192 
DE. T. J. FA. BEOMWICH ON THE 
a statement made by Prof. Loye* that there is no direction in which the scattered 
wave is completely cut out; however, on a closer examination of Prof. Love’s formulae, 
they appear to confirm the present conclusion. 
The formulse in question are (42) and (43) of the paper just quoted, but apparently there is a slip in (43). 
In the last line of (43) the factor given as 0 should really be {z^ - y^)lr^; the source of the inaccuracy 
being apparently in the passage from the formula (39) to (41). On introducing this additional term in 
the magnetic force, it apjjears that the electric and' magnetic forces are zero in the direction given byt 
a; = 0, 
^ _ (K + 2)(K-1) 
r 15(2K + 3) 
{Kaf 
in Prof. Love’s notation ; of course 
“ zero ” means that the forces are really of order (my at most. 
It is not difficult to prove that the formulse (5’6) agree with those found by Lord 
RayleighJ and Prof. Love ;§ the method to be adopted is similar to that used in § 4 
of my paper in the ‘ Philosophical Magazine’ (quoted on p. 179 above). But it should 
be observed that in the specification of the incident wave adopted by Lord Bayleigh 
and Prof Love, the electric force is parallel to the axis of y ; but here the electric 
force is parallel to the negative direction of x. Thus if (j)' denotes the azimuthal angle 
corresponding to the former specification, it is evident that (p! = corresponds to 
0 = TT; and accordingly we shall have in general the relation 
because both angles are measured in the right-handed sense about the axis of 2 . 
Lord Bayleigh’s paper contains tables and graphs from which it is easy to 
determine the variation of the field with d; and in order to connect his tables with 
our formulse, let us write (5‘6) in the form 
— S sin (p, 
kV 
Consider, first, points in the plane given by a; = 0, in Lord Bayleigh’s notation; 
this gives = jtt, or (p — tt. Hence, omitting the factor e~‘''’'f{Kr), the electric force 
is equal to B (in the direction of 0 decreasing) ; and accordingly B is represented hy 
the gy'aph of the Cartesian component {yZ—zY)lr, given hy Lord Bayleigh. 
Secondly, consider the plane y = 0 ; that is f = 0, or (p = ^ir. Here the electric 
* ‘Proc. Loud. Math. Soc.,’ vol. 30, 1899, p. 318. 
t A numerical slip in the first line of each of the formulse (42) and (43) has to be corrected; the 
correction was given in the Errata, vol. 31, ‘ Proc. Lond. Math. Soc.’ 
I ‘ Scientific Papers,’ vol. 5, p. 559, {u) and (v). 
§ Formulse (42) and (43) of the paper just quoted (allowing for the corrections just mentioned). 
(57) 
Y = -f-Cy = -B cos cp, Z = — c/3 = 
Kr 
whert 
T? 
