in Moving Viscous Liquids. 473 



with equation (5) of the preceding paragraph, we find 

 y* = ± 2 sin © cos 6 -'/ T §dt &*{e—f) 



± (sin 2 - cos 2 ©) e-^ J dt e'/ T c ... (8) 



§ 5. Using equations (3), (4), (5) of § 2, as well as (3) of 

 § 1, the preceding equation (8) may be written, after some 

 transformation, 



y* = | (sin 2 0-.cos' 2 0)e-^j ^e^' T (sin 2 /^-cos 2 ^0 



+ 4sin0cos©e-^ T j^e^ T sin/^cos^^ ||^2_£.l (1) 



The integrals entering into this expression are easily 

 calculated. We find finally 



^=tt^(£-:) ® 



Let the liquid be traversed by a ray of light whose 

 direction is parallel to the axis of rotation. The double 

 refraction produced, referred to unit length, is, according to 

 F. E. Neumann's theory, proportional to the value of the 

 corresponding component y*^ of the actual deformation. 

 Thus the observable optical effect will in the first place 

 depend on the kinematical conditions of the experiment, such 

 as the velocity of rotation, the nature of the function q{r), 

 &c. In the second place, it will vary with the duration, for 

 the liquid in question, of the time of relaxation T. It will 

 finally depend on a purely optical coefficient ; but it would 

 be difficult, if not impossible, to advance any definite con- 

 clusions as to the nature and exact value of this coefficient. 

 Even if it were supposed that its value does not differ greatly 

 for different liquids (certain very special cases being ex- 

 cepted), the only conclusion which one could arrive at is the 

 one already pointed out by Maxwell, viz. : the double refrac- 

 tion observed in using different liquids under identical kine- 

 matical conditions, depends above all upon the time of 

 relaxation T of the liquid. Now the viscosity of a liquid 

 does not depend solely on the value of T ; it is equally de- 

 pendent on the value of an entirely different constant, the 

 momentary rigidity of the substance. To sum up, there is 

 nothing to justify the assumption that accidental double 

 refraction in a liquid depends solely on its viscosity. 



§ 6. Equation (2) of the preceding paragraph contains the 

 term 



dr r' {L 



