AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
327 
components of the magnetic force due to the assumed distribution are 
Cty 0 , 
^0 = ^ 
yo 
= _2-V2eV.-^‘g‘-<(v?+y) 
and therefore the principal parts of the components of the magnetic force at the point 
P are 
a = 0, ^ = 0, y = (/u, 
J — X 
for ^0 is of order compared with the magnetic force in the incident waves. 
When p is small compared with a. 
0 
e '""’r 
■^1 dpi d4i = d e 
Ja Jo 
^LKCl + tKppp/ ^ COS (<^»J — </>) — 
Pi dpi dfj)!, 
that is, the principal part only being retained, 
c/S = 27rd~^e"‘^ j" (/cppi/d) pi c/pi. 
e "‘h’ ^ 
or 
^ dS = 277 {lk) ^e"'^ — 27rd e (K-ppi/d) pi dpi. 
Therefore, when p is small, the principal parts of the components of the magnetic 
force at a point near the axis of y on the negative side of the screen are given by 
a = 0, 
/3 = r (KpRi/d) pi^ dp„ 
' 0 
y = (Kppifd) Pi dpi. 
Jo 
As an example illustrating the phenomenon of the bright spot, the case of a 
conducting circular disc of radius a with a Hertzian oscillator on the axis will be 
treated. Let the axis of the disc be the axis of 2 , the origin being at the oscillator 
and the equation of the plane of the disc 2 = 2 ^ ; the components of the magnetic 
force due to the oscillator are 
a = 
K 0 
y' = o. 
V dr] 7\ ’ V 0^ ?’i 
where rj, C are the co-ordinates of any point and 
