Maxwell's Theory of Light. 291 



Let V. be the velocity of propagation of light in the dielec- 

 tric when at rest. The equation 



V \dx 2 df + cW~ dt 2 T VTite +g dy ^ dzJdt 

 reduces in this case to 



dx 2 dt 2 ^ dxdt 



Let the solution of this equation be/= A cos (qt—px); sub- 

 stituting in the equation, we get 



Y 2 p 2 z=q 2 — upq; 



u%- = Y 2 ; 

 P 



■•©' _ 



Taking the upper sign (corresponding to a wave propagated 

 in the positive direction of x), we have 



= ^ + V, approximately. 



Now — is the velocity of propagation of light in the medium; 



hence we see that the velocity of the light is increased by one 

 half the velocity of the dielectric. This result is confirmed in 

 a very remarkable way by some experiments made by Fizeau, 

 and of which an account is published in the Comptes JRendus, 

 t. xxxiii. He found the difference in the velocity of light pass- 

 ing through a tube filled with water when the water in the 

 tube was still and when it was moving; he was able to do this 

 very accurately by measuring the displacement produced in 

 some interference-fringes ; and he found that the velocity of 

 light was increased by half the velocity of the water. 



When the dielectric does not move uniformly as a rigid 

 body without rotation, the differential equations to find the 

 electric and magnetic displacements are no longer the same. 



