ON OPTICAL THEORIES. 205 
Réthy ! developed a theory which covers Fréhlich’s experiments, and 
arrived at a formula with which they agree closely, but his fundamental 
principles are at fault. 
In his solution Réthy adopts a method given by Kirchhoff to find the 
effects of a given source of light. 
The equations to be solved are, if we neglect the terms involving 
dilatation, 
du wu 
TE ae ONT AE, 
etc., with the condition 
du dv dw 
ak dy aN 0. 
Take " 
; r t 
= sin Qn fy—m teh F : . (86) 
Then ® and its differential coefficients satisfy the equations of motion, 
and we require to find such solutions as will satisfy the equation of 
continuity. 
Réthy takes as solutions— 
db d® 
1 Hei, oI anv Mirafo 0 wsivay igay, AE) 
and 
- Bs d?® ~ d?® eg io d?® 
° U =~ dedy C= dydz Sg Naga Typ a - (88) 
The distance r, of course, is measured from a point on the grating to 
the point at which the motion is being considered. 
Now each of these expressions of course represents the solution due 
to some arbitrary motion set up somehow over the grating. In Case I. 
the motion is a periodic twist of each element about the axis of z, while 
in Case II. it is an oscillation parallel to that axis. But Réthy does not 
show how this motion is to be set up, nor whether it can represent the 
effect of a train of plane waves falling on the grating and there diffracted ; 
and a little consideration shows that it cannot, for, according to the 
ordinary assumed properties of the ether, we cannot get the wave of 
twist only without linear displacement ; the second solution corresponds 
to that due to the action of a periodic force at the origin generating a 
certain amount of momentum, and not to the complete effect of a train 
of waves. If we compare it with Stokes’s solution, we see that it is that 
part which arises from the effects of the velocity propagated across the 
element, and omits the part due to the displacement. Stokes’s solution 
applies to the case in which energy is being propagated by waves passing 
across the orifice into the medium beyond, and depends on the direction of 
motion of these main waves. Réthy’s solution is that which arises from 
a centre of vibration situated on the surface, kept in motion by some 
external force and sending out waves in all directions into the medium. 
Still, we can arrive at a formula of the same nature as that given by 
Réthy, and which does agree with Fréhlich’s experiments, by means of a 
simple extension of Stokes’s principles. This consists in supposing that 
1 Réthy, Wied, Ann, t. xi. p. 504. 
