134 REPORT— 1885. 
This relation seems inconsistent with the previous one; it may, how- 
ever, be reconciled with it in the following way :— 
The potential due to a quantity E of electricity at a point distant. 
r from it is proportional to 
E 
(1+4:re)r° 
If ¢, be the value of « for air, the potential under the same circumstances: 
in air is proportional to 
pees, 
(1+ 4re))r’ 
if, then, we define unit potential as the potential at unit distance from 
unit of electricity in air, the potential due to a quantity E in another 
medium will be 
1+47e r. 
Tae} EK 
We see that this is equivalent to increasing the unit of potential, and 
therefore the unit electromotive force, 1+4:e) times, so that if we use 
the new unit the equations will be 
€ 
X=T 4 Arey x, 
df 1t+4re d 
Ta Tedee, det Wht eS oAeE, 
These will coincide with Maxwell’s equation if we make « and ¢) each 
infinite and put K=e/€>. 
Returning to Helmholtz’s theory, if w, v, w are the components of the 
total current 
u=pt+%, 
v=qTD, 
w=r+3, 
where p, q, 7 are the components of the conduction current. 
Helmholtz puts 
du dv dw dp 
dat dy + da =~ ae? 
where p is the volume-density of the free electricity, and if o be the 
surface-density of the free electricity at any point of a surface separating 
two media, w,, 1, W,3 U2, V2, W, the components of the current in the 
two media, 1, m, n the direction cosines of the normal to the surface 
drawn from the first medium to the second, then according to vy. Helm- 
holtz 
de 
1 (u,—u2) +m (v1; —%9) +n (Ww, —uy) =F. 
According to Maxwell the corresponding equations are 
du do | dw_ 
da* dy da TP 
I (u, —Ug) +m (vj —v2) +2 (w, —wWy)=0. 
ta et te et 
