DYNAMICAL THEORY OF HEAT. 157 
of which the remainder is the standard metal, there will be reversible thermal 
action, consisting of the following parts, each stated per unit of time. 
(1.) Absorption amounting to (1) 2 y, ima locality at the temperature T. 
(2.) Evolution amounting to a wv)? y,. ina locality at the temperature T’, 
(3.) Absorption amounting to my at one end, (that beyond C C’,) 
and (4.) Evolution amounting to my at the other end; 
where, for brevity, a(t) and a(7’) are assumed to denote the values of 
5 (p—8) sin w cos w, at the temperatures T and T’; and mn the mean value of 
; (0 cos? w +@ sin? w) for either end of the bar. The contributions towards the sums 
appearing in the general thermo-dynamic equations which are due to these items 
of thermal agency, are as follows :— 
E (1) — aw) | 5 4 Y towards =H,, 
and oa es oo) 57 Bul towards — 
the thermal agencies at the ends disappearing from each sum, in consequence of 
their being mutually equal and opposite, and being similarly distributed through 
localities equally heated. Now when every reversible thermal effect is included, 
the value of = must be zero, according to the second general law. Hence 
either ag) = 2) must vanish, or there must be a reversible thermal agency 
not yet taken into account. But probably —— = a may not vanish, that is, 
= may vary with the temperature, for natural crystals, and it certainly does vary 
with the temperature for metallic combinations structurally crystalline: (for a 
bar cut obliquely from a solid consisting of alternate layers of copper and iron, 
for instance, the value of o decreases to zero, as the temperature is raised from 
an ordinary atmospheric temperature up to about 280°, and has a contrary sign for 
higher temperatures.) Hence, in general, there must be another reversible ther- 
mal agency, besides the agencies at the ends and at the sides of the bar which we 
have investigated. This agency must be in the interior; and since the substance 
is homogeneous, and uniformly affected by the current, the new agency must be 
uniformly distributed through the length, as different points of the same cross 
section can only differ in virtue of their different circumstances as to temperature. 
If there were no variation of temperature, there could be no such effect anywhere 
in the interior of the bar; and therefore, if d¢ denote the variation of tempera- 
