AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
323 
where 
p" = {x-a\y+if, 
therefore 
Z= — (27r)“h/c sin 
Jo - CO 
whence the principal part of Z is given by the principal part of Zq, where 
Zo = — (27r)“hK sin .'ll [ (tK:/ 2 p)“'- ^.K(vt+x,cosi,-p) . 
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now Xi cos .^ 1 —p is stationary when 
X = Xi—p cos .9^1, y z= ±p sin .9i, 
the upper sign corresponds to the case where P is on the positive side of the screen 
and the lower sign to the case where P is on the negative side of the screen. When 
P is on the negative side of the screen, let the line through P parallel to the 
direction of the waves cut the screen or the plane of the screen produced at the point 
Q (^ 1 ) 0), then, writing a?i = ^+^i and P for the distance QP, 
p^ = + 
:t\ cos dj —p = fi cos di —P—siiP di/Pt, 
and the principal part of Zq is given by 
— (27r)“^ {2ik 
that is, by 
p LK (Yi + a: C(»3 -9-1sin dj) 
where 
7^0 = 2''^ (XP)-’^ ^1 sin di, 
and therefore the electric force at a point on the negative side of the screen is 
given by. 
f-«0 
2 = + + 1 ^-\\^Tnu- 
J — CO 
When the point P is on the positive side of the screen, the principal part of the 
electric force due to the assumed distribution is found in the same way to be 
f oo 
• -!'o 
where tlie point Q (£i, 0) is the point where the line through P in the plane perpen¬ 
dicular to the edge making an angle tt —di, with the plane of the screen meets it and 
therefore the electric force at a point P on the positive side of the screen is given by 
r* 
2 — ^tK(^^+^cos 5,+ysiii5i)_ 2 ~V 2 + ysin ^,) j cl'U 
J - Ho 
2 T 2 
e (III, 
)’'Pi ’'-sindie 
IK (Vt —R + |’[ cos 5|) 
>/siKf2 Bin2 5i/H 
