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 t 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 (4b*), 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-electric 

 inversions, having been described by Professor Cumming, 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. Beccluerel 

 had been very generally regarded as the first discovery of thermo-electric inversion, is there described ; 

 as the following extracts show : — 



" If 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" [occurring 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. 2 Z 



