AN OBSTACLE ON A TKAIN OF ELECTRIC WAVES. 
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have been obtained by observing that when the limits of the integral can be taken 
infinite the effect is the same as if the surface on which this distribution of electric 
and magnetic currents is placed surrounded the source and therefore at a point inside 
this surface the effect of the distribution is zero and at a point outside it equal and 
opposite to that of the source. 
When the point P is inside the boundary of the geometrical shadow and so near to 
it that the limits of integration cannot be taken to be infinite the values of X, Y, Z 
as in the case of the conducting surface are given by 
X = -(l-L)X', Y = -(l-L)Y', Z = -(l-L)Z', 
where 
L = j” 
and 
where the letters have the same signification as in the case of the conducting surface. 
Hence, at points inside the boundary of the geometrical shadow, the components of 
the electric force are 
LX', LY', LZ', 
where X', Y', Z' are the components of the electric force at the point due to the 
oscillator when there is no obstacle, and the components of the magnetic force are 
La', L^', Ly', 
where a', y are the components of the magnetic force due to the oscillator. In 
this case these values of the components of the magnetic and electric forces are valid 
up to the boundary of the obstacle, therefore the principal parts of the components of 
the magnetic and electric forces at a point P inside the boundary of the geometrical 
shadow are the same whether the obstacle is perfectly conducting or perfectly 
absorbing, provided the point P is at a distance from the surface of the obstacle 
measured along OP of a higher order than p [kpY^'^, where p is the radius of curvature 
of the section of the surface through the tangent in the plane of incidence, and the 
value of the principal part of the magnetic force tangential to the surface of the 
obstacle at a point on it inside the boundary of the geometrical shadow when the 
obstacle is perfectly conducting is double the value it has when the obstacle is 
perfectly absorbing; the value of the principal part of the component of the electric 
force normal to the surface of the obstacle at a point inside the boundary of the 
geometrical shadow when the obstacle is perfectly conducting is also double the value 
it has when the obstacle is perfectly absorbing. 
When the point P is near to the boundary of the geometrical shadow and outside 
