ELECTRIC AND MAGNETIC INDUCTIONS IN THE SURROUNDING FIELD. 299 
The values of the components of magnetic induction a, b, c are not in any way 
dependent on p. For taking the first of equations (1) and substituting from (5) we 
have 
dM dN_dM'_dN / 
dz dy dz dy 
dm d 2 R _dM? 
dydz' dzdy dz 
dW 
dy 
( 9 ) 
where M' and N' depend on the currents in the system and not on the charges. 
Comparing our equations with Maxwell’s we see that the important point of 
difference is that we can no longer put the quantity corresponding to his J equal to 
, , . . dF dG dH 
zero, J being given by 
This does not affect the determination of velocity of propagation of disturbance in a 
homogeneous non-conducting medium. 
For in such a medium we shall have 
_rj/_K dP 
dt 47r dt 
with corresponding values for v and w. 
Substituting in (3) the first equation becomes 
dP d (dL dM dN 
K/X dt~~ dx\dx dy + dz 
differentiating with respect to t 
rr 
] /X df 
0 dL did dL d dM d dN 
^ dt dx\dx dt dy dt dz dt 
and putting ^=P+~ 
1 ° dt ' dx 
„ d 2 P d 0 d /dP dQ dR\ d 2 n 
K ^d^ = - v2p -^-d,(^+^+^j + d, V ^ = - vP 
( 10 ) 
since 
cZP I dQ dR 47r/ bj^.dg dJdx 
dx ' dy ' dz K \dx'dy ' dz) 
within a homogeneous non-conductor. 
This gives the velocity of propagation of electric induction equal to l/\/K p. 
We can also obtain the corresponding equation for the magnetic induction. 
Substituting in (3) for u, v, and w in terms of P, Q, and R, as above, 
differentiating the second with respect to z, and the third with respect to y, and 
subtracting 
