788 
MR. J. LARMOR OR A DYRAMICAL THEORY OF 
f{- 
^^1 
(It (It J 
h^n J- .V. 
\dz (hi) \ dx dy 
dr 
dt \dij d: 
(^^v\ , [dh^ 
+ \lh 
dm , ^3 ^ (d^V 
dx / ^ V dx 
d^ 
dU 
m]\dT=0. 
On integrating by parts so as to eliminate the difierential coefficients of the variation 
S (fj V’ 0> neglecting the terms relating to the limits of the time, this gives the 
integral with respect to time of the expression 
- f I f W - wb Sf + & - '^) h dr 
dy dz y ' V J '' ' ' V dy j 
+ ^{{mcdi — nh~g) S£ + {iicdf ~ IcVi) Br] + {Ih'^g — ma~f) S^] c7S 
_ [11 _ AiA 4- T 4. ± _ ‘IiV\ sA 
'■'-?) +V - 'it j + i i'ii - 'ir } 
J [f/^ \ dy 
cl_ 
dt 
+ 
{mc% - nh\j) 8^ + ~ {naj ~ lc'%) Srj + ^ {lh'^~g - mcC^f) SC ^ dS. 
(It 
ITence the equations of propagation of vibrations are of the type 
that is 
wnere 
_L 4. tL 
^ dt" dy dz dt \ dy dz 
= 0 , 
(l"C dcdC d&jb? 
f’.ip + 
<iy 
dz 
- 0 , 
(a,\ h,\ c.=) = {c( + , ?/= + 6'= A , 
dt 
dt 
Tims on the assumption that the principal axes of the dissipation function are the 
same as those of the optical elasticity, the equations of ^propagation in absorptive 
crystalline media dilfer from those of transparent media only by the principal indices 
assuming complex values. 
96. To determine how the absorption affects the interfacial conditions on which the 
solution of the problem of reflexion depends, let us transform the axes of co-ordinates 
so that the interface becomes the plane of yz, and (Z, m, ii) — (1, 0, 0). The potential 
energy function and the dissipation function will now be quadratic functions of the 
rotation and its velocity respectively, U and U' say, as in § 14; and we can now 
