COLORS IN PERFECTLY TRANSPARENT MEDIA. 191 



infinitesimal variation in the type of a vibration, due to a constraint, 

 will not affect the period. If we first consider a certain system of 

 stationary waves, then a system in which the wave-length is greater 

 by an infinitesimal dl (the direction of oscillation remaining the same), 

 the period will be increased by an infinitesimal dp, and the manner in 

 which the flux distributes itself among the molecules and intermole- 

 cular spaces will presumably be infinitesimally changed. But if we 

 suppose that in the second system of waves there is applied a con- 

 straint compelling the flux to distribute itself in the same way among 

 the molecules and intermolecular spaces as in the first system (so that 

 ', rf, f ' shall be the same functions as before of r\ y f, a supposition 

 perfectly compatible with the fact that the values of r\, f are 

 changed), this constraint, according to the principle cited, will not 

 affect the period of oscillation. Our equations will apply to such a 

 constrained type of oscillation, and A, B, etc., and A', B', etc., and 

 therefore H and H', will have the same values in the last described 

 system of waves as in the first system, although the wave-length and 

 the period have been varied. Therefore, in differentiating equation 

 (18), which is essentially an equation between I and p, or its equivalent 

 (19), we may treat H and H' as constant. This gives 



2 



_ 

 ~n*d\~ X 3 



We thus obtain the values of H' and H 



, X 3 dn 27r& 2 2-7r& 3 X dn 



By determining the values of H and H' for different directions of 

 oscillation, we may determine the values of A, B, etc., and A', B', etc. 



By means of these equations, the ratios of the statical energy (S), 

 the kinetic energy due to the regular part of the flux (T), and the 

 kinetic energy due to the irregular part of the flux (T'), are easily 

 obtained in a form which admits of experimental determination. 

 Equations (8) and (9) give 



Therefore, by (20), 



~W~ = "~ dX = ~dl^~X' 



_ 

 h ~' 



m 



T~ T dlogX ~dlog\ 



T dlogn 

 - - 



