Rev. J. Challis on the Aberration of l^ght. 93 



rection of the object, and the required condition is satisfied 

 by the undulatory theory of light. 



I admit the correctness of Mr. Stokes's strictures on that 

 part of my communication to which he principally objects. 

 Mr. Stokes's own reasoning in the July number, or the fol- 

 lowing, may be substituted for the part objected to. The 

 point a is carried with the velocity V— w, and the point b with 

 the velocity V— w/, in the direction of the axis of z. As w is 

 less than w, a is carried further than b in the small time $t, 



(1 IS) 



by (V-w)$t-(V-w')dt, that is, by (a/— w)8/, or — 8*8*. 



Dividing by 8#, the interval between a and b, the angular dis- 



d w 

 placement of the front of the wave in the plane of z x is — 8 /, 



(J *153 2! Z 



which is equal to -y-. -^j, since V = j- very nearly. To in- 



, . ... . dw du 



tegrate this expression, it is necessary to assume that -j— = -j- . 



So considering the motion in the plane z y, the integration re- 

 quires that -r- = -r~. These conditions, which are alluded to 



' dy d z 



above, I agreed with Mr. Stokes that it was necessary the 

 motion of the aether should satisfy. I went a step further, and 

 endeavoured to show that they do not restrict the motion. 

 The reasoning for this purpose was based on hydrodynamical 

 equations, in which the squares of the velocities were neg- 

 lected. This may generally be done when the motion is 



small. But obviously all cases of motion for which ~r~. — , 



J dt dt 



and -j- vanish are to be excepted, and the instance before us 



may be one of this class ; for the motion must be nearly sym- 

 metrical about the line in which the earth's centre moves, and 

 if the earth's centre be taken for origin of co-ordinates, the 

 velocity must be very approximately a function of co-ordi- 

 nates independent of the time. On this account I doubt the 

 applicability of those equations, and in the present state of 

 our knowledge of the subject, it seems the best course simply 

 to suppose the motion of the tether to be such as to satisfy the 



... dw du , dw dv m, . . . 



two conditions -r- = -p- and -. — = -=—. lliere is nothing 

 dx dz dy dz n 



improbable in the supposition : it saves the undulatory theory; 



but I must protest against its being considered necessary for 



the explanation of the aberration of light. 



Cambridge Observatory, January 8, 1846. 



