322 Rev. J. Challis on the Abei-ration of Light. 



direction siioe?. But at this instant the object "do is at tsd (ww' 

 being taken equal and parallel to e^), and the directions of 

 the objects from ^ are really separated by the angle se'w'. 



Let us now consider two objects which both partake of the 

 earth's motion, and let p, w^ and e, be simultaneous positions 

 of the objects and the spectator's eye in the same straight 

 line. Draw pp' and w^ te/ parallel and equal to e^e', and join 

 elis^j^. Then, since w^'ro is to wp in the ratio of the earth's 

 velocity to the velocity of light, it follows that the object at w, 

 and the light which started from p in the direction pw when 

 the eye was at e^, arrive at w at the same instant. Hence the 

 eye at e' receives at the same time light from p and w coming 

 in the common direction pwe', and consequently sees the two 

 objects in the same direction when they are really at p' and 

 w', and therefore really in the same direction from e'. 



It thus appears to be a necessary consequence of the earth's 

 motion and the temporaneous and rectilinear transmission of 

 light, without making any hypothesis about the nature of light 

 or the manner in which the eye receives impressions, that the 

 directions of two objects, one of which partakes of the earth's 

 motion and the other is fixed in space, are separated by a cer- 

 tain angle when they appear to [)e coincident, while two ob- 

 jects, both of which partake of the earth's motion, are really 

 in the same direction when they are seen in the same direc- 

 tion. The angle of separation, it is plain from the figure, is 

 equal to the ratio of the earth's velocity to the velocity of 

 light, multiplied by the sine of the angle which the direction 

 of the earth's motion makes with that in which the light comes. 

 This result is a complete explanation of the phaenomenon of 

 aberration, if only the following remark be added, which, as 

 far as I am aware, has not been before made with reference 

 to this subject. The visual direction of a celestial object is 

 necessarily referred to the visual direction of an object which 

 partakes of the earth's motion, and astronomical observation 

 has discovered that these directions are relatively affected by 

 aberration, but does not determine whether the star or the 

 wire of the telescope is seen out of its true place. We are 

 therefore at liberty to suppose, as the foregoing theory re- 

 quires, that the apparent place of the wire is affected by aber- 

 ration. It is clear that observations of terrestrial objects 

 alone could not detect aberration (its maximum amount being 

 very small), simply for the reason that two objects partaking 

 of the earth's motion are really in the same direction when 

 they appear to be so, though they may not be seen in their 

 true direction. On this account geodetical observations are 

 unaffected by the aberration of light. 



