I’EOFESSOK A. E. H. EOYE ON THE INTEGRATION OF THE 
;,3 ,,5 
■'7/ 
7 
xz 
r~ 
7’" 
the magnetic displacement lias the form 
f + ^y 
rW 
wliere 
j(x + Yx)> -5(x + i:x)’ 
(25), 
(20), 
(27), 
and the electric displacement has tlie form 
-p,-3 ,.i j(X+eXy'+ -,.3cS X 
XJ/ 
- :n 3x + 3px + ;^x 
~ lA (^X + 0 X + ^,2 X 
(28). 
Tlie most important ^^ai't of the radiation due to a Hertzian vilirator appears to lie 
of this type."^ 
The functions (•/> and x, wliich figure in the expressions for the electric and magnetic 
disjilacements due to sources of the two types, will lie referred to as the “radiation 
functions ” for the sources. 
In the expressions here obtained the source is at the origin, and its axis is the 
axis of X ; the expressions for the displacements due to a source, of arliitrary position 
and direction, can be deduced as before. 
The Reciprocal Iheorcm. 
14. Let (a, r, «’) he a possible system of magnetic dis])lacements, and [f, g, h) the 
corresponding electric disjilacements, wliich are free from singularities in space 
hounded liy one or more closed surfaces, denoted collectively by 8. Then u, . . . are 
functions of .r, y, z, t, which, with their first and second differential coefficients, 
are finite and continuous throughout this space. Denoting differentiation with 
inspect to t by a dot, we observe that the eipiations of motion might he obtained by 
transforming tlie variation of the Action functionf 
f<ft f||{/r + + «v5 _ + >f + lr)}dT 
* IIriitz, ‘ Electric Waves,’ ]). 14.3. 
t A factor 1/8- is omitted. 
