AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
321 
to 0 which balances the unbalanced tangential electric force there, due to the 
oscillator and the assumed surface distribution, is of lower order tlian that due to the 
oscillator. Further, if M is the actual magnetic force at P tangential to the surface, 
the magnetic force at P due to the distribution in the neighljourhood of P is 
tangential to the surface ; now it lias been shown that the magnetic force tangential 
to the surface at P, due to the oscillator and the assumed surface distribution, is LM', 
where M' is the tangential magnetic force due to the oscillator alone and L has the 
value previously determined, therefore 
M = pi + LM', that is, M = 2LM'. 
Hence, at points P inside the tangent cone on the side of the surface remote from 
0, the principal part of the magnetic force tangential to the surface is 2L]VP, and the 
principal part of the electric force perpendicular to the surface is 2LE', where M', E' 
are the principal parts of the magnetic force tangential to the surface and of the 
electric force perpendicular to the surface due to the oscillator. Similarly at points 
on the surface on the side nearest to the oscillator the principal part of the tangential 
magnetic force is 2(1—L) M', and the principal part of the electric force perpendicular 
to the surface is 2 (1 — L) E'. 
The preceding analysis can be adapted to the case of a conducting screen when the 
radii of curvature of the screen are large compared with the wave-length of the 
oscillations. The same assumed distribution as above on the two surfaces of the 
screen, viz., double the electric current distribution that would produce the magnetic 
force tangential to the screen on the side on which the waves are incident and a zero 
electric current distribution on the other side, give the important part of the 
asymptotic solution of the problem. The analysis only differs from the j)receding 
owing to the presence of edges, and it will be proved that the effect of the actual 
distribution at the edge differs from that due to the oscillator and the assumed 
distribution by a quantity of lower order than the corresponding component in the 
waves due to the oscillator. At an edge the radius of curvature is zero, and therefore 
the distribution in the neighbourhood of the edge is the same as if the wave-length 
were indefinitely great; hence the electric current distribution in the immediate 
neighbourhood if the edge varies as where '}\ is the distance along the screen 
perpendicular to the edge, that is, the electric current distribution in the neighbour¬ 
hood of the edge is multiplied by a quantity of the order of the magnetic 
force in the incident waves. The effect of this distribution in the neighbourhood of 
the edge is of the order 
K' = K 
at a point P compared with the corresponding component in the waves due to the 
oscillator. Let Q be the point on the edge such that QP is at right angles to the 
VOL, CCXII.—A. 2 T 
