INTENSITY OF ORDINARY AND EXTRAORDINARY RAYS. 411 
in which A’ and C’/ form new constants. The refracted vibra- 
tion must satisfy the differential equations of the second me- 
dium, which differ from those in (1.) in the value of a, which I 
shall call a’; it is parallel with x and forms the angle 9/ with y. 
If we express its vibrations by w’, v” and w”, and call A’? = a’ T? 
the length of its undulations, we have 
u”’ =— A” sin $’sin = 8G PONY *) Qa 
rv A 
v’ = A’'cos 9’sin S| ase = ak = 2a (7:) 
eh af ase 
wo! = C” sin (see ane T 2 x. J 
A’, C’ and A”, C”, i.e. the amplitudes of the reflected and re- 
fracted waves, are estimated from the amplitudes of the incident 
waves A and C. Thus, my principles are,—1, that the motions 
which the particles experience at the borders of the two media, 
i.e. 2 = 0, are similar to the two waves of the first medium in 
direction and in the amplitude of the motions which they ob- 
tain from the waves of the second medium; 2nd, that the active 
power of the incident waves is equal to the sum of the active 
powers in the reflected and refracted waves; 3rd, that the ether 
possesses the same density in both media. Now the quadratic 
equation between the magnitudes A, A’, A”, C, C’, C’, which 
the principle of obtaining the active forces yields, may always 
be replaced by a linear one, as shown by caleulation, and in un- 
crystalline media, it is this which expresses that the pressure on 
the refracting surface, which takes place from the dislocation of 
the portions in the first medium, contains the same component 
perpendicular to the plane of incidence, but the pressure which 
is produced by the dislocation in the second medium, i. e. the 
equation of the active force, may here be replaced by 
dw dw’ ,dw”’ 7 
tdi tae. 2 ae 
ad _ sin?¢’ b 
or because a Site ve 2) (S.) 
dw.., OW ei ee 
> Nea $+ ae = ne 
We thus immediately ascertain the motion from the equality 
of the components : 
sin? $’. 
2a@2 
