Show 4 4 1 d ASTRONOMY t lii I 1 V 1 nhe il st VO 1 BY proe PROF ORS oti oll ITT SEN in ii V ju I 1 rt U 00 i egure ym iii lis EG ube ugE Y V I 1 sw t his eds eis pace d nce and we 11 t terms erms defined su serfs hys dys alume alume beight of un sou sov mar lato law mhd we tin as B bodies od tes ies density of the sun weight of materials on tiie qu 4 Ts i surface ce bow ascertained ascertain ea Rota eota of ai sun determined ty b spots on bis his surface 0 of the huns AWs equa equal warto td the nhip Edip ecliptic tic velocity vedo Vido ctol clop of tie the suni tua quator equator qUa tor tOT distance through wilch which a wy tody X one second at the sun suns s equal jegua ton tor capul vibrations ofa of a clock cloch pendulum on the sus Suns Surface mat What velocity of rotation will unil destroy the weighton ane Weight of bodies at the suny zorator Eyia tor 2 71 of oku the tie sens suns nure figure git r t our ofir inquires I 1 have hitherto been beeh principals ly restricted to the tha porm form magnitude diurnal and annual or 0 the earth eiith to the tha form positions of As arbir anil ilia to the principal phenomena syi AYI arising p from transition its n in space the next nest mst import important int and interesting suba subject 0 c t of Inqui inquiry rylis is the stin sun the great central luminary from irom which is rec ree received elved elvea an aw inexhaustible supply of light and heat and b by which the countless species of organized beings which our globe are sustained inslfe in life ilfe I 1 f I 1 I 1 i 1 1 1 weli we eave have ave already learned by bv our foriA formen former pr investigation that the sun is situated in one oner of the fog foci of the elliptic orbit d des i crded by the earthy as il it wheels it anana annual 1 course around that resplendent luminary 11 lt t woula certainly be a subject of great graat interest to thearn learn the distance magnitude motieus mot ious ions weight density physical constitution and all other important features of the great centre of oui our system I 1 the distance of the sun is as we have already observed obtained by a simple computation from the observed horizontal parallax and is in round numbers about of miles lehme let me here that though we wb have hitherto been somewhat particular in expressing magnitudes distances times and motions within a small smail fraction of their true numerical value yet we shall shail her hereafter gafter dafter abandon this strictness as being for general anfor i mation matlon not only unnecessary but inconvenient Te veni teni rilent ent round hound numbers are more easily remembered than thin others and for nor conveying ying general information they anster answer answer every pur pose tose where gi eai eat accuracy of or strictness is required d tables are constructed with the which the astronomer can at any time zefer refer for the numerical elements necessary to ibe ibo used in his bis researches I 1 I 1 knowing the distance of oz he sun sunset let iet us next inquire how bow 4 its magnitude can carl ascertained this problem like that that thit of orthe the distance Is solved by nr the simplest simplot of tri trl trigonometry on I 1 I 1 I 1 As the tho magnitude of all the heavenly which have been determined have been by the same principles it may not be uninteresting to explain some ol 01 the tho principles of trigonometry an angle is the inclination or opening between two tavo straight lines the angle is greater or less as the lines are more or less opened A right angle is the opening made when each line is perpendicular to the other the opening of a right angle Is equal tol toi to 1 4 ora of a circle all angles less than a right angle are called acute angles all angles greater than a right angle are called obtuse angles the feibes fences enclosing our city blocks are in tow tox tended to stand at right angles to each other At triangle Atri angIe angle id is a plane enclosed by three sides side suto ruto every triangle there thero are three angies angles sas sab as well as three throe sides it if in a triangle the three sides or two sides acdan addan and an angle or one side and two angies angles be 1 the other angles or sides easily calculated eyloe sow now lf if we ive conceive lines drawn from our egeto each ach sido side of bf the suns disc it is evident at the length of these lines will be knowin leach teach each being equalito equal to thesues the suns distance U a 4 A 1 I the angle or opening of these two lines may be measured by a micrometer or an any y accurate acau ate instrument this angle is equal to th oTsuna sums i fl apparent dia dla diameter meter whose disc iti iii subtends bk or opeus openS P ulese two lines iines neue nene hence honce ideall 11 hp have two sides and nhia their included udea angle augle alvenor gl venor tenor known to find fina tha thi the e other othey side oath of the triangle be the rehl rehi diame eroff he diun it Is 13 upon th this simple prin 4 tuat aba tha nal nai ral diameter of the tha sun is ascertained to be in equal to V r this ma may r be simplified in another vvs wiy so as to ba be brought more fully within ake thom of who are bat in the tho abit of reflecting upon these subjects it is ii a tact fact well known by every one that the sun and full moon appear to be of the same size if ir their aal angular sular lular breadth be measured by instruments they will on an avera gebe gehe found to sull suil subtend en d about the st same bame m angle I 1 this is apparent to an any one who will compare the breadths bf of the two to discs in adolar eclipse for theotho then tho moon moan Is in a a direct line between the earth earm and sem sim sun and when their bentres centres cen tres are in a direct line it will be le observed served that the moorea i disc olse some dome sometimes times entirely covers the disc atthe at sun a tou total eclipse at other times a arrow narrow n I 1 circular ring of light will be se seen en while the other portions ot his disc wiil wid be hid by the central interposition of the dark bod boo body y of the moon this is called an AU alAn annular ular J ii eclipse this slight deviation in I tha the app apparent a rent size of the two discs is owing to the variation of the relative distances stanos di of the sup sun snug mooned moon bd earth ai at different seasons of the liar iyar at upon the whole then it may be safely as sorted that the average apparent a arent dimensions odthe of the sunai sunar sun and ano moons I 1 P aises aises alses are equal oqual the distance of the loayon from the earth is about mues miles or about times nearer the earth parth than the sun yet these two bodies hodies appear to toi be of the same size nom nov suppose the moon to be removed as far from the earth as the sun the apparent breadth of its ita disk would be times less than the apparent breadth of the sun it the 06 moon were werd really of or the same dimensions as the suri surl sun it would have llave thelka thelia the tha same i me apparent size as the sun when removed VL af the same distance but as it has the same apparent dimensions only when it is js situated doo times nearer it follows of necessity that it its real I 1 I 1 diameter must be times less than the suns now the real diameter of the moon has been determined by the most careful ob and measurements to be a little over oter two thousand miles let this babul miles by the product will bebop beon be therefore the diameter of the sun must musi be ibe miles or snoie accurately aa we observed before miles it is very difficult for Us to form any conception of such stupendous mao magnitudes inthe if the centre centro othe qun sun coincided coincided ith aa centre of the earth earthy would extend more 0 miles nilles beyond the moons orbit I 1 the diameter of the earth is i s about miles but the suns suits diameter Is ill ili I 1 tp times greater I 1 having once ascertained the diameter of ar a globe IMs ad ari easy matter to calculate its volume por for the v volumes 0 or real roal bulks of globes are aro to each other as the cubes ot of weir mein diameters therefore by multiplying ill ili I 1 into itself three times we get theo the volume lume of the sun compared nth with ath the earth which Is equal to times the volume of the earth or in the sun is about 1400 4 times larger than the earth another in other words if globes of the size of the earth were united and into one they khey would form a globe of the dimensions of f the sun cfall if all ali the planets and satellites of our system were united in one their bulk would not bo be the one five hundredth part of that of the sun in some of our former lectures we pointed out the method of weighing the earth but the astro astronomer nomer is required to perform still greater wonders than this it is his duty not only to weigh the globe which we inhabit but to soar aloft with his Is astronomical balances through the vast spaces which separate the planetary bodies aind nd accurately weigh those stupendous globes and de declare clarethe the quantity of matter which each contains even the sun sunt itself can be weighed with ithe most unerring certainty buchow can this be accomplished where can balances be found of sufficient magnitude to contain thase vast bodies what astronomer is capable of wa winging ginging q his flight to those distant worlds to examine the materials of which they thoy are composed to place them in balances or make mako experiments of any kind so aa as to form an accurate judgment as to their weights sl I 1 I 1 I 1 we e reply that the astronomer has his bis aia ala rices on hand band balandes balances too of the most perfect kind lie he is not under the necessity of leaving his bis native earth to explore the solar system but can with the greatest of ease balance world with world and determine which is the heaviest every astronomer Is in possession of such a balance the great astronomical balance for weighing worlds was nob not made by vy our american or london artists but was can constructed ted by the great greab architect of nature its ats use was entirely unknown until discovered by the gigantic u ind af the aig mortal li newton nowton ewton since whose time astronomers have been as fir fit familiar nillar with weighing worlds as chemists are in weighing the I 1 ingredients which enter into itne ithe various compounds which come under their investigation but what hat is ig the nature orthis of this balance A 4 I 1 we reply that it is the amount of defection which one body has towards another which determines the quantity or weight of the matter towards which the deflections are made for instance the relative quantities of matter in the earth and sun are ascertained by comparing the moonta deflections towards the earth with the earths deflections towards the sun the amount of these deflections can an be calculated if we know the distances and periodic peri perl odie odle times now the distances of the sun and moon from us are known as also the periods of the moons revolution around the earth and of the earths revolution around the sun suri therefore from these data the deflections and consequently the relative quantities of matter contained in the earth ear h and an sun can easily be deduced it may not be uninteresting to this audience d if this principle should bo be illustrated by a reference fj tj some of the most common and familiar experiments with which we are all more or less acquainted we all know that when a body is made to revolve in a circle it has a tendency to recede from the centre this tendency will bo be greater as the velocity of revolution becomes greater and as the distance from the centre increases this fact is manifest by tha th whirling of a stone atone iq iff a sl sling iii ill g the longer the string oi 0 the greater t the e velocity with which ip is whirled the more wal vui the hb string be stretched s i if the velocity ba sufficiently augmented the string wilt will break and the stone wiil will becede recede from the centre it is not the forb force af gravity which tightens the string for if the stone be whirled in a horizontal instead or 0 a vertical plane the same ten tendency dency deney to recede from the centre will be manifested if the string be lengthened or shortened while ahil 0 the finne time of revolution ren ron remains lains the same the tendency to stretch the string will be proportionally increased or diminished on the other hand if the string remain ot the same length while the velocity of the stone in its revolution is inc increase akse d dor or diminished or which amounts to tnie trio same thing while the time of revolution is diminished mini shed or increased the ther tendency to stretch the string will be proportionally increased or diminished thus awill be perceived that there are two causes eaues which increase or diminish the tendency batho of the whirling body to re recede cede code from the centre one ia Is the increased or 0 r decreased distance from the centre of motion the other lother is tile the decreased or increased time of its period now let us endeavor ta to ascertain ascer taid talu the mhd exact law of the force which stretch stretches ds the string as depending on n each of these causes separately what will be the force which stretches a string that Is twice the e length of another string if they be attached to equal weights and be made to td whirl round in a circle in equal times it is evident that the tho weight attached to the long string siring would have twice as far to move inove aa as the other weight and the deflections from the tangent would be twice aa as great as in the smaller circle therefore he the tension of the longer string will be twice twice that of the shorter when the time of revolution ia Is the same if the string 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 Js about miles which is equal to feet hen ceif a string equal in length to the moons distance with a weight attached be made to whirl round in the same time as aftring a string one fogt oat in length the tension or the centrifugal tri trl fugal force which stretches the longer string will ibe be times greater than tie the the tension or centrifugal force of the again if one string equal in length ta the dista distance nee ned 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 forte of the longer string would be about times greater than the tension of the shorter for fhe he distance of the sun is about times greater than the distan distance ce of the moon in 11 all these case cashait sit alt ait it is supposed that the weights or maies males masses ot 0 matter attached lo 10 the ands of these several strings ard are equa equal land lard ard and that the periods or times of completing comp letin their respective revolutions revolution gp are also equal egnal under these conditions we easily perceive tho the ho law of the iho Increase increased il or depro decreased eased tension of the string depending on the distance of theT thee evolving weighty weights that is the tension varies directly as at the distance 1 thi thia Ss is the thalah lane lase I 1 sod what will be bb the force which stretches tret trot crotches ches two strings of equal lengths the eights weights attached to them be equal arid arld they be made to revolve in circles in unequal times Ag according cording to the mathebat math mathe mat ernat ical cil principles of mech mechanic anlo anlu the strings would be stretched inversely as the squares of the times of their respective revolutions for instance if one dt 6 the weights bemauer be mauei mauet to revolve twice as quick as theother tho the other the tension tenison of the string will be 4 times greater than the one having the |