330 
MR. J. J. THOMSON ON SOME APPLICATIONS OF 
or since q and r both vanish 
= -l| I pj r («&)dxd,ych 
(63) 
We see by Lagrange’s equation for p that this corresponds to an electromotive 
force at each point of the bar equal to 
(64) 
and if we remember that cIk/cIx becomes infinite in the limit at the junction of the 
wires we see by integrating over this region that the potential close to the junction in 
the wire (2) will exceed that close to the junction in wire (1) by — (/c 2 — /q)®, where 
k . 2 and /q are the values of k in the wires (2) and (1) respectively. 
The force — d(K@)/dx is that which corresponds to the Thomson effect; the difference 
of potentials at the junction is analogous to the Peltier effect; it is, however, pro¬ 
bable that other terms of the form 
| j" | pK®dxdydz 
may occur in the expression for the kinetic energy near the junction, and the effects 
due to these terms may add on to the others; indeed, if the other terms explain the 
Thomson effect, there must be some additional terms of this kind required to explain 
the Peltier effect, for otherwise the total electromotive force round the circuit would 
vanish. 
Since 
dp dq dr _ 
dx + dy + dz = P 
where p is the volume density of the free electricity, we may write 
as 
I'll ' Kp®dxdydz 
If we keep the term in this form, and consider the temperature effects to which it 
corresponds, we are led to suspect the existence of some very remarkable phenomena. 
Writing © in full we see that in the expression for the energy per unit volume 
there is the term 
Ke{{u 1 u 1 }u 1 2 + «V+ 
I 
i 
(65) 
