Show astronomical LECTURES BY BT PROT PROF ORSON PRATT LECTURE FOURTH in our last laa lecture we demonstrated upon strict mechanical principles that the gravitating force which pres preserves cIrves the moon in in its orbit w would aw be entirely insufficient to preserve a body at the distance odthe of the sun in in an orbit that should be described in one year but should any one feel disposed to doubt that the force that binds ehfe moon in in her orbit was extended to the sun and suppose that the sun revolves around the earth under an entire different force from that exerted upon the moon then we should be under the necessity of sear searching chiq for some other phenomena to decide the question whether the suns annual motion were apparent or red real fortunately the great discovery of the aberrations of light furnishes is with the moat moat evidence of the earths earth annual motion around the sun oun roemer a danish astronomer in in the year a comparison of the observed times of the eclipse eclips ew of jupiter Ju s satellites sat elites with their computed times discovered the progressive motion of light he found its velocity to be about mi gilesper lesper miles per second A little over a half century afterwards dr bradley an english astronomer of great emi eminence commenced need a series series of observations of great accuracy upon the fixed stars to ascer ascertain taia it po possible ible whether they were subject to any minute apparent changes in in their relative post positions ions in in consequence of the annual revolution of the earth in in its orbit he soon found that there were apparent changes constantly taking place but not adt such as should result from the di different positions of the earth in in its ita orbit each star m in the heavens seemed to revolve once a year in in a very small elliptical orbit whose fe greatest a t tes t di diameter iame ter never exceeded 41 a of h a degree those h 0 e stars t ars situated near the poles of the ecliptic or at right angles to the plane in in which the sua aunt performs its apparent annual motion appeared tw to revolve in in small orbits very nearly approaching air circles As you proceed from these polar points to wards the ecliptic the eccentricity of these small malt elliptical orbits seemed to increase the major axis in all these ellipses was observed to remain con COB stant being equal to 40 72 see sec while the kinoe minor a axis 9 seemed to vary in in proportion to the latitude vr af the stars decreasing as the latitude decreased A s tar star situated in in the ecliptic seemed to Hate in in a straight line the minor being reduced to noth ki S ing ing these strange phenomena were such as could goo nual n not t be accounted for upon the principle of the annual parallax of the stars or upon any other principle ithen known dr bradley Br ailley after many trials to reduce these phenomena to a general law at last happily succeeded in in discovering the true causes cause of these cu rious appearances he demonstrated that they were the results of the combination of the motion of light with the motion of the earth in in its annual revolution around the sun if the motion oali of light were instantaneous that is is if it required no appreciable time to come from a dis tant luin luminous inous body to the eye then all these displacements of the stars inthe in the form of little elliptical orbits would entirety entirely cease and the staw star would be seen in in their true places directly in the centre of those ellipses whether the earth afre afe af t rest or in in motion but the velocity of light in is an ay W preci able quantity and when combined with the velocity of odthe the earth baah it appears to come from a df ferent direction from what it would if the earth were at rest this may be illustrated in in the following nka aner suppose that the wind should blow directly direct direr tty ty from the north with a velocity of 30 miles per hoara weather tec cock or vane on tl alt top of a railroad car at WA JB a would point out the true direction of the wind vand suppose now that the rail ear car should be put pat in in mo ipa ton tion due east with a velocity of 30 mile per how hoary the direction of the wind would no longer appear tw to be north but it would seem to come from thes north east next let the car go directly to the west with the same velocity the vane upon the top adl wul naw point to the northwest north west which will be the apparent direction of the wind the less the velocity of the car the less will be the angle of the ap apparent patent displacement of the wind from froin its true direction suppose then that the velocity odthe of the car be about 10 times less than that odthe of the wind the apparent en t displacement of the wind would then be about of a dek dag from its true place now let us apply this principle to the tion of the motion of light with the motion of tj earth let us suppose the light to come hom from ad a star in the pole of the eel ecliptic i itic with a velocity of miles per second if the earth were at rest we should see the star in its tipe tape place suppose next neit that the earth should be put m ln motion in in the plane ol of the ecliptic to the east eastward wilid with a velocity of about 19 miles per second we should no BO longer seer see the star in its true place but the rays of light would have an apparent displacement of about of a degree to the eastward of its true place if the velocity of the earth were imre increased ased to per second the star would apparently be displaced 45 46 deg being equal to the apparent displacement of of the wind when the velocity of the car was wag equal to the velocity of the wind As the vel velocity city of the earth decreases so will the angle of apparent displacement decrease if the earth should go to the westward in the ecliptic at the rate of 19 miles per second the apparent position of the star would be of a degree to the westward fifita of its true place placed pla cei 4 in whatever direction the earth may maybe be mo moving bt iff the plane of the ecliptic the stars will appear to we bf displaced in a direction parallel to that motion towards a point in the heavens which the earth for tho the moment seems to be approaching hence as the motion of the earth is ia not in ia ft a straight line but nearly in a circle it is evident that a star situated in the pole of the ecliptic perpendicular ie to that motion must constantly alter its apparent direction as the earth in its orbit alters its direction and therefore it must mart necessarily have an apparent annual revolution in a very small orbit around its true place which will be exactly in the centre we will suppose next that the wind was blowing from the northeast north east while the car was going with the same velocity east the vane would now point east north east hence the displacement odthe of the apparent direction of the wind would be only one half what it would have been had the motion of the car been at right angles to the motion of the wind were the true direction of the wind to the northwest while the direction of the cur was east toe the vane would point if the velocities were equal equi to the north north west in this case the apparent direction would be more nor thedy than toe the true direction while in the other case it would be more mare southerly southerly and in both cases the wind by the motion of the car would seeni seem to shift 22 2212 12 1 2 degrees towards the point to which the car was moving thus it will be seen that the nearer the true direction of the wind is to the line of the motion of the car the less will be its apparent displacement when it blows in the direction that the ear car is ia moving or in the opposite direction its displacement will be noth nothing ingo and the vane will point out its true direction now how inthe if the motion odthe of the earth be taken for that of the car and the motion of light fw for that of the wind phen phenomena omeria precisely of the same kind will happen in regard to the apparent direction of a star situated in the ecliptic for instance if about the time of sunset sun seton on the alst of december we observe a star sac ir situated in that portion of the ecliptic which is on ou our meridian we mitlee wit lee it in its true place because the earth will be going in ia its orbit directly from the star if the star be observed every day for three months to come it will be seen to move apparently to the westward arriving at its it maximum distance about the of march next when 6 direction of the motion of the earth would be at right angles to the motion of light from thea star it would then gradually begin to recede back again i I 1 I 1 leoo I 1 Z 30 3 0 1 A 4 towards its true position and at the end of three more or about the of june it would be 11 seen in its its true po position as the motion of the earth would then be directly towards the star during the I 1 next three months its apparent motion would be to the eastward in the ecliptic obtaining its maximum distance about the of september when anen the motion of the earth would be again at right angles to th the motion emotion of the rays of light from the star and for the next three months it would apparently recede back again to its true place at the end of which it would be seen in the same position as it occupied one year before thus each year it would appear to oscillate in a straight line in the ecliptic deviating from its true place on each side about 20 seconds these phenomena will perhaps be more clearly perceived by supposing a railroad car to be drawn round the circumference of a circle once a year while khi N the wind blows constantly from one direction say aay from the north let the car start from a point on the east side of the circle towards the south with a velocity ve times less than the wind which is about the proportion of the earths velocity to that of light when the car starts it will be going directly from the wind hence the vane will point the true direct direction iop of the wind while the thecae car gradually describes the first quarter of the circle it will gradually deviate from a southern to a western direction during which the weather vane will deviate more and more from the north towards the west and at the end of three months the direction of the car I 1 will be due west or at right angles to the true direction of the wind the deviation of the vane will now be at its maximum pointing about of a de gree grec west of north As the car describes the next quarter of the circle the weather vane will gradually recede back again and at the end of the second quarter the direction of the car would be due north and the vane would point out the true direction of the wind in the third quarter while the car is going inar from the west to the north point of its circumference I 1 fer ence the weather vane would again deviate by degrees to the east of north and at the end of the third quarter the direction of the car would be due east or at right tingles angles to the direction of the windy wind and the deviation of the weather vane would again be at its maximum value namely past east of north during the last quarter the wind would apparently recede arain again towards its true position and having performed one entire revolution the direction of the I 1 car would again be due south and the vane would again point the true direction of the wind thus a true north wind would by the motion of a car in a circle appear to oscillate each side of its true position precisely in the same manner that a star in the ecliptic appears to oscillate as the earth moves in its circular orbit As all the stars of heaven are arc affected by the combination of the earths with that of light it 1 is evident that their true places cannot be known only as they are deduced from their apparent places tables table s of aberration have been calculated iby by which these deductions can be conveniently I 1 made I 1 T the laiq phenomena of the aberration of light 11 are evidences 1 which can never be controvert ed in proof of the annual motion of the earth round the sun for if the sun revolved around the earth while the earth remained at rest there would be no appearances of aberration As we have demonstrated that the earth has an annual revolution around the sun let us next enquire what the form of the orbit is it was sup posed for many centuries during the dark ages that all the heavenly bodies revolved in exact circles but modem astronomy has overthrown this conjecture and has proved that the planetary orbits deviate from the circular form we shall now point out bout the process by which this is ascertained I 1 if the sun be observed at different seasons of the i I 1 year lie he will be seen to vary in his apparent angular angui diameter this can be easily determined by measuring with some accurate instrument the apparent breadth of his disc it will be found that I 1 about the first of january the sun will subtend an angle of 32 min see sec on the first of april his apparent diameter will be having decreased 33 see sec in three months on the first of J july lily his diameter will appear smaller than at any other time of year being only on the first of october his hie apparent diameter will be the same as on the first of april thus it ii will be seen that from the first of january to the first of july the sun decreases in its apparent size and from the first of july to the first of january he increases in size the difference between the greatest and least apprent apparent diameters is im now it cannot for one moment be supposed that the real magnitude of the sun undergoes a periodical change therefore the difference in his apparent size MUST result from a change of distance one half the sum of the greatest and least diameters is equalito equal to which is the mean diamente or the diameter which the sun gives on the of march and ad of october in the year 1852 this mean diameter must correspond to the suns mean distance from the earth while the greatest and least leant 4 diameters ia meters correspond to the least and greatest dis I 1 I 1 bances of the sun from the earth if we call the 1 suns mean distance 1 then the greatest ard and least distances may be found by the following proportions As the suns suna mean apparent r 3 isto is to I 1 the suns greatest appart ap parit diameter as the suns mean 40 distance istance 1 is to the suns greatest distance also the mean diameter is to the least diameter as the mean distance is ia to the least distance thus it is ascertained certa eert ined mined that the greatest the mean and the leat leaa Ai distances stances of the sun from tho earth are inthe in the respective ve proportions of the numbers and these numbers are very nearly in the proportion kofl of 1 1601 1 60 1 aad 59 60 now if the earth revolved around the sun in a circular orbit with the sun in the centre his apparent diameter and distance would be ba precisely the same the year round but from the above numb era rs it will be clearly perceived that the situation of the sun wither within the earths orbit is ECCENTRIC the amounting to or nearly 1 60 of odthe the mean distance these observations and calculations do not demonstrate that the orbit of the earth about the sun is not a circle but they merely demonstrate that the sun is placed nearly 1 of his mean distance from the centre of odthe the orbit in order to obtain the true form of the earths orbit let the suns apparent diameter be taken when i he is at the beginning of af each of the twelve signs I 1 in the ecliptic or in other words observe his apparent di diameter 1 ameter for every 30 deg of longitude from these observations calculate the proportional distances corresponding to the apparent diameters assuming the mean distance equal to with these data the form of the orbit can be delineated upon paper in in the following manner let any point upon the paper |