500 
PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
If we determine ^ from the equation 
( 73 ) 
and F', G', H' from the equations 
F'=F-^, G'=G-^, H'=H-^, .... (74) 
dx dy dz x ' 
then 
dF' , dG' , tfH' _ 
7i + W + ^ !=0 ’ (/5) 
and the equations in (94) become of the form 
*VT'=4^ +J- it (y+I)) (76) 
Differentiating the three equations with respect to x, y, and z , and adding, we find that 
Y =-f +?(*>■?>*)> ( 77 ) 
and that £V 2 F' — 4^ . 
^V 2 G'=4^^,P (78) 
W 2 H'=4^£J^, ! 
1 dr 2 j 
Hence the disturbances indicated by F', G, H' are propagated with the velocity 
V = a / — through the field ; and since 
V 47TjU. 
dF' dG' <ZH' 
dx dy dx ’ 
the resultant of these disturbances is in the plane of the wave. 
(99) The remaining part of the total disturbances F, G, H being the part depending 
on %, is subject to no condition except that expressed in the equation 
W d*x _ 0 
dt + dt 2 “ U - 
If we perform the operation V 2 on this equation, it becomes 
ke= ^-Jc\7 2 p(x, y, z) (79) 
Since the medium is a perfect insulator, e, the free electricity, is immoveable, and 
therefore ^ is a function of x, y, z, and the value of J is either constant or zero, or 
uniformly increasing or diminishing with the time; so that no disturbance depending 
on J can be propagated as a wave. 
(100) The equations of the electromagnetic field, deduced from purely experimental 
evidence, show that transversal vibrations only can be propagated. If we were to go 
beyond our experimental knowledge and to assign a definite density to a substance which 
