DYNAMICAL THEORY OF HEAT. 171 
act to drive currents through it, we may, possibly in all, certainly in many cases, 
neglect the entire second member of (49) without sensible loss of accuracy; and 
we then have a differential equation of the second order for the determination of 
the temperature in the interior of the body, simply from ordinary conduction, 
according to the conditions imposed on its surface. To express these last condi- 
tions generally, a superficial application of the three equations (48) with their nine 
independent coefficients is required. 
181. When ¢ is either given or determined in any way, the solution of the 
purely electrical problem is, as was remarked above, to be had from the seven 
equations (45), (46), and (47). These lead to a single partial differential equa- 
tion of the second order for the determination of V through the interior, sub- 
ject to conditions as to electro-motive force and electrical currents across the 
surface, for the expression of which superficial applications of (45) and (46) will 
be required. When V is determined, the solution of the problem is given by (45) 
and (46), expressing respectively the electro-motive force and the motion of elec- 
tricity through the solid. 
[Additional Note Regarding the Discovery of Thermo-electric Inversions.] 
In a foot-note on the passage quoted above from the Proceedings of the Royal Society of London, 
I referred to phenomena observed in the use of certain alloys of bismuth and antimony in thermo- 
electric circuits completed by copper and by silver, as constituting the first discovery of thermo-clectric 
inversions, having been described by Professor Cummrne, in a paper published as early as 1823 in 
the Transactions of the Cambridge Philosophical Society. On becoming farther acquainted with 
the experimental results contained in that important paper, I find that they include inversions, not 
only in cases like those first mentioned, which might be regarded as anomalies dependent on singular 
properties of strange alloys, but between pure metals, in various cases ; and that the actual pheno- 
menon in the case of copper and iron, the observation of which several years later by M. Brcquerer 
had been very generally regarded as the first discovery of thermo-electric inversion, is there described ; 
as the following extracts show :— 
“« Tf silver and iron wires be heated in connection, the deviation attains a maximum; diminishes 
on increasing the heat, and again attains the former maximum on cooling.”—Camb. Phil. Trans., 
1823; Note on p. 61. 
«« Addition to p. 61” [oceurring in a page of additions at the end of the paper]. “ If gold, silver, 
copper, brass, or zinc wires be heated in connection with iron, the deviation, which is at first posi- 
tive, becomes negative at a red heat.” 
VOL. XXI. PART I. Zaz; 
