192 DE. T. J. I'A. BROMWICH ON THE 



a statement made by Prof. LOVE* 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 formulae 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 should really be (z 2 - y 2 )/r 2 ; 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 appears that the electric and magnetic forces are zero in the direction given byt 



_ _ (K+2)(K-1) , y, 



r ~ 15(2K + 3) 

 in Prof. LOVK'S notation ; of course " zero " means that the forces are really of order (ca) 7 at most. 



It is not difficult to prove that the formulae (5 '6) agree with those found by Lord 

 EAYLEIGH! 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 RAYLEIGH 

 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 $' denotes the azimuthal angle 

 corresponding to the former specification, it is evident that <p' = ^TT corresponds to 

 <l> = TT ; and accordingly we shall have in general the relation 



because both angles are measured in the right-handed sense about the axis of z. 



Lord EAYLEIGH'S paper contains tables and graphs from which it is easy to 

 determine the variation of the field with ; and in order to connect his tables with 

 our formulae, let us write (5 '6) in the form 



(57) 



Y=+c y = - -Ecose6, Z = -c/3 = 



. KT /cT 



where 



E = fCj-f A, cos 0+ |A 2 cos 29, 



S = f AJ fC^ cos 6 I -A.J cos 0. 



Consider, first, points in the plane given by x = 0, in Lord EAYLEIGH'S notation ; 

 this gives <{>' = %ir, or <p = TT. Hence, omitting the factor e """/("">')> the electric force 

 is equal to E, (in the direction of 9 decreasing) ; and accordingly E, is represented by 

 the graph of the Cartesian component (yZ-zY)fr, given by Lord EAYLEIGH. 



Secondly, consider the plane y = ; that is <f>' = 0, or <j> = %TT. Here the electric 



* 'Proc. Lend. Math. Soc.,' vol. 30, 1899, p. 318. 



t A numerical slip in the first line of each of the formulae (42) and (43) has to be corrected; the 

 correction was given in the Errata, vol. 31, ' Proc. Lond. Math. Soc.' 

 } ' Scientific Papers,' vol. 5, p. 559, () and (v). 

 Formulae (42) and (43) of the paper just quoted (allowing for the corrections just mentioned). 



