AS EXPLAINED BY THE HYPOTHESIS OF FINITE INTERVALS. 165 



. „ "TOO 



= 22 {d>{r) + ^-^ Sx'} ——±- . 



The first remark suggested by this equation is, that when the dist- 

 ance between the particles is exceedingly small, the values of Sp for 



which 2 ((pr + Sar) will have a sensible magnitude, must be incon- 

 siderable: if they are so small that ( — ^j may be neglected, we shall have 



which coincides with that obtained from equation (2), and the velo- 

 city is independent of the length of the wave. 



If this reasoning do not appear entirely conclusive, I shall in the 

 sequel offer another argument to shew that, assuming the velocity in- 

 dependent of the length of the wave, the particles of aether (by which 

 name we designate the medium of light) are nearer each other than 

 in dispersive media. 



Now it is a well known fact, that the direction in which a star 

 appears to the eye is that of the diagonal of a parallelogram whose 

 sides represent in magnitude and direction the velocity of the Earth 

 and of light. It is manifest then that if the velocity of light in vacuo 

 varied considerably by the variation of the colour, a star would be 

 stretched out into a spectrum and not appear a point as it actually 

 does. This is one of the old objections to the theory, but it is imme- 

 diately removed by the considerations above, introducing, however, as 

 a necessary consequence, the condition that the particles of aether are 

 very much nearer to each other m vacuo than in refracting media, and 

 of course the density greater. 



With respect to the velocity of transmission in this case, the second 

 factor of v' is clearly a maximum, and as the function cp {?•) is doubtless 



