324 M. L. Lorenz on the Determination of the Direction 
becomes equal to nothing, then 
A?F= — ss con Fh 
dz dy 
dz 
aja FO hex | 
(6) 
dx? ' dy ' dz* | 
To the components w,, V,, W of the reflected wave we give the 
same values as to w,, ¥,, w,; Only it must be observed that in 
the first 2 is always negative, in the latter positive. 
Assuming now that 
TB ae 
[F]*-°=0 and =) =0, ». 2. (7) 
the truth of which will appear from what follows, we get by 
means of (1) for z=0, 
U+U, —U, =u —29,(wt, y, z)=0,> 
V+V, —¥, =V— 2p, (wt, y, z)=0, ~ + (8) 
W+ WoW, = W—2yx, (wt, y, z)=0; 
and by means of (2) for =O, 
avg ehh _ Oe oda yaaa 
dz dz 
d(v+vu,—v d 
eS. = 5 — yp (ut, y, 2a U, » (9) 
d(w+wo—w dw 
Aut aw) _ 9 vot,y, 2)=0. | 
All the conditions are hereby fulfilled, and the functions ¢, ¢,, 
a, &e. determined. The truth of equations (7) may now also 
be easily demonstrated. 
The problem of diffraction is therefore completely solved by 
equations (5), (6), (8), and (9). If-we now pass to the parti- 
cular case in which the incident waves lie in a plane, the compo- 
nents are determined by the following equations, 
u= £6, v=o, w=, 
where 
6= cos k(wi—ax —by — cz), 
a&+bn+cf=0, a?+?+c?=1. 
Since, moreover, we only require to determine the motion at 
a point at a considerable distance behind, the opening in the 
screen must be very great; and putting p for the distance of the 
