Propagation of Waves i7i a Resisted Fluid. 333 



will be -T-, where k is given by the equation 



.A.^=«{x/frr|77(|f.(..^)}. 



Also the amplitude of vibration will decrease as the wave ad- 

 vances, the proportional rate of decrease being h, where h is 

 given by the equation 



. . N T 



The quantities — and — are unknown, but they can vary 



only with n and the amplitude of vibration. Experiment 

 shows that in ordinary cases, where the light is of moderate 

 intensity, the velocity of propagation does not sensibly depend 

 upon the intensity*, and therefore we may conclude, from the 



N T 

 above expression for ^, that — and — do not sensibly depend 



upon the amplitude, and consequently vary only with w, when 

 the light is not intense. 



I'i. The application of these results to the general explana- 

 tion of the dispersion and absorption of light is obvious ; they 

 show that the velocity of propagation depends upon the co- 

 lour, that light is weakened or absorbed in passing through 

 transparent substances, and that the degree of absorption is 

 different for different colours. 



15. It is worth remarking, that the absorption is produced 

 by the tangential resistance (T), for if we put T = we find 

 A = 0. If, on the other hand, we suppose the normal resist- 

 ance (N) to be zero, the above formulae for h and Jc are not 

 materially altered ; the existence of a normal resistance is not 

 therefore in any way necessary to the explanation here given 

 of dispersion and absorption. 



16. So far we have assumed nothing respecting the resist- 

 ances exercised by the particles of matter upon the aethereal 

 fluid beyond the existence of such forces; we shall now exa- 

 mine what consequences result from the supposition that the 

 resistances do not sensibly interfere with the principle of the 

 superposition of small motions. 



The first consequence that obviously presents itself is this, 



* The difficulty of observing the exact positions of the fringes of diffrac- 

 tion formed by strong light of varying intensity, seems to show that the ve* 

 locity of propagation may depend in some degree upon the intensity. 



