484 PROFESSOR C, NIVEN ON THE 

therefore 1 for (1+a)?.., whence we obtain 
2 2 2 
P + q + r =, 
V2 V2 V2 
e——2D,-a ©-—2p,-b * —_2D,—c 
nN 17 
an equation not unlike that occurring in the theory of double refraction. | 
It cannot be said that our investigations, so far at least, throw much light on 
the true cause of double refraction in strained glass beyond the fact that such 
glass is no longer isotropic. Nor, indeed, was it to be much expected, in our 
ignorance of the true nature of the luminiferous medium and the mode of its 
connection with terrestrial bodies. | 
§ 14. I add the calculation of the constants for the case of a substance wnder 
longitudinal stress F. 


Here e 0 @ 
a=(e—il)e, B=O—)e, 7 ==, V=Hi02 oO 
00A ‘fe 
TG EN 0 = (m — 2n)J, —n +n)’, . 
eVF=|(m — 2n)J, — nj e+ne, 
whence | (38k — 2n)e* + 2(8k + n) = 9k 
2__ 2 
tye a ) 
In the case of glass, for which we have, very nearly, 34 = 8n, we find 
eg N=a4, Ope ieee? eee 
which latter equation has only one real root, as might have been expected. 







On the Laws of Resolution of Forces and Stresses. 
§ 15. These investigations may be fitly terminated by some general considera-_ 
tions on the law of resolution of stresses, which has been proved in § 9 to apply 
to strains, and to what I have called quasi-strains. It would seem that physical 
magnitudes possessing direction divide themselves naturally into two classes, in 
one of which the law of resolution along rectangular axes is that of ordinary 
forces, and in the other that of elastic stresses. To each class pertains a series 
of divariants and invariants, and each possess groups of derived directed magni- 
tudes in some of which the law of resolution is that of their primitives, and in 
others the opposite law. We may term these shortly the law of forces and the 
law of stresses, and the corresponding groups force-groups and stress-groups 
respectively. 
