EQUATIONS OF PROPAGATION OF ELECTRIC WAVES. 7 
transverse, although, when synthesised, the disturbance, to which they give rise, is 
transverse. 
[The criterion of transversality of a vector disturbance, propagated by wave motion, 
is that the vector concerned is everywhere circuital; and this implies that, in the 
case of diverging waves, the direction of the vector tends, at great distances from the 
source, to he at right angles to the radius, drawn from the source. Now, if we take, 
for example, the electric radiation rejjresented by tlie expressions in § 13 infra, and 
choose, as tlie surface S, a sphere, witli its centre at the source Q, the magnetic force 
Fig. 1. 
at the point Z {x ■= 0, y = 0) would be parallel to the axis y. Kirchhoff's integral 
would represent the magnetic force, at any point O, as made up of components, con¬ 
tributed by secondary waves, diverging from the elements of S ; and, in the wave 
diverging from Z, the magnetic force would he everywhere parallel to the axis y. It 
can be verified readily, by forming the expression for this force, that it is not circuital; 
but it can be seen at once, without forming this expression, that the secondary wave 
is not transverse; for, at any distance, however great, it is not at right angles to the 
radius vector ZO, unless O is in tlie plane (.r, z). The particular example is sufficient 
to substantiate the criticism ; but a little reflexion shows that there is nothing 
peculiar to the example. In general, let (a, /3, y) he the vector, and suppose that at 
some point the direction of the vector is independent of the time, we may take the 
surface S to pass through the point, and take the axis y parallel to the direction of 
the vector at the point; then a and y vanish ; the equations a = 0 and y = 0 will 
represent two surfaces passing through the point, and we may take the direction of 
the normal to S, at the point, to be the line of intersection of these surfaces. Then 
a, 0a/3q dct/dv and y, 0y/0h dy/dv vanish at tlie point, at all times. In the secondary 
wave sent out from the point, the vector is everywhere parallel to the axis y ; and. 
accordingly, the secondary wave is not a transverse wave.] 
