160 REPORT—1885. 
This fanction is then expanded in the form 
=P thi thot. --- 
$v, &e., being homogeneous functions of the orders 0, 1, 2 of the small 
quantities s), sy, &e. 
The equations of motion depend on 6¢, and so, $9 being constant, it 
does not appear. If the medium in its equilibrium position is unstrained 
@, vanishes also, and in general ¢, contains twenty-one arbitrary coeffi- 
cients. 3 may be neglected compared with ¢,. If the medium be not 
initially free from strain, ¢, will introduce six more coefficients, so that 
finally we find the most general form of # for our purposes involves 
twenty-seven coefficients.’ 
Green then supposes the medium to be symmetrical with regard to 
three rectangular planes, and obtains finally as the form for ¢, taking the 
case in which the medium is initially strained, the valuae— 
du dv dw 
— 26 = 2A—— + 2B — + 2C - 
? da es dy ze dz 
du? dvu\? dw? 
+ a(y+ +} 
da de da 
An 2 Iy\ 2 2 
ee he) Gad 
du\? dv\? dw? 
ee eee ay t 
+ 0 (H+ m (241 (3) 
dx dy dz 
4 2P du dw + 2Q du dw 49 du dv 
dy dz de dz da dy 
dv dw? du , dw? du , dv? 
1D py hoe ae Mi oa NG see 
cs G . i) T G * 7) “ihe he % z) (1) 
If the medium be initially unstrained A=B=C=(0, while, further, if 
it be completely isotropic, 
G=H=I1=2N+R 
L=M=N (2) 
Petes 
And introducing two new constants, A and B, 
du dv dw? 
Suis, SSN chi ous Ser \ 
Pe (Ss dy ot dz ] 
du dv\? du dw? dv dw\? 
B ade Wi ade Eat) 2 SOS hs 
‘3 Ge + 7.) iy Gr a a) i (= t a 
dv dw dwdu , du dv 
~~ \dy dz eda Sas as 2 y ttl cara 
1 For the difference between this and Cauchy’s theory see Prof. Stokes’s report. 
