322 M. L. Lorenz on the Determination of the Direction 
The change of the plane of polarization by diffraction conducts 
us by another road to the determination of the same question. 
Several years ago Mr. Stokes furnished a mathematical proof 
that the plane of polarization must be changed by diffraction. 
Doubts have, however, justly been entertained as to the accuracy 
of his conclusions, because he only succeeded in solving the 
problem of diffraction imperfectly ; and I have therefore sought 
the complete solution of the problem by other methods, which I 
have found particularly applicable in the theory of elasticity. 
When an undulation passes through an opening in a solid 
plane, waves proceed from the opening on both sides of the 
plane. The motion in the plane is not known, except inso- 
far as it is determined by the fact that the sum of the compo- 
nents of the incident and reflected waves are equal to the com- 
ponents of those transmitted, and that the normal and tangen- 
tial pressures on both sides of the plane of the opening are the 
same at every point. Let the components of the incident rays 
be denoted by w, v, and w; those of the transmitted rays by w,, 24, 
and w,; of the reflected by w,, vo, and w.; and let the plane. of 
‘coordinates 2, y, 2 coincide with the plane of the opening. 
The first condition gives, for x=0, 
U+Ug—Uy;=0, V+V,~—1,=0, wt+wo—w,=0; « (1) 
and by the help of these equations it may easily be deduced from 
the second condition for =O, that 
dictate th) 324) d(v+,—2) aU; d(w+We—W)) _ ¢, (2) 
dx dx dx : 
If the incident waves are waves of light, then 
du dv dw 
de a dy Ai a =0; 
and equations (1) and (2) may be satisfied by the supposition 
that 
RO Ds i Pal 
dx ° dy ' dz ” (3) 
du, . dv, . dwe ian dhe 
de dy a s2.Q); 
from which it is evident that no waves of condensation can be 
formed. 
The law of the motion is expressed by the differential equation 
a + & + a = i a (4) 
te ay ew ae eo 
which must satisfy all the components, where w expresses the 
