472 Prof. L. Natanson on Double-Refraction 



Among these components, the only one which we shall 

 have to consider is y* qr . For calculating its value we use 

 the well-known equation 



y* =. 2e*cos (#!#) cos [y x x) + 20* cos (##) cos (y-y) + 2ip cos (a?^) cos [y x z) 



-f a*{cos (%$) cos (y t s) + cos (y^) cos (a^s) 



+ ^8*{cos (a?!-?) cos (yia?)+ cos (y ± z) cos (a?^)} 



+ y*{cos (a?!*?) cos {y^y) + cos (y^) cos (a?^)}. . . (3) 



I£ in this equation we put, in accordance with what has 

 been said above, 



cos (w\x) = ± sin ; cos {yyv) = cos © ; cos (#ia?) = 0; (^ a ) 



cos (a?j^) = + cos ; cos (jy x y) = sin ; cos (2,3/) =0; (4 5) 



cos (a?!*) = ; cos (y x z) = ; cos faz) = 1, (4 c) 

 then it takes the form 



7<2* = ±2(e*-<£*) sin cos + y*(sin 2 0-cos 2 0). (5) 



§ 4. The components of the actual deformation are capable 

 of being expressed in terms of the components of the velocity 

 of apparent deformation. We have, in fact, 



e* -$&* = *:*-*/* + e-W$dt€ l / T (e-- : |a>); • - (1) 



^*_.iA^ = ^e-^ + e-^j^6^ T (/-io>); . . (2) 



ry* = k a2/ 6-V T + e-^]dt6V T c, .... (3) 



where k xx , k yyj k xy denote three constants, e the base of the 

 naperian logarithms, T the time of relaxation, &> the sum 

 e-t-f-\-a, A* the sum e* -f 0* + ^r*. These equations may 

 be established by the aid of considerations contained in our 

 previous communication. Compared with the equations 



/l«-l>o=-M^-iA*)--*A*, • • . (4) 



PM-po=-M<l>*-i&*)-kA*,. • • (5) 



Pzy=-ny*, (6) 



and 



p-p =-kA*, ...... (7) 



which express the generalization of Hookers law (as explained 

 in the memoir referred to), they lead directly, in the case 

 where it is permissible to put li=k > to equations (9) and (10), 

 § 8 of the previous memoir. 



In equations (1), (2), (3), let us neglect the terms which 

 contain k XX} k yyi and k^; then, using these equations along 



