Jan. 30, 1S85.J 



♦ KNOWLEDGE ♦ 



When the star is somewhere between cither ))ole of the 

 ecliptic and the ecliptic itself, it describes an ellipse, as 

 A B C D, Fig. 5, always reaching its greatest excursion as 

 at B and D, when the earth is travelling in a direction at 

 right angles to the line of sight to the star (which neces- 

 sarily hiippens t'vice a year), and its least excursion at A 

 and C, when the earth is travelling as nearly as it can 

 towards or from the star (which also necessarily happens 

 twice a year). 



Is'ow it is to be noticed here that though 1 have made 

 use of the accepted theory to describe the observed motions, 

 this by no means involves the assumption that the accepted 

 theory is correct It k the fact, and it is a striking fact, 

 that we canuot even describe st«?llar aberration conveniently 

 without a reference to the accepted theorj-, so that even 

 though that theory were false, it would still be convenient 

 to speak of the aberrations of the stars, as being such as 

 would correspond t) such and such assumptions respecting 

 terrestrial motion. 



But here we have a phenomenon to explain. We have 

 every star on the heavens announcing some great fact to us, 

 or rather I'-riting for ns year b;/ year on the celestial concave 

 a lesson/or our instrriction. To reject the lesson as meating- 

 less, would be to abandon one of the highest and noblest 

 faculties given to man, his desire to search out and investi- 

 gate the problems set by nature for his interpretation. 

 What, then, is the meaning of this million-on -million-fold 

 repeated lesson? Can astronomers explain the matter? 

 Perhaps astronomers have some far-fetched explanation, 

 which they would force on the world by crafty argu- 

 ment. 



The case is otherALse. Astronomy can not only inter- 

 pret the aberration motions of all the millions of stars 

 revealed by the telescope, but the accepted theory of astro- 

 nomy would have to be abandoned if those motions did not 

 take place. Stellar aberration was discovered as by an 

 accident, was long looked on as a great source of doubt and 

 perplexity, was honestly s^ubmitted by astronomers to the 

 inquiry of the world — and then suddenly it was seen that 

 the aberration motions could not but take place if the 

 earth moves as the accepted theory ^asserts. Let us inquire 

 how this is. 



It has been independently discovered, by observations 

 made on the eclipses of Jupiter's satellites, that light travels 

 with finite, though inconceivable, velocity. Always when 

 Jupiter and his family were farthest from the earth, the 

 satellites seemed tardiest to announce by appearance or by 

 disappearance, their motion through the shadow of their 

 primary. And so it was seen that th3 light messages 

 swe ping to us from these bodies come at a definite speed 

 lO the earth. A consequence of this 

 peculiarity had been wholly overlooked 

 by astronomers. The light travelling 

 in appreciaVjly parallel lines from a star 

 towards the solar system, may be com- 

 pared to a shower falling in parallel 

 liaes on moving bodies. ISow we know 

 that in moving through a vertical 

 shower of rain, the rain seems to fall 

 somewhat towards the face. The reason 

 is obvious ; thus, suppose a traveller's 

 face at 1, Fig. 6, when a rain drop is at E.', and that by 

 the time he reaches 2, the rain drop is at H', it is clear 

 that the drop will teem to have fallen from a position in 

 front of hiai, and in the direction indicated by the dotted 

 lines. If we consider the motion of a small body travelling 

 in a circle under a vertical thower, we shall see at once 

 that this property may be made to illustrate every case of 

 stellar aberration, by assuming different positions, as 1,2, 3^ 



^ 



Fij?. 



Rz 



Fisr. 7. 



in Fig. 7, for the circle in which the body moves under 

 the shower. 



It will be seen, though, that, in order that this explana- 

 tion may hold, it is necessary that the 

 rate of motion of the earth should bear 

 an appreciable relation to the enor- 

 mous velocity of light. If rain fell a 

 thousand times as fa;;t iis it actually 

 docs, the fastest runner would not find 

 that a vertical rain sliowtr would seeni 

 to fall a])preciably towards his face. 

 Now, apart from all considerations of 

 the real size of the earth's orbit, or 

 of the rates of motion either of ligh' 

 or of the earth in her orbit, we can at 

 once test this explanation of aberra- 

 tion. It had been independently 

 shown by Eeimer that liglit takes 

 about eight minutes in crossing the 

 ladius of the earth's oibit; the earth 

 occupies a year in travelling round the circum- 

 ference of tlie circle ; all we want to know is, 

 whether the displacement of a .star over an arc 

 of about one-third of a minute, corresponds to 

 these relations. What .we require w, that sup- 

 posing S B (Fig. 8) to be the distance traversed 

 by light in any time, B A the distance tra- 

 versed by the earth in the same time, S B A 

 being a right angle, the angle A S B should be 

 about one third of a minute of arc. Let it be 

 remembered that this was the problem as pre- 

 sented in Bradley's time by mere observation, 

 and before any had noticed what a noble proof of the true 

 theory of astronomy was to be adduced from it. 



Now for the test of figures. 



Since the eai-th comf)lete3 a circuit of her orbit in one 



yeir, she would traverse a length equal to the radius in the 



period 



,365 X 24 X 60 . , , , , ^ 

 minutes (toughly), 



'2tt 



where tt rejiresents the number -'MIloO ... or the 

 ratio of a circle's circumference to its diameter; and 

 light traverses this distance in 8 minutes. Hence 

 the velocity of light is to that of the earth as 



365 X 21 X 60 . 8 . oi- ^g 32850 : tt. Now the proportion 



2;r 

 of B S to A B where A S B is an angle of about one-third 



Fig 



D 

 8. 



of a minute of arc is 1 : 



360 X 60 X 3 



or 32400 



It is 



seen then at once, that we have a satisfactory exjjlanation 

 even with these rough assumptions, since the difiVrence 

 b.-tween 32400 and 32850 is but one seventy-second part 

 of 32400. But if I had taken the mean of the estimates of 

 the velocity of light from observations male on Jupiter's 

 eclipses, as determined before Bradley's observation, and 

 Bradley's estimate of the aberration of the star y Draconis 

 as made before he knew what theory required, the coin- 

 cidence would have been found very much cleser. 



Here, then, we have a perfect proof of the earth's revo- 

 lution. No question can remain that the lesiou really 

 taught us by the stars as they annually traverse their 

 aberration ellipses is this, that the earth annually tiaversses 

 a nearly circular path round the sun. This interpretation 

 accounts for all the peculiarities of the stellar aberration 

 motions; nay, the theory of the earth's motion requires 

 every one of those peculiarities. No other theory ha? ever 



