150 Mr Glazebrook, On the general equations [April 28, 



Now the equations L = l, M=m, N=n, when substituted in 

 (34) lead to 



(m 2 + n 2 ) (V 2 - a 2 ) - m 2 (V 2 - b 2 ) - n 2 (V 2 - c 2 ) = 0, 



or a 2 (m 2 + n 2 )=b 2 m 2 + c 2 n 2 (39), 



and two similar equations. This is impossible, thus we must have 



l-(b 2 -c 2 ) + ^(c 2 -a 2 )+ 1 ±(d 2 -¥) = 0, 



and this is the only relation between I, m, n and L, M, N. 



The fundamental equations may as we have seen, be written 

 K t (dV dn dF\ 



• / -~47rU^ + dec + dt ) (4U) ' 



etc 



Hence 



MiI4J^g + (v^v*n + f)=o..,«, 



Lorentz in the paper referred to, following Helmholtz in mea- 

 suring the current by f , tj, £, puts O = <I>, and J = — fik -^- . 



y 2 ^ is zero for the electrostatic forces arise by hypothesis from 

 electricity outside the space considered, and the equation thus 

 modified becomes his fourth equation. We have in the former 

 paper seen reasons against putting 12 = <1> when we adopt Maxwell's 

 definition of the current. 



Again, from the assumed values for f, g, h, we have, as in the 

 paper in the Camb. Phil. Proc. iv. 



dt X dz dy) ' 



d ~ = 4tt ^ B {b 2 Mn - <?Nm] cos 8, 



4tt7? - 

 and a = - ^- [b 2 Mn - c 2 Nm) sin 8 (42), 



also la + m/3 + ivy = (43), 



thus a, /3, 7 is in the wave front. 



Again Lot + M/3 + Afy = in virtue of (38). Hence a, /3, 7 is 

 at right angles to L, M, N. Also multiplying by a 2 L, ffM and 

 c 2 N and adding the sum is zero. Hence a, /3, 7 is at right angles 



