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X. The Efect j^rodiiced hy an Obstacle on a Train of Electric Waves. 
By Prof. H. M. Macdonald, F.P.S., U^iiversity of Aberdeen. 
Received June 21,—Read June 27, 1912. 
Integrals of the equations of propagation of electric disturbances in terms of the 
electric and magnetic forces tangential to any surface enclosing the sources of the 
disturbances have been already obtained.* It is proposed in what follows to apply 
these expressions to obtain the effect of an obstacle on a train of electric waves. The 
effect of the obstacle can be represented hy a distribution of sources throughout the 
space occupied by the obstacle, and the determination of this distribution or, as 
appears from the investigation referred to above, the determination of the electric 
and magnetic forces tangential to the surface of the obstacle due to this distribution 
of sources, constitutes the solution of the problem. If X', Y', Z', a', y denote the 
components of the electric and magnetic forces respectively at the point 77 , ^ on the 
surface of the obstacle due to the distribution of sources inside it which represents its 
effect, X'l, Y'l, Z'j, aY d>\-> y'l denote the values of these quantities when t — rfY is 
substituted for t, where V is the velocity of propagation of the disturbances, and 
r= {(x—^y+[y—r]y+[z — QW^ is the distance of any point x, y, z from the point 
7], C, and I, m, n are the direction cosines of the normal to the surface at the point 
y, ^ drawn into the space external to the obstacle, the components of the magnetic 
force at any point outside the obstacle due to the obstacle are given by 
a 
Alff 
a y 
d (T 
[ 0 ^ x^ a^ Y_^ a^ z_ 1 a^x] 
An dt J J 
[dy r 
dz r_ 
An J J 
_d.P r dxdy r dxdz r V ^ dd r _ 
_L1 
An dt 
a a d y 
f/S-— [[ 
■ a^ X 0' Y 0' z 1 0 ^ Y" 
dz r dx r_ 
An J J 
dxdy r dy‘‘ r dydz r dd r_ 
_L1 
4n dt 
An 
~ 3^ X Y 3^ Z 
_dxdz r dydz r r 
1 z^ 
de r 
(/S, 
* Macdonald, “Electric Waves,” 1902, pp. 16-17, ‘Proc. Lond. Math. Soc.,’ 1911. 
VOL. CCXII.- A 493. 2 Q 2 Published separately, Noyember 13, 1912. 
