 ,by attraction ,i think you mean that property in bodies whereby they have a tendency to approach each other4 ,i remember you told me that the magnet ,i had the other day attracted the needle4 ,,tutor4 ,yes4 ,and you may recollect that when ,i took a feather suspended by a thread1 and put it near the conductor of the electrical machine1 it was strongly attracted by it1 and adhered to it as long as the machine was kept in motion4 ,,pupil4 ,i remember it well4 ,but what am ,i to understand by attraction of gravitation8 ,,tutor4 ,the sun1 being the largest body1 attracts the earth and all the other planets1 they gravitate or have a tendency to approach the sun2 the earth being larger than the moon attracts her1 and she gravitates towards the earth2 the planets are attracted by and gravitate towards each other2 a stone when thrown from the earth1 by its attraction and the gravitating power or weight of the stone1 is brought to the earth again2 the waters in the ocean gravitate towards the center of the earth2 and it is by this power we stand on all parts of the earth with our feet pointing to the center4 ,,pupil4 ,this information affords me great pleasure4 ,,tutor4 ,having mentioned attraction of magnetism1 electricity1 and gravitation1 it may not be amiss to inform you of another kind1 called attraction of cohesion4 ,,pupil4 ,any thing which tends to my improvement1 ,i shall be obliged to you to communicate4 ,,tutor4 ,by attraction of cohesion is meant that property in bodies which connects or firmly unites the different particles of matter of which the body is composed4 ,,pupil4 ,pray1 ,sir1 inform me what you mean by the laws of attraction8 ,,tutor4 ,you are to understand1 #ast4 ,that attraction decreases as the squares of the distances between the centers of the attracting bodies increase4 ,,pupil4 ,i must beg you1 ,sir1 to explain to me the meaning of the squares of the distances4 ,,tutor4 ,any number multiplied into itself is a square number1 thus #a is the square of #a2 #d is the square of #b2 #i is the square of #c1 and so on1 because #a multiplied into itself is #a2 #b by #b is #d2 #c by #c is #i1 c4 ,now suppose1 that when the planet is at ,b 7,plate ,,ii4 fig4 #d47 it is twice as far from the sun as it is at ,a3 how much more will it be attracted by the sun at ,a than at ,b8 ,,pupil4 ,you say1 ,sir1 that the distance is twice as great at ,b as at ,a8 ,,tutor4 ,i do4 ,,pupil4 ,then as the square of the distance #b is #d1 the decrease of attraction at ,b1 the planet at ,a will be attracted with four times the force it would be at ,b4--,am ,i right1 ,sir8 ,,tutor4 ,perfectly so4 ,and if the distance at ,b were three times as great as at ,a1 it would be attracted with a force nine times as great4 ,,pupil4 ,i perceive it must be so4 ,,tutor4 ,i shall now give you the #b;d law1 namely1 ,that bodies attract one another with forces proportionable to the quantities of matter they contain4 ,,pupil4 ,do all bodies of the same magnitude contain equal quantities of matter8 ,,tutor4 ,no1 certainly3 ,for a ball of cork may be as large as one of lead1 and yet not contain the same quantity of matter1 because it is more porous1 and not so compact or dense a body as the lead2 neither will a ball of lead of the same magnitude as one of gold contain an equal quantity of matter4--,so the sun1 though a million of times as big as the earth1 contains a quantity of matter only #bjj1jjj as great1 therefore attracts the earth with a force #bjj1jjj as great as the earth attracts him4 ,,pupil4 ,i think this is clear4 ,,tutor4 ,we will now suppose that in the river are two boats of equal bulk1 at the distance of twenty yards from each other1 and that a man in one boat pulls a rope which is fastened to the other1 what effect will be produced1 or where do you think the boats will meet8 ,,pupil4 ,had you not told me that bodies attract one another with forces which are proportioned to the quantities of matter they contain1 ,i should say the boat to which the rope is fastened would come to that in which the man stands3 but as ,i imagine you mean to apply this to attraction1 by the above rule1 they will meet at a point which is half way between them4 ,,tutor4 ,if one boat were three times the bulk of the other1 how then8 ,,pupil4 ,the lightest would move three times as far as the heaviest1 or #ae yards whilst the heaviest moved only #e4 ,,tutor4 ,upon my word you reason philosophically4 ,in both cases you are perfectly right4 ,,pupil4 ,as the sun is so immense a body that his quantity of matter is so much greater than the planets1 ,i am at a loss to know why they are not by the power of attraction drawn to him4 ,,tutor4 ,and so they would if the attractive power were not counteracted by another of equal force4 ,,pupil4 ,did you not say1 ,sir1 that the planets are kept in their orbits by attraction8 ,,tutor4 ,i did4 ,but you find that by attraction only the sun would draw all the planets to himself4 ,,pupil4 ,that is evident4 ,but ,i wish to know what this counteracting power you speak of is8 ,,tutor4 ,i will tell you presently4--,you must remember that simple motion is naturally rectilineal1 that is1 all bodies1 if there were nothing to prevent them1 would move in strait lines4 ,,pupil4 ,then as the planetary motion is circular1 it cannot be simple8 ,,tutor4 ,no4 ,it is a compound of the two forces ,i have been mentioning3 the one is called the attractive or centripetal force2 the other1 the projectile or centrifugal force4 ,,pupil4 ,the former ,i clearly comprehend1 but not the latter4 ,i can conceive1 that if two bodies approach each other by attraction they must move in a right line4 ,,tutor4 ,if you shoot a marble on a smooth piece of ice1 in what direction will it run8 ,,pupil4 ,strait forward4 ,,tutor4 ,this is a projectile force4--,could you1 do you think1 shoot it in any other direction8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,then is not this motion also rectilineal8 ,,pupil4 ,it is4 ,,tutor4 ,when you strike a ball with your cricket-bat1 or throw a stone with your hand1 is it not projected or thrown forward by the force of the bat or hand8 ,,pupil4 ,certainly4 ,,tutor4 ,and does it not move in a strait line8 ,,pupil4 ,at first it appears to do so2 but afterwards it inclines towards and falls to the earth4 ,,tutor4 ,cannot you account for this8 ,,pupil4 ,i suppose it must be drawn to the earth by attraction4 ,,tutor4 ,you are right4 ,the attraction of the earth1 and the resistance of the atmosphere or air through which it moves1 retards its progress1 or it would continue moving in a strait line1 with a velocity equal to that which was at first impressed upon it4 ,in like manner the beneficent ,creator of the ,universe impressed a force on all the planets which should be equal to that of the attractive power of the sun1 that one might not overcome the other4 ,,pupil4 ,this wants explaining4 ,,tutor4 ,i would willingly gratify you1 but as ,i have much more to say on the subject1 ,i fear it will be too great a burthen on your memory2 it will therefore be better to postpone it4 ,,pupil4 ,as you please1 ,sir4 ---------------------------------------- -------------------------------- ,,dialogue ,,vii4 ,,tutor4 ,having at our last meeting explained to you the nature of the attractive and projectile forces1 ,i shall proceed to shew you that it is by the joint action or combination of these two forces that the planets are retained in their orbits4 ,,pupil4 ,i am all anxiety1 as ,i wish to be informed how1 or in what manner they can act against each other1 to produce that effect4 ,,tutor4 ,answer me a few questions1 and you will soon know4 ,,pupil4 ,as many as you please1 ,sir4 ,,tutor4 ,if you whirl a stone in a sling1 what will be its motion8 ,,pupil4 ,circular4 ,,tutor4 ,is you let it suddenly slip out of the sling1 will it continue its circular motion8 ,,pupil4 ,no1 ,sir1 but fly off in a strait line4 ,,tutor4 ,this line you must remember is what mathematicians call the tangent of a circle1 as ,a a1 ,b b1 c4 7,plate ,,ii4 fig4 #e47 for all bodies moving in a circle have a natural tendency to fly off in that direction4 ,thus a body at ,a will tend towards a2 at ,b towards b1 and so on2 but the central force acting against it preserves its circular motion4 ,,pupil4 ,by the central force here you mean the action of the hand1 do you not8 ,,tutor4 ,yes4 ,for1 as soon as the stone is released and that power is lost1 it assumes its natural1 that is1 its rectilineal motion4--,again4 ,if you are left at liberty1 cannot you run strait forward8 ,,pupil4 ,yes1 ,sir4 ,,tutor4 ,now1 suppose one of your companions were to fasten a rope round your body1 and at the extent of it were to stand still and hold it tight1 with a force equal to that with which you run1 could you1 do you think1 move in a strait line1 that is1 in a tangent of a circle8 ,,pupil4 ,no1 ,sir4 ,i must run in a circle4 ,,tutor4 ,why8 ,,pupil4 ,because1 whilst the rope is extended ,i am prevented running in any other direction4 ,,tutor4 ,just so it is with the planets3 the attractive or centripetal force of the sun being equal to that of the projectile or centrifugal force of the planets1 they are by attraction prevented moving on in a strait line1 and1 as it were1 drawn towards the sun2 and by the projectile force from being overcome by attraction4 ,they must therefore revolve in circular orbits4 ,,pupil4 ,what ,i have so long wished is now accomplished4 ,i understand it perfectly4 ,,tutor4 ,what ,i have now explained relates not only to the primary planets which have the sun for their center of motion2 but1 you must remember that the secondary planets are governed by the same laws1 in revolving about their respective primaries2 for1 as by the attractive power of the sun combined with the projectile force of the primary planets they are retained in their orbits2 so also the action of the primaries upon their respective secondaries together with their projectile force1 will preserve them in their orbits4 ,,pupil4 ,pray1 ,sir1 what have you else to observe8 ,,tutor4 ,have ,i not told you that the orbits of the planets are not true circles1 but a little elliptical8 ,,pupil4 ,yes1 ,sir2 and ,i shall be glad to know the reason of it4 ,,tutor4 ,if the attractive power of the sun were uniformly the same in every part of their orbits they would be true circles1 and the planets would pass over equal portions of their orbits in equal times2 that is1 they would move from ,b to ,c1 7,plate ,,ii4 fig4 #e47 in the same time as from ,a to ,b1 c4 ,,pupil4 ,that is clear1 but as their orbits are elliptical1 when the planets are farthest from the sun1 the velocity with which they move must be lessened as the attraction is decreased4 ,,tutor4 ,and they must consequently pass over unequal parts of their orbits in equal portions of time4 ,and1 as a double velocity will balance a quadruple or fourfold power of gravity or attraction1 it follows1 that as the centripetal force is four times as great at ,a as at ,b 7,plate ,,ii4 fig4 #d47 the centrifugal force will be twice as great1 and would carry a planet from ,a to a in the same time it would from ,b to b1 and in its orbit from ,a to c as soon as from ,b to d1 and thereby describe the area1 or space contained between the letters ,a ,s c1 in the same time as the area or space ,b ,s d4 ,for according to the laws of the planetary motions1 in their periodical revolutions1 they always describe equal areas in equal times4 ,,pupil4 ,the orbits of the comets being very elliptical1 the irregularity of their motions must be exceedingly great4 ,,tutor4 ,great1 indeed6--,one of them passed so near the sun as to acquire a heat which ,sir ,isaac ,newton computed to be two thousand times hotter than red hot iron4#ab ,footnote #ab3 ,dr4 ,herschel is of opinion1 that bodies near the sun do not acquire so great a degree of heat as has been generally imagined4 ,,pupil4 ,astonishing6 ,if they pass so near the sun1 the centripetal force must act powerfully on the body of the comet4 ,,tutor4 ,and that force1 you know1 must be equalled by the projectile force2 so you find they move when near the sun with amazing celerity4--,but when arrived at their aphelion1 where the influence of the sun is weak1 what a transition6 ,,pupil4 ,wonderful1 indeed6--,their motion is excessively slow1 and the sun must appear little more than a fixed star4 ,surely they cannot be inhabited1 can they8 ,,tutor4 ,we cannot speak positively2 but1 as they differ so much from the planets1 which we have reason to suppose are so1 it is imagined they are designed for some purpose unknown to us4 ,,pupil4 ,when is the earth in its perihelion8 ,,tutor4 ,in ,december2 and our summer half year is longer than the winter half1 by about eight days4 ,,pupil4 ,i suppose this is occasioned by the inequality of the earth's annual motion4 ,,tutor4 ,it is2 and this inequality is the cause of the difference of time between the sun and a well regulated clock2 the latter keeps equal time1 whilst the former is constantly varying4 ,,pupil4 ,i have often seen in the almanack clock fast1 clock slow1 but did not know the meaning of it3 ,i imagine it is that the clock should be so much faster or slower than the time by the sun as is there mentioned4 ,,tutor4 ,it is3 but there are tables calculated to shew the difference of time for every day in the year2 so that if you know the exact times of the day by the sun1 and have one of these tables1 you will see what the time should be by the clock1 to a second1 which is not shewn in a common almanack4 ,,pupil4 ,in speaking of the annual or yearly motion of the earth1 you have no where mentioned the cause of the seasons2 will it be agreeable to do it now1 ,sir8 ,,tutor4 ,the vicissitudes of the seasons1 the cause of day and night1 c4 shall be the subject of future lessons3 we shall find sufficient to employ us at present4 ,,pupil4 ,i think you told me just now that the earth is nearest the sun in ,december2 that is our winter2 this seems a little mysterious4 ,,tutor4 ,it may appear so to you now1 by-and-by you will be of a different opinion4 ,i shall explain this matter to you with that of the seasons1 c4 ,,pupil4 ,i fear ,i have interrupted you4--,as you said you had sufficient employment for us1 ,i shall be glad to know what it is4 ,,tutor4 ,hitherto ,i have spoken of the sun's being fixed1 and that the planets revolve about him as a center4 ,instead of which the sun and planets move round one common center1 called the center of gravity4 ,,pupil4 ,what is this center of gravity8 ,,tutor4 ,have you never seen a person raise a heavy weight by means of a long pole or leaver1 which it was not in his power to lift without it8 ,,pupil4 ,yes1 ,sir1 and it excited my astonishment4 ,,tutor4 ,now1 suppose the weight to see raised to be #aj ,cwt4 and the prop on which the leaver rested #a foot from the body to be raised2 and the person at the other end of the leaver #aj feet from the prop2 with what weight must he press to raise the #aj ,cwt48 ,,pupil4 ,i think that very easy2 for1 as he is ten times as far from the prop as the weight is1 a pressure of #a ,cwt4 which is one-tenth of the weight to be raised will do it4 ,,tutor4 ,to be sure2 and yet you say you were astonished when you saw it6 ,every thing we do not understand at first appears difficult4--,to apply this to our present purpose4 ,you see that a weight of #a ,cwt4 at #aj feet from a prop1 will balance another of #aj ,cwt4 at one foot from it4 ,now1 instead of a prop let the two weights be nicely poised on a center1 round which they may freely turn2 the heaviest would move in a circle1 whose radius1 or distance from the center would be one foot1 whilst the lightest would move in one #aj feet from the center in the same time4 ,,pupil4 ,is the center round which they move the center of gravity8 ,,tutor4 ,it is2 and round an imaginary point as a center the sun and planets move1 always preserving an equilibrium4 ,if the earth were the only attendant on the sun1 as his quantity of matter is #bjj1jjj times as great as that of the earth1 he would revolve in a circle a #bjj1jjjth part of the earth's distance from him1 in the same time as the earth is making one revolution in its orbit1 or in one year2 but1 as the planets in their orbits must vary in their positions1 the center of gravity cannot be always at the same distance from the sun4 ,,pupil4 ,if it were1 the balance could not be preserved4 ,,tutor4 ,clearly so4 ,but you must know that the quantity of matter in the sun so far exceeds that of all the planets together1 that even if they were all in a line on one side of him he would never be more than his own diameter distant from his center of gravity2 therefore1 astronomers consider the sun as the center of the system1 and express themselves accordingly4 ,,pupil4 ,as you told me the secondary planets are governed by the same laws as the primaries1 ,i imagine they also with their primaries move round a center of gravity4 ,,tutor4 ,they do so4--,the earth and moon1 ,jupiter with his satellites1 ,saturn and his attendants1 revolve about their respective centers2 these1 with the sun and the rest of the planetary system1 make their circuits round their center2 every system in the universe is supposed to revolve in like manner2 and all these together to move round one common center4--,how are we lost in contemplating the omniscience of the ,deity6 ,how difficult to conceive so many millions of bodies of dead matter constantly in motion1 so nicely balanced and governed by such unerring laws6--,well may we say with the ,psalmist1 8,lord6 how manifold are thy works1 in wisdom hast thou made them all40 ---------------------------------------- -------------------------------- ,,dialogue ,,viii4 ,,tutor4 ,i shall now1 agreeably to my promise1 explain to you the cause of day and night1 and then proceed with the vicissitudes of the seasons4 ,,pupil4 ,that is what ,i much wish to know2 and had you not told me that the earth moved round the sun every year1 ,i should have found no difficulty in accounting for the succession of day and night1 since the sun appears to rise and set every day4 ,,tutor4 ,that is true2 but ,i think ,i must have convinced you that so immense a body as the sun cannot revolve about the earth2 as well may you suppose that in roasting a bird it is necessary that the fire should move round it4 ,,pupil4 ,that ,i think would be very absurd1 as it is much easier for the bird on the spit to turn to the fire1 than for the fire to go round the bird4 ,,tutor4 ,you are certainly right1 and if the earth revolve on its axis every twenty-four hours1 will not the different parts of it be alternately turned to the sun1 as the bird on the spit is to the fire8 ,,pupil4 ,i do not clearly comprehend what you mean by the axis of the earth2 for1 as it moves in open space and has no support1 it can have nothing to resemble the spit on which it turns4 ,,tutor4 ,certainly not4 ,by the earth's axis is meant an imaginary line passing through its center1 on which it is supposed to turn2 as your ball if rolled on the ground would revolve on an axis whilst it was moving forward4 ,,pupil4 ,i can now answer your question in the affirmative3 and1 as our year consists of #cfe days1 ,i imagine the earth must make as many revolutions on its axis whilst it is going once round the sun4 ,,tutor4 ,undoubtedly3 and as only one half of a spherical body can at any time be enlightened by a luminous body1 that part of the earth only which is turned to the sun1 can receive the benefit of his enlivening rays1 when it will be day2 whilst the opposite part will be involved in darkness1 and it will be night4 ,,pupil4 ,i perceive it must be so4 ,but1 if the earth move in the manner you describe1 ,i cannot conceive how it is that we are not sensible of its motion4 ,,tutor4 ,if the motion of the earth were irregular it would be perceptible2 but as it meets with no obstruction the motion must be so uniform as not to be perceived4 ,,pupil4 ,had ,i recollected this1 ,i need not have given you this trouble4--,but ,i am continually meeting with fresh difficulties4 ,,tutor4 ,you have only to mention what they are1 and ,i shall take a pleasure in removing them4 ,,pupil4 ,i thank you1 ,sir2 and shall be obliged to you to inform me1 how the motion of the earth can cause the sun to appear to move8 ,,tutor4 ,when in a carriage which went smoothly on the road1 or in a boat whose motion was scarcely perceptible on the water1 did you never fix your attention on the objects you passed8 ,,pupil4 ,yes1 often1 ,sir4 ,,tutor4 ,and had you not known that you really moved1 and that the trees1 c4 were immoveable in the ground1 what then would have been your opinion8 ,,pupil4 ,that the trees1 c4 moved in a direction contrary to that in which ,i was moving4 ,,tutor4 ,is not this sufficient to convince you that the apparent motion of the sun may be occasioned by the revolution of the earth on its axis8 ,,pupil4 ,it is3--,but if so large a body as the earth make a revolution on its axis in #bd hours1 it must move with great velocity4 ,,tutor4 ,it does so2 and the inhabitants of ,london by this motion are carried at the rate of #efj miles an hour#ac4 ,footnote #ac3 ,the hourly motion under the equator is #ijj miles4 ,,pupil4 ,what an astonishing rapidity6 ,,tutor4 ,now1 the sun with the rest of the heavenly bodies must move round the earth1 or the earth must revolve on its axis in #bd hours1 to cause that appearance4 ,,pupil4 ,that is plain4 ,,tutor4 ,well then1 great as you may suppose the velocity of the earth on its axis to be1 if the sun move round the earth his hourly motion will be nearly #be millions of miles2 and beyond conception would be that of the fixed stars4 ,which now do you think is most probable1 that the sun and stars should move round the earth1 or that they1 by the simple motion of the earth1 should appear to be in motion8 ,,pupil4 ,the latter1 to be sure1 ,sir4--,i have one difficulty remaining1 which is this2 if a lark rise from a field near ,london and remain in the air a quarter of an hour1 if the earth move at the rate of #efj miles an hour1 it will go #adj miles whilst the lark is suspended1 and yet it continues over the field1--how can this be8 ,,tutor4 ,this objection to the motion of the earth has been made by those who were older and who thought themselves wiser too than yourself4 ,they either did not know or did not consider1 that the atmosphere which surrounds the earth is a part of itself1 and gravitates towards it1 and therefore partakes of the earth's motion and carries the lark along with it4 ,besides1 as the ,sun1 ,venus1 ,mars1 and ,jupiter are known to revolve on their axes1 we have reason to suppose that the other planets1 together with the earth1 must have the same motion#ad4 ,footnote #ad3 ,dr4 ,herschell says that several of the fixed stars revolve on their axes4 ,,pupil4 ,how is it known that they do revolve on their axes2 and in what time do they perform their revolutions8 ,,tutor4 ,by the assistance of telescopes dark spots have been seen on the disc of the sun1 by the motion of which it is found that he revolves on his axis in #be-a_/d days2 ,venus performs her diurnal revolution in about #bc ho4 #ba min42 ,mars goes round his axis in #bd ho4 #ci min42 and ,jupiter in #i ho4 #ef min42 as to the rest1 no spot or any fixed point has been discovered to ascertain the length of their day2 ,mercury being too near the sun1 and ,saturn and the ,georgium ,sidus too remote for our observations4 ,,pupil4 ,i can no longer doubt of the earth's motion3 and1 if it will not be improper1 a description of the atmosphere will give me pleasure4 ,,tutor4 ,that ,i can have no objection to4 ,the atmosphere is a thin1 invisible fluid1 most dense or heavy near the earth1 but grows gradually rarer or lighter the higher we ascend1 so much so1 that at the tops of some high mountains it is difficult to breathe4 ,it serves not only to suspend the clouds1 furnish us with wind and rain1 and answer the common purposes of breathing1 but is also the cause of the morning and evening twilight1 and of all the glory and brightness of the firmament4 ,,pupil4 ,how1 pray8 ,,tutor4 ,if there were no atmosphere1 the sun would yield no light but when our eyes were directed towards him2 and the heavens would appear dark and as full of stars as on a dark winter's night2 but the atmosphere being strongly illuminated by the sun1 reflects the light back upon us1 and makes the whole heavens to shine so strongly1 that the faint light of the stars is obscured1 and they are rendered invisible4 ,,pupil4 ,i find then the atmosphere is of more use than ,i imagined4 ,but how is it the cause of the twilight8 ,,tutor4 ,the atmosphere is about #de miles above the surface of the earth1 therefore the sun's rays falling upon the higher parts of it before rising1 by reflection causes a faint light1 which increases till he appears above the horizon2 and in the evening it decreases after he sets1 till he is #ah degrees below the horizon1 where the morning twilight begins1 and the evening twilight ends4 ,,pupil4 ,by the horizon1 ,i think you mean that distant boundary of our sight where the heavens and the earth seem to join all around us1 as it appears from an eminence4 ,,tutor4 ,the very same4 ',tis that imaginary circle which intercepts from our view the sun1 moon1 and stars each night2 and when1 by the rotation of the earth1 they appear to descend below it1 we say they are set2 as on the contrary1 each morning1 when they appear above it1 we say they rise4 8,to find the spacious line1 cast round thine eyes1 8,and where the earth's high surface joins the skies1 8,where stars first set1 and first begin to shine1 8,there draw the fancy'd image of this line40 ,,pupil4 ,a very pleasing description1 indeed4 ,,tutor4 ,you will remember that this is called the rational horizon2 but that which respects land and water is called the sensible horizon4 ,the former divides the heavens into two equal parts1 and is #ij degrees distant from a point directly over our heads1 called the zenith1 and the opposite point of the heavens directly under our feet1 called the nadir4--,but ,i must resume the subject of the atmosphere4 ,,pupil4 ,had ,i not thought you had finished your description of the atmosphere1 ,i should not have presumed to interrupt you4 ,,tutor4 ,what ,i have told you respecting the horizon is necessary for you to be acquainted with2 therefore1 the suspension is immaterial4--,you must1 ,i make no doubt1 have observed the sun and moon at rising and setting to appear larger than when higher above the horizon4 ,,pupil4 ,i have1 frequently1 ,sir4 ,,tutor4 ,and cannot you tell the reason of it8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,the reason is this3 ,in viewing them1 when near the horizon1 you see them through a thicker medium than when they are higher1 that is1 you see them through a greater quantity of the atmosphere2 and you not only see them larger1 but really above the horizon whilst they are actually below it4 ,,pupil4 ,how do you account for this1 ,sir8 ,,tutor4 ,light1 like material bodies1 if it meet with no obstruction1 will move in right lines2 now1 the rays of the sun in coming to the earth must pass through a great quantity of the atmosphere1 which being a fluid1 refracts or bends the rays of light1 by which refraction it is that we are favoured with the sight of the sun #c-a_/d minutes every morning before he rises above the horizon1 and every evening after he sinks below it1 which in one year amounts to more than #dj hours4 ,this refraction is greatest near the horizon1 and ends in the zenith4 ,,pupil4 ,pray1 ,sir1 can you make this clearer by an experiment8 ,,tutor4 ,i have just thought of one4 ,take a bason filled with water1 and a strait stick or piece of wire2 put it perpendicularly into the water1 that is1 that it lean neither way1 and there will be no refraction2 incline it a little towards the edge of the bason and it will appear a little bent at the surface of the water2 incline it still more1 and the refraction will be greater4 ,,pupil4 ,i have often seen this appearance when ,i have put my stick into water1 but did not before know the cause4 ,,tutor4 ,you may try one more experiment4 ,pour the water out of the bason1 and set the bason on the floor2 put a guinea into it1 and let it represent the sun4--,why do you smile8 ,,pupil4 ,because ,i have not the sun's representative to try the experiment with4 ,,tutor4 ,well1 well1 put a shilling into the bason and call it the moon1 and it will answer the same purpose3--,walk backward till you just lose sight of it1 then the right line from your eye continued over the edge of the bason must pass beyond the money at the bottom of it4 ,,pupil4 ,that is evident4 ,,tutor4 ,keep your position1 and desire some friend to pour the water gently into the bason so as not to remove the money1 and you will clearly distinguish it4 ,now1 if you call the edge of the bason the horizon1 the water the atmosphere1 and the shilling the moon1 is it not clear that you will see it above the horizon1 when it is really below it8 ,,pupil4 ,i think so1 ,sir4 ,,tutor4 ,well1 try the experiment1 and let me know the result when ,i next see you4 ---------------------------------------- -------------------------------- ,,dialogue ,,ix4 ,,tutor4 ,i presume1 ,sir1 you have made the experiment ,i recommended to you4 ,,pupil4 ,i have1 ,sir2 and am so well convinced of what you told me1 that nothing farther need be said on the subject4 ,,tutor4 ,as that is the case1 ,i shall proceed4--,i dare say you do not forget what the plane of the ecliptic is4 ,,pupil4 ,i do not1 ,sir2 but have a perfect recollection of it4 ,,tutor4 ,now1 remember1 that the axis of the earth is not upright or perpendicular to the plane of the ecliptic1 but inclines to1 or leans towards it1 #bc-a_/b degrees1 and makes an angle with it of #ff-a_/b degrees4 ,,pupil4 ,an angle signifies a corner2 but that cannot be the meaning here4 ,,tutor4 ,that is what is generally understood by an angle3 but1 in geometry1 it means the meeting of any two lines which incline to one another1 in a certain point4 ,now1 if you conceive the axis of the earth to be one line1 and the plane of the ecliptic the other1 the point where they meet or cross each other will form an angle4 ,,pupil4 ,i think ,i understand it2 but how can it contain #bc-a_/b or #ff-a_/b degrees8 ,,tutor4 ,you know what a degree is4 ,,pupil4 ,if ,i remember right it is the #cfjth part of a circle4 ,,tutor4 ,it is so3 and the measure of an angle is an arc or part of the circumference of a circle1 whose angular point is the center3 and so many #cfjth parts as any arc contains1 so many degrees the measure of the angle is said to be2 thus1 ,z ,c ,p 7,plate ,,iii4 fig4 #a47 makes an angle of #bc-a_/b degrees1 because the arc ,z ,p contains #bc-a_/b #cfjth parts of the whole circle4 ,then if ,a ,b represent the plane of the ecliptic1 and ,n ,c ,s the axis of the earth1 as ,d ,n contains the same number of degrees as ,z ,p1 will not its inclination from a perpendicular be #bc-a_/b degrees8 ,illustration3 ,plate ,,iii4 ,t4 ,conder ,sculpt4 ,,pupil4 ,nothing can be plainer4 ,,tutor4 ,for the same reason1 as ,p ,b contains #ff-a_/b parts of the whole circle1 the axis of the earth makes an angle of #ff-a_/b degrees with the plane of the ecliptic4 ,and1 if you add #bc-a_/b to #ff-a_/b the sum will be #ij1 which is the measure ,z ,b1 or the fourth part of the circle1 and makes what is called a right angle1 at the point or center ,c4 ,,pupil4 ,it is very clear3--but what do the other letters refer to8 ,,tutor4 ,the extremities of the earth's axis are called the poles1 ,n the north1 and ,s the south pole1 and ,p the north-pole star1 to which1 and to the opposite part of the heavens1 the axis always points4 ,these extremities in the heavens appear motionless1 whilst all other parts seem in a continual state of revolution3 the circle of motion appears to increase with the distance from the apparently motionless points to that circle in the heavens which is at an equal distance between them1 called the equinoctial1 represented by the letters ,q2 and is the same ,i promised some time ago to explain to you4 ,,pupil4 ,i recollect it3 and as the line ,a ,b represents the plane of the ecliptic1 ,i suppose the line ,q is the plane of the equinoctial1 which ,i see crosses it as you then told me4 ,,tutor4 ,you are right3 and it makes an angle with it of #bc-a_/b degrees4 ,it is called the equinoctial1 because when the sun appears there1 that is1 in ,aries or ,libra1 the days and nights are equal in all parts of the world1 which ,i shall shew you in due time2 and shall now explain to you what ,i have just mentioned1 that the axis of the earth always points to the same parts of the heavens4 ,i am apprehensive you will think it strange that this should be the case1 and the axis keep parallel to itself4 ,,pupil4 ,what am ,i to understand by the axis being parallel to itself8 ,,tutor4 ,two lines are said to be parallel when they do not incline to but keep at equal distances from each other2 so that if they were infinitely continued1 they would never meet4 ,now1 if you can conceive a line drawn parallel to the earth's axis in any part of its orbit1 it will be parallel to it in every other part of it4 ,a little drawing ,i have by me1 7,plate ,,iii4 fig #b47 where the earth is represented in four different parts of its orbit1 ,i think will make this plain to you4 ,,pupil4 ,i comprehend your meaning clearly4 ,but1 as the orbit of the earth is #aij millions of miles in diameter1 ,i have not the least conception how it can incline to the same points4 ,had you not told me to the contrary1 ,i should have thought it must move round them in every revolution of the earth about the sun4 ,,tutor4 ,that such a motion would be perceptible is evident1 if the fixed stars were near the earth2 but1 compared with their distance1 #aij millions of miles is but a mere point3 therefore1 the axis always inclines to the same points of the heavens4 ,,pupil4 ,this is a greater proof of the inconceivable distance of the stars than what you mentioned before1 and ,i thought that very astonishing3 ,wonders on wonders constantly arise1 ,whene'er we view the earth1 or sea1 or skies4 ,,tutor4 ,it is very true4 ,and the more we search1 the more we have cause to admire the works of the ,almighty4 ,,pupil4 ,pray1 ,sir1 what is the next thing you propose8 ,,tutor4 ,to make you acquainted with the other circles you see in the figure 7,plate ,,iii4 fig4 #a47 as it is very necessary you should know them4 ,,pupil4 ,will you be kind enough to tell me their names1 ,sir1 and ,i will endeavour to remember them8 ,,tutor4 ,that line which divides the globe into two equal parts1 called the northern and southern hemispheres1 which answers to the equinoctial in the heavens1 and is equally distant from the two poles1 is called the equator2 the other which crosses it1 as ,i before told you1 is the ecliptic2 the smaller circle1 north of the equator1 is the tropic of ,cancer2 that south of it1 the tropic of ,capricorn2 the circles next the poles are called the polar circles2 or that next the north pole1 the arctic circle1 and that next the south pole1 the antarctic circle2 each of which is #bc-a_/b degrees distant from its respective pole1 as are the tropics from the equator4 ,,pupil4 ,you have not mentioned the lines which cross the other circles1 and terminate in the poles2 what are they called8 ,,tutor4 ,they are called meridians1 because when any of them1 as the earth revolves on its axis1 is opposite to the sun1 it is mid-day or noon along that line4 ,twenty-four of these lines are usually drawn on the globe to correspond with the twenty-four hours of the day2 but you are not to suppose there are no more than twenty-four2 for every place that lies ever so little east or west of another place has a different meridian4--,to make this clearer to you1 we will suppose the upper #ab 7,plate ,,iii4 fig4 #a47 to be opposite the sun1 it will of course be noon along that line2 the next meridian marked #a1 being #ae degrees east1 will have passed the meridian #a hour1 consequently it will there be one in the afternoon1 and so on1 according to the order of the figures1 till you come to the lower #ab1 which being the part of the earth turned directly from the sun1 it will be midnight on that meridian2 on the next meridian1 as you proceed round1 it will be one in the morning1 the next two1 and so on till you arrive at the upper twelve1 where you set off4 ,so you see there must be a continual succession of day and night4 ,this difference of time between places lying under different meridians is what is called longitude4 ,,pupil4 ,i think ,i have heard of a ,mr4 ,harrison1 who made a time-keeper for determining the longitude4 ,shall ,i trespass at all if ,i beg a little farther information on this subject8 ,,tutor4 ,it is my wish at all times to satisfy your curiosity1 when ,i can do it with propriety4 ,i shall therefore comply with your request4--,mr4 ,harrison's time-keeper1 and those made since by other artists1 are so constructed1 that the heat and cold of different climates will not affect them2 for1 all metals are more or less expanded by heat1 and contracted by cold2 for which reason it is1 that a clock or watch made in the usual way will not keep equal time4 ,now1 all that is required of these time-keepers to ascertain the longitude is this3 ,suppose a captain of a vessel sailing from ,london to the ,west ,indies1 we will say ,kingston1 in ,jamaica4 ,on his passage thither he makes an observation1 and finds the sun on the meridian1 or that it is twelve o'clock in that situation1 when by his time-keeper it is two in the afternoon in ,london1 whence he concludes he is #cj degrees west of ,london4 ,,pupil4 ,i must beg you to explain this to me1 as ,i do not understand why two hours of time should be equal to #cj degrees of longitude4 ,,tutor4 ,you must consider1 that as the earth makes a complete revolution on its axis in #bd hours1 it must pass over #cfj degrees in that time3 now1 if you divide #cfj by #bd1 the quotient #ae1 will be the number of degrees passed over in one hour2 #cj degrees will be equal to two hours1 c4 ,the difference of time between ,london and his situation is two hours1 consequently the difference of longitude must be #cj degrees3 and1 it must be west1 because the sun had passed the meridian of ,london2 for1 as the earth revolves from west by south to east1 one place which lies east of another must come first to the meridian or opposite to the sun4 ,therefore1 when longitude is reckoned from ,london1 if the place lie east of that meridian the time will be before2 if west1 after ,london4 ,,pupil4 ,i see it clearly2 and as #fj minutes make an hour1 if ,i divide it by #ae1 the quotient #d will be the minutes answering to one degree4 ,,tutor4 ,you are right3 and for the same reason1 #d seconds of time are equal to one minute of longitude1 which you know is the #fjth part of a degree4--,our captain when arrived at ,kingston1 finds the difference of time between it and ,london #e ho4 #f min4 #cb sec4 ,can you tell me the longitude of ,kingston8 ,,pupil4 ,if ,i bring the hours and minutes to minutes1 and divide by #d1 the quotient ,i think will be degrees1 will it not8 ,,tutor4 ,it will3 and the seconds of time divided by #d1 will be minutes of longitude4 ,now try if you can do it4 ,,pupil4 ,five hours #f minutes1 multiplied by #fj will be #cjf minutes1 this divided by #d1 will give #gf degrees and #b over1 which #b is half a degree1 or #cj minutes3 and #cb seconds of time divided by #d1 will be #h minutes of longitude1 the sum of which is #gf degrees #ch minutes for the longitude of ,kingston4 ,,tutor4 ,very well4--,i have just now thought of another method of reducing time to longitude1 and longitude to time1 which you may probably find easier4 ,however1 when you are in possession of both1 you may use which you please4 ,,pupil4 ,that which is easiest must1 ,i think1 be best4 ,,tutor4 ,i will give it you1 and let me have your opinion of it4 ,to reduce time to longitude4 ,multiply the hours1 minutes1 and seconds of time by #ae1 or rather by the factors as they are called1 namely #c and #e1 carrying one for every #fj in the minutes and seconds1 and setting down the remainder1 thus3 ho4 min4 sec4 #e #f #cb difference of #c time4 #ae #ai #cf #e ,degrees #gf #ch #j longitude4 ,divide the degrees and minutes of longitude by #e and #c and the quotient will be the difference of time4 ,,pupil4 ,i give this the preference4 ,,tutor4 ,as longitude is seldom mentioned without being accompanied with latitude1 that you may not be ignorant of its meaning when you meet with it1 ,i shall just tell you that it is the distance of any place from the equator1 reckoned in degrees and minutes on the meridian1 and is either north or south as the place lies north or south of the equator4 ,the latitude of any place is equal to the elevation of the pole above the horizon4 ,the latitude of the heavenly bodies is reckoned from the ecliptic1 and terminates in the arctic and antarctic circles3 and their longitude begins at the point ,aries4 ,,pupil4 ,what is the measure of a degree8 ,,tutor4 ,a degree of latitude is #fj geographical1 or #fi-a_/b ,english miles3 and a degree of longitude on the equator is equal to it1 because the equator as well as the meridians divides the globe into two equal parts4 ,but a degree of longitude decreases as you approach the poles3 for at the poles the meridians meet in a point1 consequently a degree there can have no dimension4 ,to-morrow ,i will shew you the cause of the seasons4 ---------------------------------------- -------------------------------- ,,dialogue ,x4 ,,pupil4 ,i think1 ,sir1 when you left me last night you told me our next business would be to explain the nature of the seasons8 ,,tutor4 ,i did so1 and am persuaded you will find no great difficulty in comprehending it4--,cast your eye on the little drawing ,i gave you1 7,plate ,,iii4 fig4 #b47 where the earth is represented as situated at the four quarters of the year1 namely1 ,spring1 ,summer1 ,autumn1 and ,winter4--,but before we proceed to an explanation it will be necessary to remark1 that1 in the little scheme the eye is supposed to be elevated above the plane of the earth's orbit1 and that we see it very obliquely4 ,the orbit by this means appears very elliptical2 and1 the enlightened hemisphere1 or that half of the earth which is turned to the sun in the spring1 and the darkened hemisphere1 or that turned from him in the autumn1 are there represented4 ,,pupil4 ,this ,i understand4 ,,tutor4 ,well then1 we will begin with the spring4--,in this situation of the earth the equator is exactly opposed to the sun3 and1 as he always enlightens a hemisphere1 or half of its surface1 his rays will reach to both the poles3 whence1 from the diurnal revolution of the earth1 the day and night are equal all over the globe4 ,,pupil4 ,this ,i remember you told me happened when the sun was in ,aries and ,libra4 ,the sun is now entering ,aries3 and1 as we are in the rays of the sun one half of the diurnal revolution1 and in the shadow of the earth1 or dark1 the other half1 the day and night must be equal4 ,,tutor4 ,certainly4 ,and as the sun enters ,aries in the equinoctial1 it is then called the ,vernal1 that is1 ,spring ,equinox4 ,when the sun enters the opposite sign ,libra1 the same effects are produced1 and it is then called the ,autumnal ,equinox4 ,,pupil4 ,you have passed on from ,spring to ,autumn4 ,,tutor4 ,i have so4--,we will now return1 and trace the earth in its orbit from spring to summer4--,you have already seen that the north and south poles are both enlightened1 and that the day and night are equal at the equinoxes4 ,if the axis of the earth were perpendicular to the plane of the earth's orbit1 this would constantly be the case1 and we should have no diversity of seasons3 for1 the sun being over the equator1 the poles must be perpetually enlightened1 and of course we should have equal day and night at all times of the year4 ,,pupil4 ,that is plain4 ,i suppose then that it is to the inclination of the earth's axis we are indebted for the increase and decrease of days4 ,,tutor4 ,it is occasioned by the inclination of the earth's axis and its preserving its parallelism1 which ,i explained to you last evening4--,as the sun is now in the first point of ,aries1 the earth you know must be in the beginning of ,libra1 it being the opposite sign4--,now fix your attention on the scheme1 and imagine the earth to be advancing in its orbit through ,libra1 ,scorpio1 and ,sagittarius3 and at the first degree of ,capricorn give me your opinion of the earth's position4 ,,pupil4 ,the north pole is turned to the sun1 the south pole from him1 and the tropic of ,cancer is opposite to him4 ,,tutor4 ,how many degrees are the tropics from the equator1 or1 in other words1 what is the inclination of the earth's axis8 ,,pupil4 ,twenty-three degrees and a half4 ,,tutor4 ,and so far are the rays of the sun cast beyond the north pole1 and fall short of the south pole3 so that the whole of the arctic circle is enlightened1 and the antarctic circle involved in darkness4 ,,pupil4 ,what conclusion am ,i to draw from this8 ,,tutor4 ,that in the northern half of the globe it is the longest day1 or summer1 and in the southern half the shortest1 or winter1 whilst under the equator the days and nights are equal4 ,,pupil4 ,i used to think that when it was winter or summer here it was so in every part of the world4 ,,tutor4 ,you now find your mistake4 ,for as the earth is making its progress from ,libra1 the north pole is approaching the sun1 and the south pole receding from him3 consequently the length of the day is increasing in the northern hemisphere and decreasing in the southern4--,the sun has now been three months above the horizon of the north pole1 and the same time below that of the south pole1 and in three months more1 when the earth arrives at ,aries1 the scene will be reversed3 the sun will be over the equator1 both poles will be again enlightened1 and the day and night will be equal in every part of the globe4 ,the sun will now be rising to the south and setting to the north pole4 ,this is our ,autumn4 ,,pupil4 ,and as the earth is advancing towards winter1 the south pole will be turning to the sun1 and the north pole from him1 whence ,i conclude that when the earth is in ,cancer it must be summer1 south of the equator1 when it is our winter4 ,,tutor4 ,most assuredly4 ,for you see that the sun is over the tropic of ,capricorn1 which you know is as much south of the equator as the tropic of ,cancer is north of it1 where the sun was in our summer4 ,the antarctic circle is now enlightened1 and the arctic obscured in shade2 but1 under the equator there is neither increase nor decrease1 the days and nights being each twelve hours4 ,,pupil4 ,it is now our winter1 the sun has been three months above the horizon of the south pole1 and will continue so till the vernal equinox1 when he will again rise to the north pole1 and so on in regular succession4 ,,tutor4 ,it must be plain then to you that there can be but one day and one night at each of the poles1 reckoning the time the sun is above or below their respective horizons2 under the arctic and antarctic circles1 the longest day is twenty-four hours1 and in the shortest the sun is just visible in the horizon at noon4 ,the longest day decreases in length the nearer we approach the equator1 where ,i before observed there is no variation1 because the circle bounding light and darkness1 in every position of the earth1 divides the equator into two equal parts2 and1 it must be observed1 that the longest day and longest night are equal to each other in every part of the globe4 ,,pupil4 ,if the longest day under the arctic circle be just twenty-four hours1 the sun must rise in the north4 ,,tutor4 ,he does so1 makes a complete circle and sets in the #aenorth again4 ,from the arctic circle to the equator1 he rises north of the east and sets north of the west3 at the equator he rises due east and sets due west1 thence southward to the antarctic circle1 he rises south of the east1 and sets south of the west3 and under the antarctic circle1 as ,i observed just now1 he is visible in the horizon in the south at noon4 ,footnote #ae3 ,here it must be observed that there will be a little variation from sun-rising to sun-setting1 as the earth is advancing in its orbit4 ,,pupil4 ,we usually say1 the sun rises in the east and sets in the west4 ,,tutor4 ,at the equinoxes it must be so in all parts of the globe1 the poles excepted3 in every other situation1 except under the equator1 there is a continual change4 ,what ,i have now told you1 respecting the northern hemisphere1 will be reversed at our shortest day3 that is1 in the northern hemisphere the sun will rise south of the east and set south of the west2 and1 in the southern hemisphere the contrary1 the sun will be in the horizon1 at noon1 under the arctic circle1 and the day will be twenty-four hours under the antarctic circle4 ,,pupil4 ,pray ,sir1 are the regions within the polar circles inhabited8 ,if they are1 their situation1 in winter1 must1 ,i think1 be dreadful4 ,,tutor4 ,it is foreign to my present purpose to speak of the inhabitants of the earth1 as that more properly belongs to ,geography4 ,thus much however ,i shall tell you1 that1 although it must be very cold and dreary1 they are not so long deprived of light as you may imagine2 for1 even under the poles1 when the sun is hidden from them1 they are but a short time in total darkness1 for1 you must recollect1 that the twilight continues till the sun is eighteen degrees below the horizon2 and the sun's greatest depression1 you know1 can be but twenty three degrees and a half1 equal to the inclination of the earth's axis4 ,besides this1 the moon is above the horizon of the poles a fortnight together2 being half her period north1 and the other half south1 of the equator2 and1 as the moon at full is in the sign opposite to the sun1 the tropical full moons must be twenty-four hours above the horizon at the polar circles4 ,,pupil4 ,this description is very pleasing1 as ,i had no idea of their being favoured with so much light in the absence of the sun3 and1 ,i find1 as the sun is longer above the horizon in summer than in winter1 the moon1 on the contrary1 continues longer with us in winter1 when we most need her assistance1 than she does in summer4 ,,tutor4 ,as you seem to understand what ,i have been explaining1 ,i shall shew you1 that the reason why it is hottest when we are farthest from the sun is1 that in winter when we are nearest to him the days are shorter1 his rays sail very obliquely on us1 and are more dispersed than they are in summer1 when he not only remains longer above the horizon1 but being higher1 his rays fall more direct on us1 by which means the earth becomes so much heated that it has not time in the short nights to get cold again4--,when the earth is nearest the sun it is summer in the southern hemisphere1 therefore it is reasonable to suppose that the heat there must far exceed ours in the same latitude2 but to counteract this their summer is shorter by eight days than ours3 and it is well known that it is much colder near the poles in the southern than in the northern hemisphere3 but this is accounted for from there being more land to retain the heat in the latter than in the former4 ,,pupil4 ,my doubts on this head being now removed1 ,i must beg you to give me such other information as you may think proper4 ,,tutor4 ,as there are different degrees of heat and cold1 the earth has been divided into five zones1 namely1 one torrid1 two temperate1 and two frigid zones4 ,,pupil4 ,how are they distinguished8 ,,tutor4 ,the torrid zone is all that space surrounding the globe contained between the tropics1 having the equator running through the middle of it4 ,it is so called on account of its excessive heat1 for1 twice every year the sun is vertical to the inhabitants1 that is1 he shines directly on their heads1 and casts no shadow1 but under their feet1 at noon4 ,,pupil4 ,we find it sometimes extremely hot here in our summer2 surely1 in the torrid zone it must be almost insupportable8 ,,tutor4 ,they are inured to it from their infancy4--,but we are departing from our subject4--,the temperate zones are comprehended between the tropics and polar circles1 that between the tropic of ,cancer and the arctic circle is called the north temperate zone1 and that between the tropic of ,capricorn and the antarctic circle the south temperate zone4 ,,pupil4 ,i suppose they are called temperate because the heat is not so intense as in the torrid zone8 ,,tutor4 ,true4 ,neither is the cold so severe as in the frigid zones1 which are those regions comprized within the polar circles1 and are denominated north and south1 as they are contiguous to the north or south poles4 ,,pupil4 ,why are they called frigid8 ,,tutor4 ,they are called frigid or frozen zones1 because near the poles there are perpetual fields of ice1 the heat of the sun1 even in summer1 being insufficient to dissolve it4--,now try if you can tell me the breadth of each zone in degrees4 ,,pupil4 ,the torrid zone being twenty-three degrees and a half on each side the equator must be forty-seven degrees1 which must also be the breadth of the frigid zones1 as the polar circles are distant twenty-three degrees and a half from the poles1 which are their centers4 ,and1 as from the equator to either pole is ninety degrees1 from the equator to the tropics twenty-three and a half1 and from the polar circle to the pole twenty-three and a half1 if the sum of these1 that is1 forty-seven1 be taken from ninety1 the remainder1 forty-three1 will be the breadth of each of the temperate zones4 ,,tutor4 ,very well4 ,,pupil4 ,from what you have told me ,i have no doubt but that the earth is globular1 but ,i have no proof of it3 ,i must therefore beg your assistance4 ,,tutor4 ,that it cannot be an extended plane1 as some have imagined1 is very evident2 for1 if it were1 the angle made with that plane and the north pole star would be always equal1 for reasons ,i have before given you3 neither can it be cylindrical1 that is like a garden roller1 as others have supposed4--,if a person travel northward the pole star becomes more elevated1 and if he could penetrate to the north pole of the earth the star would be in the zenith1 or directly over his head3 on the contrary1 if he travel southward1 it is more and more depressed till he arrives at the equator1 where the star is in the horizon2 as he proceeds it disappears1 and other stars rise to his view1 invisible to us4 ,here then you see it must be circular northward and southward4 ,,pupil4 ,i am convinced it must be so4 ,,tutor4 ,and it is as certain that it is so east and west3 for1 navigators have often sailed round it steering the same course3 that is1 if they sail an easterly or westerly course at setting off1 by continuing the same course they will return to the port whence they departed4 ,this you know they could not do if it were not round1 any more than an insect could1 by crossing a round table1 arrive at the place it set out from2 but1 by going round the edge it would be still going forward and come again to the point it had left4 ,,pupil4 ,it is very evident4 ,,tutor4 ,again4 ,in every direction1 if a ship be seen at a distance1 the first things observed are the top-mast and rigging1 whilst the hull or body of the ship is hidden behind the convexity1 that is roundness of the water1 just as you would see a man coming over a hill1 you would first see his head1 he would be rising more and more to your view till he arrived at the top1 where he would be full in sight4 ,,pupil4 ,i am at a loss to account for the convexity of the water4 ,how can its surface be round8 ,,tutor4 ,have you never observed the drops of water falling from the eaves of a house8 ,,pupil4 ,often1 ,sir4 ,,tutor4 ,of what shape were they8 ,,pupil4 ,globular4--,but what is the cause of their being so8 ,,tutor4 ,attraction4--,for as every particle of water which composes the drop tends to the same center1 every part of the surface must be equidistant from the center1 it must therefore be spherical4 ,in like manner if you separate quicksilver1 each portion will form itself into a globe4 ,,pupil4 ,all this is very clear4 ,and1 for the same reason1 the water in the ocean must be convex2 for1 ,i remember you told me that it gravitated towards the center of the earth4 ,,tutor4 ,once more4--,i think you must have seen an eclipse of the moon4 ,,pupil4 ,i have1 ,sir4 ,,tutor4 ,of what figure was the darkened part8 ,,pupil4 ,circular4 ,,tutor4 ,take this ball1 and hold it before the candle between your finger and thumb1 so that the shadow may be thrown on the wall1 and in all positions you will find it circular4 ,,pupil4 ,it is so4 ,,tutor4 ,apply this crown piece in the same manner1 with the flat side to the candle4 ,,pupil4 ,it is a circle4 ,,tutor4 ,turn it a little obliquely4 ,,pupil4 ,it is now an ellipsis4 ,,tutor4 ,now turn the edge to the candle4 ,,pupil4 ,the shadow is a strait line4 ,,tutor4 ,you now see that no other body than that of a globe can in all positions cast a circular shadow4 ,,pupil4 ,i do1 ,sir4 ,,tutor4 ,the darkness on the disc of the moon at the time of an eclipse is the shadow of the earth1 which in all situations is circular2 the earth1 therefore1 which casts the shadow1 must be a globe4 ,,pupil4 ,it must be so4--,but---- ,,tutor4 ,the earth is mountainous4--,it is so3 but remember that the highest mountain bears no greater proportion to the bulk of the earth than the small irregularities on the peel of an orange bears to that fruit3 that objection therefore is soon removed4 ,and yet it is not a true sphere4 ,,pupil4 ,what then8 ,,tutor4 ,a spheroid1 that is1 it is a little flattened at the poles1 and is in shape not unlike an orange or a turnip4 ,this you will not be surprized at when ,i tell you that the equatorial parts are about four thousand miles from the center of motion4 ,,pupil4 ,i suppose then you infer that as the centrifugal force is greater the farther it is removed from the center1 that the parts near the poles have a tendency to fly off towards the equator4 ,,tutor4 ,i do4 ,and as we have finished this part of our subject1 ,i shall take leave of you4 ---------------------------------------- -------------------------------- ,,dialogue ,,xi4 ,,tutor4 ,i now propose giving you a description of the moon1 and ,i doubt not it will afford you some degree of pleasure4 ,,pupil4 ,indeed it will1 as ,i know little more than that she is a secondary planet or satellite1 revolving round the earth1 and with it round the sun4 ,,tutor4 ,you know her mean distance from the earth4 ,,pupil4 ,i did not recollect that3 #bdj thousand miles4 ,,tutor4 ,right4 ,her diameter is about #bafa miles1 and her bulk about a fiftieth part of the earth's4 ,her axis is almost perpendicular to the plane of the ecliptic1 consequently she can have no diversity of seasons4 ,,pupil4 ,what is her period8 ,,tutor4 ,the time she takes to revolve from one point of the heavens to the same again is called her siderial or periodical revolution1 and is performed in #bg days1 #g hours1 #dc minutes2 but synodical revolution1 or the time taken up to revolve from the sun to the same apparent situation with respect to the sun again1 or from change to change1 is #bi days1 #ab hours1 and #dd minutes4 ,,pupil4 ,i do not clearly comprehend it4 ,,tutor4 ,if the earth had no annual motion1 the period of the moon would be uniformly #bg days1 #g hours1 #dc minutes2 but you are to consider that whilst the moon is revolving round the earth1 the earth is advancing in its orbit1 and of course she must be so much longer in completing her synodical revolution as the difference of time between that and her siderial revolution4 ,this ,i will make clear to you in a few minutes4--,what is the situation of the hour-hand and minute-hand of a watch at twelve o'clock8 ,,pupil4 ,they will be in conjunction4 ,,tutor4 ,and will they be in conjunction at one8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,yet the minute-hand has made a complete revolution3 but before they can be in conjunction again the minute-hand must move forward till it overtakes the hour-hand4 ,,pupil4 ,i now understand it1 and must beg you to explain to me the different phases of the moon4 ,,tutor4 ,take this ivory ball1 and suspend it by the string with your hand between your eye and the candle4 ,let the candle represent the sun1 the ball the moon1 and your head the earth4 ,in this situation1 as the candle enlightens only one half of the ball1 the part turned from you will be enlightened1 and the part turned to you will be dark4 ,this will be a representation of the moon at change1 and as no part of her enlightened hemisphere is turned to the earth1 she can reflect no light upon it1 and consequently is invisible to us4 ,she now rises and sets nearly with the sun4--,turn yourself a little to the left1 and you will observe a streak of light like what is called the new moon4 ,,pupil4 ,i see it clearly4 ,,tutor4 ,move round one quarter4 ,,pupil4 ,one half of the side next me is now enlightened4 ,,tutor4 ,you may conceive it to be the moon at first quarter4--,go on1 and you will see the light increase till the ball is opposite to the candle1 when the side next you will be wholly illumined1 and will give you a just idea of the moon at full1 which now rises about the time of sun-setting1 being opposite to the sun3 and1 the farther she advances in her orbit the later she rises4 ,,pupil4 ,it is plain it must be so4 ,she rises with the sun at change1 being then in conjunction3 and as she revolves in her orbit the same way as the earth does on its axis1 the earth will have farther to revolve each day before it can see the moon4 ,at the full she is in opposition1 and of course rises when the sun sets3 and so continues to rise later and later1 till the change again4 ,,tutor4 ,you imagine that the moon rises exactly with the sun when she is at change2 and when he sets1 at full4 ,i will presently convince you of your mistake2 and would have you now proceed with your ball4 ,place it again opposite to the candle1 and as you turn round you will find the light gradually decrease as it before increased1 that the side that was before enlightened is now dark1 and the dark side light4 ,when you have gone three quarters round1 one half of the side next you will be enlightened1 and will resemble the moon at last quarter4 ,as you go on the darkened part will increase1 till you arrive at the place you set off from1 where the light is quite obscured4 ,,pupil4 ,i have now completed the circuit1 and am much delighted with it1 as by this simple contrivance ,i can perceive the various changes of the moon1 and that the western side is enlightened from the change to the full1 and the eastern side from the full to the change4 ,,tutor4 ,i find then it has fully answered the purpose intended4 ,,pupil4 ,indeed it has4 ,but if you will give me leave ,i will use the ball again4 ,,tutor4 ,by all means4 ,,pupil4 ,i perceive1 as ,i move round1 that the same side of the ball is turned towards me whilst every part is turned to the candle4 ,is it so with the moon8 ,,tutor4 ,it is3 and as every part of the moon is turned to the sun1 she makes one revolution on her axis whilst she makes one in her orbit4 ,,pupil4 ,this is very singular4 ,if the same side of the moon be always turned to the earth1 the opposite side of course can never see it4 ,,tutor4 ,and they must likewise be deprived of the earth as a moon4 ,,pupil4 ,true4 ,but how is it known that the same side of the moon is always opposed to the earth8 ,,tutor4 ,the moon1 like our earth1 consists of mountains and valleys1 which1 when seen through a good telescope1 are very beautiful4 ,the mountainous parts appear as lucid spots and bright streaks of light3 and as the same spots1 c4 are constantly turned to the earth1 she must keep the same side to the earth4 ,,pupil4 ,it is very clear4 ,are there no seas8 ,,tutor4 ,it was formerly imagined that the dark parts were seas1 but later observations prove that they are hollow places or caverns1 which do not reflect the light of the sun4 ,besides1 if there were seas there would consequently be exhalations1 and if exhalations1 clouds and vapours1 and an atmosphere to support them4 ,that there are no clouds is evident1 because when our atmosphere is clear1 and the moon above our horizon in the night-time1 all her parts appear constantly with the same clear1 serene1 and calm aspect4 ,,pupil4 ,has the moon then no atmosphere8 ,,tutor4 ,if she has it is imperceptible to us3 for1 when she approaches any star1 we cannot discover with our best telescopes any change of colour or diminution of lustre in the star till the instant it is lost behind her3 whence it is clear1 that she can have no such gross medium as our atmosphere to surround her4 ,,pupil4 ,may we not then doubt whether she be inhabited or not1 as without air we cannot breathe8 ,,tutor4 ,the same ,almighty ,being who created us and gave us air to breathe1 may have provided a different way for their existence4 ,it does not hold good that1 because we could not live there1 she is not inhabited4 ,fish will live a considerable time in water under an exhausted receiver3 and1 ,i have heard of a toad being found in a block of marble4 ,your doubt therefore1 ,i think1 ought not to be admitted4 ,,pupil4 ,i am satisfied4 ,and must now beg to be informed how ,i may observe the moon's motion4 ,,tutor4 ,her real motion round the earth1 may be easily known by remarking when she is near any particular star4 ,thus1 suppose you see her west1 that is to the right of it1 she will be approaching1 then in conjunction with1 and afterwards pass it towards the east4 ,her apparent motion is that of rising and setting1 which is occasioned by the rotation of the earth on its axis4 ,,pupil4 ,i remember not long since1 when you shewed me ,jupiter1 that the moon was west of him3 the next evening ,i saw her almost appear to touch him1 and soon after at a great distance from him easterly4 ,i now see that her real motion is from west by south to east1 and her apparent motion from east by south to west4 ,,tutor4 ,if you have no objection1 ,i will now explain the cause of eclipses4 ,,pupil4 ,so far from it1 that it will give me the greatest pleasure4 ,,tutor4 ,take your ivory ball1 suspend it as before1 in a right line between your eye and the candle4--,can you see the candle8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,for what reason4 ,,pupil4 ,because the ball prevents the light coming to me4 ,,tutor4 ,this then represents an eclipse of the sun1 which can never happen but when the moon is between the sun and the earth1 which must be at the change3 for1 as light passes in a right line1 the sun is hidden to that part of the earth which is under the moon1 and therefore he must be eclipsed4 ,if the whole of the sun be obscured by the body of the moon1 the eclipse is total3 if only a part be darkened1 it is a partial eclipse2 and so many twelfth parts of the sun's diameter1 as the moon covers1 so many digits are said to be eclipsed4 ,,pupil4 ,may not the word digit be applied to the moon as well as the sun8 ,,tutor4 ,it may3 for it means a twelfth part of the diameter of either the sun1 or the moon4 ,,pupil4 ,as you have now shewn me the cause of an eclipse of the sun1 ,i am anxious to have that of the moon explained4 ,,tutor4 ,we must again have recourse to your little ball4--,turn yourself round till it is opposite to the candle in a line with your head1 and you will see that no light can be thrown on it from the candle1 because your head is between them4 ,in like manner the rays of the sun are prevented falling on the moon1 by the interposition of the earth3 she must therefore be eclipsed4 ,,pupil4 ,i see it clearly4 ,and as an eclipse of the sun happens when the moon is at change1 that of the moon must be when she is at full2 for1 it is then only the earth's shadow can fall on the moon1 the earth being at no other time between the sun and her4 ,,tutor4 ,the diameter of the shadow is about three times that of the moon1 and consequently the moon must be totally eclipsed whilst she continues in it4 ,on the contrary1 the shadow of the moon at an eclipse of the sun1 covers so small a part of the earth's surface1 that the sun is totally or centrally eclipsed to but a small part of it2 and its duration is very short4 ,but a faint or partial shadow surrounds this darkened shade1 in which the sun is more or less eclipsed1 as the place is nearer to or farther from its center2 this partial shadow is called the penumbra4 ,i have prepared for you a little drawing1 representing an eclipse both of the sun and moon1 which ,i think will enable you better to understand what ,i have been explaining4 7,plate ,,iv4 ,fig4 #a and #b47 ,in the former1 p4 p4 is the penumbra4 ,illustration3 ,plate ,,iv4 ,t4 ,conder ,sculpt4 ,,pupil4 ,in what does a central differ from a total eclipse8 ,,tutor4 ,an eclipse of the sun may be central1 and not total2 for1 those who are under the point of the dark shadow1 will see the edge of the sun like a fine luminous ring1 all around the dark body of the moon when the sun is eclipsed at the moon's greatest distance from the earth2 but when she is nearest the earth at an eclipse of the sun1 the eclipse is total4 ,when the penumbra first touches the earth1 the general eclipse begins2 when it leaves the earth1 the general eclipse ends4 ,an eclipse of the moon always begins on the moon's eastern side1 and goes off on her western side2 but an eclipse of the sun begins on the sun's western side1 and goes off on his eastern side4 ,when the moon is eclipsed in either of her nodes1 the eclipse is both central and total4 ,,pupil4 ,pray1 what is the reason we have not an eclipse at every full and change of the moon8 ,,tutor4 ,for the same reason that ,mercury and ,venus are not seen to pass over she sun's disc at every inferior conjunction4 ,,pupil4 ,is the orbit of the moon then inclined to the plane of the ecliptic8 ,,tutor4 ,it is3 and no eclipse of the sun can happen but when the moon is within #ag degrees of either of her nodes3 neither can there be one of the moon1 unless she be within #ab degrees4 ,at all other new moons she passeth either above or below the sun1 as seen from the earth3 and at all other full moons above or below the earth's shadow1 according as she is north or south of the ecliptic4 ,you now see that the moon must sometimes rise before and sometimes after the sun at change1 and before or after he sets at full4 ,,pupil4 ,i do1 ,sir1 and am much obliged to you for this pleasing account of the moon1 and of eclipses3 and if you have any thing farther to observe1 it will afford me additional pleasure4 ,,tutor4 ,you may1 at some time or other1 have an opportunity of seeing a total eclipse of the moon2 it will therefore be necessary to prepare you for a phnomenon which otherwise you might be much surprized at1 and that is1 that after the moon is immersed in the earth's shadow1 she is still visible4 ,,pupil4 ,this is a phnomenon that ,i am not able to account for2 for1 the moon being an opaque body1 she cannot shine by her own light#af1 and the rays of the sun are prevented falling on her by the interposition of the earth1 she cannot therefore shine by reflection4 ,footnote #af3 ,dr4 ,herschell supposes the moon and the rest of the planets may have some inherent light3 the side of the planet ,venus1 turned from the sun1 having been seen1 as we see the moon soon after the change4 ,,tutor4 ,it is by reflection that we see her2 for the rays of the sun which fall upon our atmosphere are refracted or bent into the earth's shadow1 and so falling upon the moon are reflected back to us4 ,if we had no atmosphere1 she would be totally dark1 and of course invisible to us4 ,,pupil4 ,what is her appearance8 ,,tutor4 ,it is that of a dusky colour1 somewhat like tarnished copper4--,i have one thing more to remark before we quit this subject1 which is1 that the moon's nodes have a retrograde or backward motion1 in a direction contrary to the earth's annual motion1 and go through all the signs and degrees of the ecliptic in little less than nineteen years1 when there will be a regular period of eclipses1 or return of the same eclipses for many ages4 ,,pupil4 ,pray1 ,sir1 what do you propose for our next subject8 ,,tutor4 ,the ebbing and flowing of the sea1 or cause of the tides4 ---------------------------------------- -------------------------------- ,,dialogue ,,xii4 ,,tutor4 ,in order to explain the cause of the tides1 ,i have since ,i saw you last prepared a little drawing for you1 7,plate ,,iv4 fig4 #c47 where ,s represents the sun1 ,m the moon at change1 ,e the center of the earth1 and ,a ,b ,c ,d its surface1 covered with water4 ,it is obvious1 from the principles of gravitation1 that if the earth were at rest the water in the ocean would be truly spherical1 if its figure were not altered by the action of some other power4 ,but1 daily experience proves that it is continually agitated4 ,,pupil4 ,what is the cause of this agitation8 ,,tutor4 ,the attraction of the sun and moon1 particularly the latter3 for1 as she is so much nearer the earth than the sun1 she attracts with a much greater force than he does1 and consequently raises the water much higher1 which1 being a fluid1 loses as it were its gravitating power1 and yields to their superior force4 ,,pupil4 ,what proportion does the attractive power of the sun bear to that of the moon8 ,,tutor4 ,as three to ten4 ,so when the moon is at change1 the sun and moon being in conjunction1 or on the same side of the earth1 the action of both bodies is on the surface of the water1 the moon raising it ten parts1#ag and the sun three1 the sum of which is thirteen parts1 represented by ,b b4 ,now it is evident1 that if thirteen parts be added by the attractive power of those bodies1 the same number of parts must be drawn off from some other part1 as ,a a1 ,c c4 ,it will now be high-water under the moon at b1 and its opposite side d1 and low-water at a and c4 ,footnote #ag3 ,by part here ,i do not mean any specific measure4 ,,pupil4 ,that the attraction of the sun and moon must occasion a swelling of the waters on the side next them1 ,i can readily conceive1 and that this swell must cause a falling off at the sides3 but that the tide should rise as high on the side opposite to the sun and moon1 in a direction contrary to their attraction1 is what ,i am not able to account for4 ,,tutor4 ,this difficulty will be removed when you consider that all bodies moving in circles have a constant tendency to fly off from their centers4 ,now1 as the earth and moon move round their center of gravity1 that part of the earth which is at any time opposite to the moon will have a greater centrifugal force than the side next her1 and at the earth's center the centrifugal force exactly balances the attractive force3 therefore1 as much water is thrown off by the centrifugal force on the side opposite to the moon1 as is raised on the side next her by her attraction4 ,hence1 it is plain1 that at ,d1 fig4 #c1 the centrifugal force must be greater than at the center ,e1 and at ,e than ,b1 because the part ,d is farther from the center of motion than the part ,b4 ,on the contrary1 the part ,b being nearer the moon than the center ,e1 the attracting power must there be strongest1 and weakest at ,d4 ,and1 as the two opposing powers balance each other at the earth's center1 the tides will rise as high on that side from the moon1 by the excess of the centrifugal force1 as they rise on the side next her by the excess of her attraction4 ,,pupil4 ,in this explanation you have mentioned nothing of the sun4 ,,tutor4 ,from what ,i have already said it must be plain to you that if there were no moon the sun by his attraction would raise a small tide on the side next him2 and1 it is as evident that the tides opposite would be raised as high by the centrifugal force3 for the sun and earth1 as well as the earth and moon1 move round their center of gravity4 ,this may be exemplified by an easy experiment4 ,take a flexible hoop1 suppose of thin brass1 tie a string to it and whirl it round your head1 and it will assume an elliptical shape2 the tightness of the string drawing out the side next to your hand1 and the centrifugal force throwing off the other4 ,,pupil4 ,this ,i clearly comprehend4 ,,tutor4 ,i shall now refer you to the next figure1 7fig4 #d47 where ,f represents the moon at full3 the sun and moon are in opposition1 and yet the tide is as high on each side as in the former case4 ,i wish you to shew me the cause4 ,,pupil4 ,i will use my endeavour to do it1 ,sir4 ,,tutor4 ,then ,i doubt not you will accomplish it4 ,,pupil4 ,when the moon is at full1 ten parts of water are raised from that side of the earth next her1 by her attraction2 and1 as the side which is next her is opposite to the sun1 three parts must be thrown off by his centrifugal force1 the sum of which will be thirteen parts next the moon4--,from the side opposite to the moon1 and under the sun1 ten parts are thrown off by her centrifugal force1 and three raised by his attraction1 making thirteen1 the same as before4 ,,tutor4 ,i could not have done it better4 ,these are called ,spring ,tides4 ,but when the moon is in her quarters1 the action of the sun and moon are in opposition to each other2 that is1 they act in contrary directions 7see fig4 #e47 ,the moon of herself would raise the water ten parts under her1 and throw off ten parts by her centrifugal force on the opposite side2 but1 the sun being then in a line with the low-water1 his action keeps the tides from falling so low there1 and consequently from rising so high under and opposite to her4 ,his power1 therefore1 on the low-water being three parts1 leaves only seven parts for the high water1 under and oppose the moon4 ,these are called ,neap ,tides4 ,,pupil4 ,this is very plain4 ,,tutor4 ,you would naturally suppose that the tides ought to be highest directly under and opposite to the moon3 that is1 when the moon is due north and south4 ,but we find1 that in open seas1 where the water flows freely1 the moon is generally past the north and south meridian when it is high-water4 ,for1 if the moon's attraction were to cease when she was past the meridian1 the motion of ascent communicated to the water before that time would make it continue to rise for some time after3 as the heat of the day is greater at three o'clock in the afternoon than it is at twelve2 and it is hotter in ,july and ,august than in ,june1 when the sun is highest and the days are longest4 ,,pupil4 ,these are convincing reasons4 ,and1 pray what time after the moon has passed the meridian1 is it high-water8 ,,tutor4 ,if the earth were entirely covered with water1 so that the tides might regularly follow the moon1 she would always be three hours past the meridian of any given place when the tide was at the highest at that place4 ,but1 as the earth is not covered with water1 the tides do not always answer to the same distance of the moon from the meridian at the same places1 because the regular course of the tides is much interrupted by the different capes and corners of the land running out into the oceans and seas in different directions1 and also by their running through shoals and channels4 ,but1 at whatever distance the moon is from the meridian on any given day1 at any place1 when the tide is at its height there1 it will be so again the next day1 much about the time when the moon is at the like distance from the meridian again4 ,,pupil4 ,are not the tides later every day than they were the preceding day8 ,,tutor4 ,yes2 and the reason is obvious3 for1 whilst the earth is revolving on its axis in twenty-four hours1 the moon will be advancing in her orbit2 therefore the earth must turn as much more than round its axis before the same place which was under her can come to the same place again with respect to her1 as she has advanced in her orbit during that interval of time1 which is #ej minutes4 ,this being divided by #d1 gives #ab-a_/b minutes2 so that it will be #f hours #ab-a_/b minutes from high to low-water1 and the same time from low to high-water3 or #ab hours #be minutes from high-water to high-water again4 ,,pupil4 ,this ,i understand perfectly well4 ,,tutor4 ,i have now finished my description of the tides1 and having a little time to spare1 if you wish to know how to find the proportionate magnitude of the planets with that of the earth1 and to calculate their distances from the sun1 ,i will employ it that way4 ,,pupil4 ,at our first conference ,i remember you shewed me the proportion that the other planets bear to the earth1 with their periods and distances from the sun2 but to have it in my power to make the calculations myself1 will certainly give me great pleasure4 ,,tutor4 ,to find what proportion any planet bears to the earth2 or1 that one globe bears to another1 you must observe that1 all spheres or globes are in proportion to one another as the cubes of their diameters4 ,so that you have nothing more to do than to cube the diameter of each1 and divide the greatest by the least number1 and the quotient will shew you the proportion that one bears to the other4 ,,pupil4 ,the operation appears very simple2 but1 as ,i do not know what a cube number is1 ,i cannot perform it4 ,,tutor4 ,you cannot forget what a square number is4 ,,pupil4 ,the product of any number multiplied into itself is a square number1 as #d is the square of #b4 ,,tutor4 ,any square number multiplied by its root1 or first power1 will be a cube number4 ,thus #d multiplied by #b will be #h1 which is the cube of #b2 #i is the square or second power1 and #bg the cube or third power of #c1 c4 ,this you will perhaps better understand by ,a ,,table ,,of ,roots4 #a4 #b4 #c4 #d4 #e4 #f4 #g4 #h4 #i4 ,squares4 #a4 #d4 #i4 #af4 #be4 #cf4 #di4 #fd4 #ha4 ,cubes4 #a4 #h4 #bg4 #fd4 #abe4 #baf4 #cdc4 #eab4 #gbi4 ,,pupil4 ,i do1 ,sir2 and am now prepared for an example4 ,,tutor4 ,the diameter of the sun is #hiceeb miles1 of the earth #gibj miles2 how much does the sun exceed the earth in magnitude8 ,,pupil4 ,the cube of #hicebb1 the sun's diameter1 is #gaccgadibbfjhgbfdh2 and of #gibj1 the earth's1 #difgicjhhjjj4 ,and #gaccgadibbfjhgbfdh divided by #difgicjhhjjj is equal to #adceieb1 and so many times is the bulk of the sun greater than that of the earth4 ,,tutor4 ,this one example may suffice1 as ,i intend by and by to give you a table of diameters1 c42 you may then calculate the rest at your leisure4 ,,pupil4 ,i shall now1 ,sir1 be glad to have the other explained4 ,,tutor4 ,the periods of the planets1 or the times they take to complete their revolutions in their orbits1 are exactly known2 and the mean distance of the earth from the sun has been also ascertained4 ,here1 then1 we have the periods of all1 and the mean distance of one1 to find the distances of the rest2 which may be found by attending to the following proportion3 ,as the square of the period of any one planet1 ,is to the cube of its mean distance from the sun2 ,so is the square of the period of any other planet1 ,to the cube of its mean distance4 ,the cube root of this quotient will be the distance sought4 ,,pupil4 ,here again ,i find myself at a loss1 as ,i have not learnt to extract the cube root4 ,,tutor4 ,i will give you #ah;,doctor ,turner's rule1 which ,i think will answer your purpose4 ,footnote #ah3 ,young ,geometrician's ,companion4 8,first1 having set down the given number1 or resolvend1 make a dot over the unit figure1 and so on over every third figure 7towards the left hand in whole numbers1 but towards the right hand in decimals72 and so many dots as there are1 so many figures will be in the root4 ,next1 seek the nearest cube to the first period2 place its root in the quotient1 and its cube set under the first period4 ,subtract it therefrom2 and to the remainder bring down one figure only of the next period1 which will be a dividend4 ,then1 square the figure put in the quotient1 and multiply it by #c1 for a divisor4 ,seek how often this divisor may be had in the dividend1 and set the figure in the quotient1 which will be the second place in the root4 ,now1 cube the figures in the root1 and subtract it from the two first periods of the resolvend2 and to the remainder bring down the first figure of the next period1 for a new dividend4 ,square the figures in the quotient1 and multiply it by #c1 for a new divisor2 then proceed in all respects as before1 till the whole is finished40 ,the following example will1 ,i trust1 make it clear to you4 ,,example4 ,it is required to find the cube root of #aefbe4 4 4 #aefbe 7#be #h #ab7 #gf #aefbe 44444 ,point every third figure1 and the first period will be #ae2 the nearest cube to which1 in the table ,i gave you just now1 you will find to be #h1 and its root #b2 the #h you must place under the #ae1 and the #b in the quotient3 take #h from #ae and #g will remain1 to which bring down #f1 the first figure of the next period1 and you have #gf for a dividend4 ,the figure put in the quotient is #b1 the square of which is #d1 which multiplied by #c is #ab1 for a divisor4 ,now #ab in #gf will be #e times2 cube #be1 and you will have #aefbe1 which1 subtract from the resolvend1 and nothing will remain2 which shews that the resolvend is a cube number1 and #be its root4 ,,pupil4 ,you say #ab in #gf is #e times2 ,i should have said #f times4 ,,tutor4 ,in common division it would be so2 but as the cube of #bf would be greater than the resolvend from which you are to subtract it1 it can go but #e times4 ,,pupil4 ,now1 ,sir1 ,i think ,i have a sufficient knowledge of the rule to solve a problem4 ,,tutor4 ,the earth's period is #cfe days1 and its mean distance from the sun #ie millions of miles2 the period of ,mercury is #hh days--what is his mean distance8 ,,pupil4 ,as the distance of the earth is given1 ,i must make the square of #cfe the first term1 the cube of #ie the second1 and the square of #hh the third term of the proportion4 ,,tutor4 ,certainly4--,take your slate1 or a piece of paper1 prepare your numbers1 and make your proportion4 ,,pupil4 ,i find the square of #cfe #accbbe2 of #hh #ggdd2 and the cube of #ie #hegcge4 ,then #accbbe 3 #hegcge 33 #ggdd to a fourth term4 ,i now multiply the second and third terms together1 and divide the product by the first1 the quotient #dihcf is the cube of the mean distance of ,mercury from the sun in millions of miles1 and the fourth term sought4 ,,tutor4 ,so far you are right4 ,now extract the root4 4 4 #dihcf 7#cf #c #cf #bg #c #cf #bg7 #bbh ,sq4 of #c #i #baf #dffef ,mul4 by #c #ajh #cahj ,divisor #bg #abif #cf #gggf #chhh ,cube of #cf #dffef ,,pupil4 ,the root ,i find to be #cf1 which is the mean distance of ,mercury from the sun1 in millions of miles4 ,,tutor4 ,you now see1 that although #bg in #bbh will go #h times1 yet here it will go but #f times2 and1 as there is a remainder1 it shews you that the resolvend is not a cube number4 ,,pupil4 ,i see it clearly4 ,,tutor4 ,you now seem perfect in the rule2 ,i shall therefore not trouble you with any more examples1 but shall give you the table ,i promised you4 ,,table4 ,names ,diameters1 ,magnitude1 ,periods1 ,mean ,distance of the in ,english compared in from the ,sun1 ,,planets4 ,miles4 with the ,earth4,years and ,days4 in ,mil4 of ,miles4 ,sun ,a#hicebb #adceieb ---- ---- ,mercury #cbfa #a_/ad #j ---- #hh #cf ,venus #gfii #e_/di #j ---- #bbd #fh ,earth #gibj #a #a or #cfe #ie ,moon #bafa #a_/di ---- ---- ,mars #ecab #a_/c #a and #cbb #ade ,jupiter #ijbee #adgi #aa ---- #cad #did ,saturn #hjjab #ajca #bi ---- #afg #ijf ,georgian #cdbag #hb #hc ---- #aba #ahab ,footnote ,a3 ,the ,diameters were taken from ,adams's ,lectures1 ,vol4 ,,iv4 p4 #ci4 ,,pupil4 ,i shall take the first opportunity of calculating the rest1 in which ,i am certain ,i shall have great satisfaction4 99 99 99 99 99 ,,tutor4 ,i have now conducted you through the elementary parts of astronomy1 have given you a general view of the system of the world1 and prepared you to pursue the study with profit and pleasure4--,in your future researches1 the more accurate you are1 the more you will discover of regularity1 symmetry1 and order in the constitution of the frame of nature4 8,hail1 ,sov'reign ,goodness6 all-productive ,mind6 8,on all thy works thyself inscrib'd we find2 8,how various all1 how variously endow'd1 8,how great their number1 and each part how good6 8,how perfect then must the ,great ,parent shine1 8,who1 with one act of energy divine1 8,laid the vast plan1 and finish'd the design60 ,,the ,,end4 ---------------------------------------- -------------------------------- ,directions to the ,bookbinder4 ,plate ,i4 to face the ,title4 -------- ,,ii4 ---- page #dj4 -------- ,,iii4 ---- ---- #hh4 -------- ,,iv4 ---- ---- #aca4 ---------------------------------------- -------------------------------- ,transcriber's note3 ,all instances of #8disk' changed to #8disc' ,errata1 instance of #8disk' on page #gi added1 8---- #gi4 -- #e4 0 ,page #aa1 #8,years' changed to #8years1' 8#acj years after ,christ0 ,page #bj1 #8h e' changed to #8the1' 8would have as much the appearance0 ,page #bd1 #8cannon ball' changed to #8cannon-ball1' 8the time a cannon-ball would0 ,page #fc1 comma changed to full stop after #8,,tutor1' 8,,tutor4 ,why80 ,page #fe1 #8a' changed to #8a1' 8carry a planet from ,a to a0 ,page #gd1 #8itaxis' changed to #8its axis1' 8if the earth revolve on its axis every0 ,page #gh1 #8,mercury' struck after #8,sun1' 8,sun1 ,venus1 ,mars1 and ,jupiter are known to revolve on their axes0 ,page #ic1 #8cancer' changed to #8,cancer1' 8is the tropic of cancer2 that0 ,page #ic1 #8capricorn' changed to #8,capricorn1' 8the tropic of capricorn0 ,page #aae1 #8othes' changed to #8other1' 8and other stars rise to his0 ,page #aae1 #8bnt' changed to #8but1' 8out from2 but1 by going round0 ,page #aaf1 #8it's' changed to #8its1' 8,how can its surface be round0 ,page #abh1 full stop inserted after #8eclipses1' 8explain the cause of eclipses40