AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
301 
into account may include waves due to the obstacle in addition to the waves due to 
the external oscillator. The electric and magnetic current distributions to be assumed 
on the surface of the obstacle are then the same at each point of the surface as if that 
point were on an infinite plane surface coinciding with the tangent plane to the 
surface of the obstacle at the point, and the principal parts of X, Y, Z, a, y8, y at any 
point X, y, z determined on this assumption are the leading terms in the asymptotic 
expressions for these quantities. 
A Perfectly Conducting Obstacle. 
When the obstacle is a perfect conductor the condition to be satisfied at the surface 
is that the electric force tangential to the surface vanishes; it follows from the above 
tliat the principal part of the effect of the obstacle is obtained by assuming an electric 
current distribution on the parts of the surface on which waves are incident which is 
double the electric current distribution that would produce the magnetic force 
tangential to the surface in the incident waves, a zero electric current distribution on 
the parts of the surface on which no waves are incident, and a zero magnetic current 
distribution on all parts of the surface. 
Taking first the case where the perfectly conducting obstacle is a convex solid, the 
waves incident on any part of the surface are due to the oscillator outside it, and, if 
M is the electric current distribution at any point on the surface which would produce 
the magnetic force tangential to the surface in the incident waves, the electric current 
distribution to be assumed at this point is 2M, if the point is on the part of the 
surface of the obstacle next the oscillator, and zero if it is on the part of the surface 
remote from the oscillator. 
Let the origin of the co-ordinates be at the point 0, the axis of the oscillator being 
the axis of 2 . The components of the magnetic force (a', y) at the point y, Q 
due to the oscillator are given by 
where 
a = 
K d 
V dy Ti 
K a e-Ai-n) 
r. 
If i, m, n are the direction cosines of the outward drawn normal to the surface at 
the point (^, y, {) on it, the components of the electric current distribution M which 
would produce the magnetic force tangential to the surface are 
my—n(3', nctf—ly, IjB' — ma', 
and the above hypothesis is equivalent to assuming an electric current distribution on 
the parts of the surface on which waves are incident whose components are 
2 {my'—n/S'), 
2 igW—ly'), 
