ON OPTICAL THEORIES. 221 
(1) X’, arising from external impressed forces ; 
(2) X, arising from the action of the other ether particles external to- 
the element ¢v ; 
(3) A, arising from the action of the matter. 
While for p, the matter particle, they are :— 
(1) 2’, arising from external impressed forces ; 
(2) &, arising from the action of the matter external to the element ; 
(3) A, arising from the direct action of the ether. 
So that the equations of motion for an isotropic medium are— 
(i er : } 
n apt X’ + X +A, ete. | 
P (19) 
mie = felt + cH + A, ete. | 
| 
J 
Tn all three theories the impressed forces are supposed to vanish, so that 
XxX’ = &'=0. The action between the matter and ether is supposed to 
be confined to the element of volume considered—7.e. the dimensions of the 
element are treated as large compared with the distance at which the 
direct action of an ether particle on a matter particle is sensible. 
This leads to the relation! A + A= 0, independently of the value 
of A. 
The term X springs from the ordinary elastic reaction of the ether. 
Helmholtz and Lommel, considering only a wave of displacement in the 
direction of x travelling parallel to z, write for this term 
9 du 
dz® 
while Voigt considers the general forms of the expression given by the 
ordinary elastic solid theory, which, of course, reduces for the case of an 
isotropic medium to 
ev*ut+ ge, 
dz 
where 
_ du ,dv , dw 
de dy dz 
Lov) 
For the forces represented by =, Voigt again considers the general 
case of a strained elastic solid, while Helmholtz and Lommel after him 
write 
9 dU 
dt * 
For the proper values to be given to A and A there is great divergence 
of opinion shown in the three theories. 
— 
Z=—aU-—y 
1 In his paper Lommel—as has been pointed out by;Ketteler, ‘ Optische Contro- 
rersen,’ Wied. Ann. t. xviii. p. 387, and Voigt, ‘Bemerkungen zu Herrn Lommel’s 
Theorie des Lichtes,’ Wied. Ann. t. xvii. p. 468—really employs the condition A —A=0, 
for he estimates ~ and U in opposite directions. In his reply, Wied. Ann. t. xix. 
p. 908, Lommel endeavours to justify the signs used, but I think withoutsuccess. The: 
effect will be to change the sign of a coefficient in one of the terms. 
