Show 3 ii LECTURES ON ASTRONOMY BY BT PROF ORSON PRATT LECTURE SIXTH I 1 the sun our oar inquiries have hitherto been principally principally rally restricted strict ed ted to the form magnitude diurnal ant and annual motions of the earth to the form dimensions and position of its orbit and to the principal I 1 phenomena benom arising from its transition in spa ii C the next most impo important tn t and interesting subject of inquiry is in the sun the great central luminary from which is received an inexhaustible supply of light and heat and by which the countless species of organized beings in s which people our globe are sustained in life we e have already learned earned by our former investigations ga gat ions tiong that the sun is situated in one of the foci of the eglip elliptic tic orbit described by the earthy earth as it wheels its annual course around that resplendent luminary it would certainly be a subject of great interest to learn the distance magnitude motions weight density physical constitution and all other important fe features tures of the great centre of our system the distance of the sun is as we have already observed obtain obtained pol by a simple computation from the observed horizontal parallax and is in round hurn numbers bers about of miles let we me here observe that though we have hitherto been somewhat particular in expressing maini magni I 1 Z I 1 j I 1 4 71 1 sudev distances time so and wado st fraction of their true numerical value yet jet we a hereafter abandon strictness as a beant being fr for general genera era information not only unnecessary but ut 1 ibon I convenient veni ent round numbers are an more mare e easily leawn bared than others and for n r why mation they bey answer every purpose W apte xe great accuracy or strictness is regu required ired nv are I 1 constructed ted with the greatest of care can to w which i ib the e antro astronomer tro nomer can at any time refer fir the baw elements necessary to be used in his s rew rese earcha 9 knowing the distance of the sun am lot let tto to en quire how its magnitude can be ascertained this hits problem like that of the distance s solved by the simplest principles of trigonometry As of all the heavenly bodies which lave have been determined have been obtained by the same prin chiples it may not he be uninteresting to explain gome gme of the principles ples of trigonometry A an n A angle I 1 ie is 0 the inclination or open opening ing between t two 0 o straight t 1 lines ine 8 the angle is greater or less as the lines are more or less opened A right angle is the opening made ahn each line is perpendicular to the other the olk opening of a right angle is equal to 14 1 4 of a circle all angles sa th than an a right angle are called acute angles all angles greater than a right angle are called balled obtuse angles the fences enclosing our city blocks are intended to stand at right angles anglas to each other A triangle is a plane enclosed by thy three sides to td every triangle there are three angles as well as three sides if in a triangle the three sides or two sides and an angle or one side and two illyes be known the other three angles or sides eam can be easily calculated now if we conceive lines drawn adawn from out oar eye to each side of the suns disc it is evident that the length of these lines will be known each being equal to the suns distance the angle or op opening taing of these two lines way may be measured b by y a ter or any accurate instrument this aagje ax wib 19 be equalito equal to the tha suns app apparent boft dister bm dx SKITS w subtends or opens these two lines awe 5 he hence we shall have two sides and their included angle given or known to find the other side of the tria triangle which will be the real diameter of the swa am 1 it t iba 4 polk this simple principle that the real dimmic diameter ui of the sun is in ascertained to be in round numbers equal to ta miles perhaps this may be simplified in another way so as to be brought more fully within the ow cow comprehension P i of those who are not in the habit of re reflecting diett upon these subjects it isa iffa is a fac twell ell known know ab by y every one that the sun and full ema appear to be of the same size if their angular breadth be meas ared by instruments they will on an average be found to subtend about the sama same angle this is apparent to any one who will compare the breadths of the two discs in a solar eclipse for then the moon i is is in in a direct line between the earth and sun W aad nd when their fentres centres are in a direct line it will be observed that the moons disc sometimes entire entirely lv covers the disc of the sun producing a total qc eclipse lipse at other times a narrow circular ring of light willbe will be seen while the other portions of his bis disc will be hid by the central interposition of the dark body of tie the moon this is called an annular eclipse this slight deviation in the apparent size of the two discs is is owing to the variation of the relative di distances of the surl sun moon and earth at different seasons of the year upon the whole then it may be safely las asserted that the average apparent dimensions a f the sun and moon s discs are equal I 1 the distance of the moon from the earth is about miles or about times nearer gwenth be earth than the sun yet these two bodies appear to be of the same size now suppose the moon to be removed as far from the earth as the sun the apparent breadth of its disc would be times less than the apparent breadth of the sun if the moon mom were really of the same same dimensions as the sua pun it would have the same apparent size as ibe sun va removed at the same distance dut but as it has the isme same apparent dimensions only when it in is situated times nearer it follows of necel necessity it that bat its real diameter must be times less I 1 than the suns sons now the real diameter of the moon hex has been determined by the most careful observations and measurements ure are ments to be a little over two thousand let this be multiplied by the product will be 6 be miles jr or more accurately s W web ed ad above mites miles it t is very d difficult ic for or s to form any conception jf of such h stupendous t pe do g it if the centra oi of the sun in coincided with it the centre of abe earth its ito surface would extend more than miles beyond the moons orbit the diameter of the earth is about miles but the buas cli diameter ameter is in I 1 I 1 I 1 12 1 2 times greater having once ascertained the diameter of a glow gloe it is an easy matter to calculate its volume fa for f the volumes or real bulks of globes are to vach other as the cubes of their diameters therefore ty by multiplying III 12 1 2 into itself three times we get the volume of the sun compared with the earth which is equal to times th e volume of the earth or in round numbers the sun is about OW times larger than the earth in other words if globes of the size of our earth were waitea ind aad into one they would forai fonn a globe of the dimension of the sun if alt the planets and sat eat celites of our system were united in one their bulk would not be the one five hundredth part of that of the sun u I 1 in some of our former lectures we pointed out the method of weigh weighing ipg the earth but the astronomer is required to perform astill abill greater wonders than this it is his duty not noi only to WI weigh ah the g globe which we inhabit but to son soar aloft WITA with kw his astronomical a balances through the vast spaces which separate ate the planetary bodies and accurately weigh those stupendous globes and declare the quantity of I 1 matter which each contains even the sun itself I 1 can be weighed with the most unerring unerring certainty but how can this be accomplished where can balaf balances ibes be found of su sufficient magnitude to contain these vast bodies what astronomer is is capable of winging his flight to those distant worlds to examine the materials of which they are cow composed posed to place them m n balances or make balte experiments of any kind so as to form any accurate judgment as to their we weights ht sr P ae we reply that the astronomer h has his balance on oft hand balances tolof too of the most perfect kind fie be is not under the necessity of leavi leaving jig his native earth to explore the solar system but can with the greatest of ease balance world with world and determine we i which is the heaviest astronomer is ia in possession sion of such a balance the the great astronomical balance for weighing wor klel was not made by our american or london artists artir ts but paean wa constructed ted by the great architect of nature its ite use was entirely unknown until discovered by the gigantic mind of the immortal newton a Y whose time as astronomers tron omers have been as thith weighing worlds as chemists are itt in weighing ta thae proportional ingredients which enter into the various compounds which come arder their investigation but what is tb the nature of this balanco balance we reply that it is toe the amount of deflection which one body has ban towards another which determines the quantity or weight of the matter towards wb on i deflections are nude mso for instance the relative 1 afsa w v titles of matter in the earth and san aun are ascertained by comparing ute the moons deflections towards the earth with the earths deflections towards the sun the amount of these deflections can if we know the distances and periodic ies now the distances of the sun and moon mom are am known as also the periods of the moons around the earth and of the earths around the sun therefore from these data the de dei sections and consequently the relative quantities of matter contained in the earth andsen and sun can easily be deduced it id may not be uninteresting to this audience if this principle ale should be a reference to some pt of the most emmon va and fkr familiar aar experiments with which we axe are an all more anore or low acquainted quain ted we all 4 know that when a body bidy is made to revolve in a circle it has a tend tendency easy to r recede frache cent centre re this R tendency inq willbe greater as the velocity of revolution bico becomes I 1 Ws greater abst ana as the ibo distance from the gentre leahm I 1 lea VM bt rt ia is manifest by the whirl tag Q estal M Z be longer the string or the great the va Tolf td v with ith which it is w whirled h r led the vior iia orew abe 0 be 1 o sW swelled elied ed if the velocity be 0 at IM W ed the string will iu bre re and an tap I 1 p I 1 recede cie do from the cen jt it is not A it ity which aw hb 1 wing r for if bo jw whirled r edin in a horizontal instead of a vertical plane able th I 1 same name tendency to recede from the centre will be if the string be lengthened op I 1 ened while the time of revolution remains the same the tendency to stretch the string will be I 1 proportionally increased or diminished on the I 1 other hand if the string remain of the same length I 1 while the velocity of the stone in its revolution is increased or diminished or which amounts to the same came think thing while the time of revolution is diminished or increased the tendency to stretch the string airing will be pro proportionally anally increased or diminished thus it will be perceived that there are two causes which increase or diminish the tendency of the whirling body to recede from the centre one is the increased or decreased distance irom the centre of motion the other is the decreased or increased time of its period now let us endeavor to ascertain the exact law of the force which stretches the string as depending on each of these causes separately I 1 st what will be the force which str stretches etche s a string that is twice the length of another string if they be attached to equal weights and be made to whirl round in a circle in equal times it is evident that the weight attached to the longer string would have twice as far to move agthe as the other weight and the deflections from the tangent would be twice as great as in the smaller circle therefore the tension of the longer string will be twice that of the shorter when the time of revolution is the same fame if the string siring be three times longer the tension will be three times greater if it be four times the length the tension will be four times greater and so on now the distance from the centre of the earth to the moon is about miles which is equal to feet hence if a string equal in length to the moons distance with a weight attached be made to whirl round in the same time as a string 1 foot in length the tension or the centrifugal tri fugal force which stretches the longer string will be times greater than the tension or centrifugal force of the shorter one again if one string equal in length to the distance of the sun be made to whirl round in the same time as another string equal in length to the distance of the moon the tension or centrifugal force of the longer string would be about times greater than the tension of the shorter for the distance of the sun is about times greater than the distance of the moon in biall all these cases it is supposed that the weights or of masses of matter attached to the ends of these several strings are equal and that the periods rhods or times of completing their respective revolutions lut ions are also equal under these conditions we easily perceive the law of the increased or decreased tension of the string depending on the distance ot the revolving weights that is the tension varies directly as the distance this is the law ad what will be the force which stretches two strings of equal lengths if the wei weights alias atta attached chea to them be equal and they be made to revolve in circles in unequal times according to the mathematical nia principles of mechanics the strings would be stretched inversely as the squares of the times of their respective revolutions for instance if one of the weights be made to revolve in one half the time of the other the tension of the string will be four times greater than the one having the greater period if one performs its iti revolution 3 times as quick as the other the tension of the string will be 9 times gri greater ater if the period of one be one fourth of the other the tension or centrifugal force will be sixteen 6 times greater and so on it makes no difference how long these strings are provided they are of equal lengths for at all equal distances at which the weights are made to whirl round the inverse squares of the respective times of their revolutions will be proportional to the tension of the two brings now let us suppose that each of the strings is miles long and one be whirled round in one year yar and the other in years in what proportion will the two strings be stretched the tring string whose period is times less than the other oth r will be stretched times more than the one having the greater period therefore the law of tension governing strings of equal length to I 1 I 1 which are attached equal weights may be expressed to in the following words square i q aar beof of i the he t ii times mes of ahe their i arre respective sp e c fi ve revolutions re vol utia it will be perceived that the law of force by which a string is stretched as depending on the lengths when the times and weights are equal and also as depending on the times of revolution the lengths and weights are are equal has been investigated I 1 from these two laws it is evident that we can I 1 calculate the proportional tensions of strings although their given lengths and periods of revolution are unequal fb for in instance siance what will be the proportional tensions of two strings one of which iv one foot long arid and the other four feet long the time of the revolution of the shorter being one second arid and that odthe of the longer being two seconds according to the law depending ing on |