AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
325 
of z, and the straiglit line in the plane of the screen perpendicular to it the axis of .r, 
the same analysis shows that, when the electric force in the incident waves is parallel 
to the edges of the slit and is given by 
2 — giic(VJ+rcosa,+i/sin 3|) 
the electric force at a point P on the negative side of the screen is given by 
where 
2 — giK(V!+xcos5,+ysin 3|) 9 
J -i<0 
,-V2 
Ho = 2-’(XP) ‘'-(fo + fO 
^<1 = sin dj, 
and (^ 1 , 0) are the co-ordinates of the point Q where the straight line through P 
parallel to the direction of the incident waves cuts the plane of the screen. The 
electric force at a point P on the positive side of the screen is given by 
2 _ giK (Vt+jTCos 5,+y Bin ^,)_g i/c (V«+J cos sin 3i) _j_ giK (Vi+i-cos S,—y sin 3]) 9 - V-: g'A’’’i 
where u-^ are the same as above and fi, 0 are the co-ordinates of the point where 
the straight line through P in a plane perpendicular to the edges making an angle 
TT—di with the plane of the screen cuts the screen. 
When the magnetic force in the incident waves is parallel to the edges and is 
given by 
Y — ^ ^ 
the magnetic force at a point P on the negative side of the screen is given by 
y = g‘''(^^+^'cos3|+y sin 3|) 2 -V> g'A’Ti 
and at a point P on the positive side of the screen by 
y _ giK (Vt + z-cos^i+y sin 3,) _j_ giK(V<+xcos 3i—y sin 3j) giK(V! + rco 3 3,—y sin 3,) 9 -Va gVi du 
where in each case have the same meanings as in the corresponding case in the 
preceding. The discussion of these results is similar to that given by Gilbert* for 
an absorbing screen. 
The corresponding results for a plane conducting screen in which there is any 
number of parallel slits can be written down immediately, provided the breadth of 
the portion of the screen between every two consecutive slits is great compared with 
a wave-length ; when the number of conducting strips in the breadth of a wave-length 
is large the effect of the edges becomes the most important. 
* ‘ Memoires couronnes de I’Acad. de Bruxelles,’ t. xxxi., 29, 1863. 
