Prof. Powell on the Theory of the Aberration of Light, 431 



" In what direction must a tube be held by a person in 

 rapid motion so as to catch at its bottom a drop of rain falling 

 vertically?" (See fig. 1.) The answer to this question, if put 

 into more geometrical language, would be simply the con- 

 struction of a parallelogram whose diagonal is the vertical di- 

 rection of the drop, and whose side and base are respectively 

 proportional to the velocities of the drop and the tube, which 

 consequently give its inclination ; and the drop which was at 

 the top of the tube at the beginning of the motion will be at the 

 bottom of it at the end. It is but to translate this into the 

 language of the actual case, to say that the light which comes 

 down the tube of the telescope in the time in which the earth 

 moves through the proportional space, will by composition of 

 motions in the same time come down the vertical or diagonal. 

 in which the light from the star comes directly, and with 

 which it will thus coincide. 



Clairaut, it is true, speaks explicitly only of the light from 

 the star; but the essential reference to the tube, which he ex- 

 pressly points out* as representing the direction of the tele- 

 scope, is surely equivalent to the consideration of the light 

 which comes along the telescope, or more precisely from its 

 wire, to the eye. And in Sir J. Herschel's description of 

 Clairaut's method t I conceive this is the interpretation im- 

 plied ; and hardly less distinctly* I think, in the same author's 

 account of aberration in his treatise on Light (§ 10), as well as 

 ih the more elaborate discussion of Professor WoodhouseJ. 

 Still that these writers fail in giving the idea its due promi- 

 nence and full import, by explicit and formal statements, and 

 the degree in which this affects the strict character of the in- 

 vestigation, will be best seen by a comparison with the pro-* 

 fessedly exact explanation as put forth by Prof. Challis. 



That explanation, in the form in which it was stated in the 

 course of the discussion referred to, was misunderstood ; but 

 it appeared to me that it readily admitted of being put under 

 a slightly different form, by which means the essential prin- 

 ciple (divested of all irrelevant and extraneous considerations 

 with which it had been sometimes mixed up) might be at once 

 rendered more perspicuous, and guarded against the possibility 

 of misconception. As the shortest mode of stating it so as 

 to obviate ail objections, I would propose the following: — 



1. Let / and e (see fig. 2) respectively be proportional to 

 the known velocities of light, and of the earth in its orbit; let 

 d be the diagonal of a parallelogram of which I and e are 



* Mem. Acad. Paris, 1737, p. 208. \ Astron. pp. 177, 178. 



+ Ibid. i. 253. 



