AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
319 
the magnetic force at P due to the electric current distribution necessary to balance 
the unbalanced tangential electric force in the neighbourhood of the curve of contact 
of the tangent cone are, compared with the components of the magnetic force at P 
due to the oscillator, of the order 
K = 
LK 
27rR 
where L varies from point to point of the surface.* 
The integration with respect to t] can be effected and it follows that 
K = 
LK / LK 
27rR \2R 
-V-i 
Let denote the perpendicular from E, on OP, ^ the perpendicular from a point Pj 
on the surface on OP, then 
L = 2“*''" i* du, 
J Uq 
where 
— 
2 
\PMi 
RMi = 
X(2p)'/^ J ’ 
in which p denotes the radius of curvature of the normal section of the surface 
through OR, hence 
Therefore K is at most of the order 
2 R/ ^ 
if 
LK 
2R 16(2p^iy'^ 
Slk'v^ 
+ 
L2R 16(2p^i)'^0 
^1 
is of the same or higher order than unity, that is, provided R is of the same or higher 
order than {p^if^^ if k^-^i is of the same or higher order than (p^i)'^*, that is, if is of 
the san“ie or higher order than p [Kp)~\ Hence, when R is of the same or higher 
order than {p^df'-, and is of the same or higher order than p {Kp)~"\ the quantity K 
is at most of the order 
which is at most of the order for K^d''^ is of the same or higher order than 
* To simplify the analysis Ri is taken infinite as the result is not affected provided the oscillator is at a 
distance from the surface of the obstacle comparable with a wavedength. 
