762 
MR. A. McAULAY ON THE MATHEMATICAL 
From the first of equations (25) it follows that the scalar SC'©' DT 9P/3D,/ must 
be constant throughout any single conductor; and from the second, that it must be 
constant throughout any number of conductors in contact, and if the conductors are 
anywhere bounded by a dielectric, i.e., invariably, this constant value must be zero. 
Hence with present assumptions SC'©' must be zero everywhere in a steady field. 
[This is not quite accurate since if P, regarded as a function of D,J is a maximum or 
minimum, 3P/0D*' = 0. It does not seem hopeful to pursue this supposition how¬ 
ever.] This presents no difficulty in ordinary cases, since C and ©—to drop the 
dashes as no longer necessary—would generally be very approximately at right angles 
in any case. If, however, we contemplate such a case as the attempt by ordinary 
means to force a galvanic current and a stream of heat in the same direction through 
a conductor, some very curious consequences are involved. The most obvious of them 
seem to be that both the heat and electric apparent conductivities would be largely 
altered. That no such large alterations in these physical quantities have been 
observed I believe to be the case. These difficulties may be wholly imaginary. If, 
which seems on other grounds most probable, P is not even approximately a scalar 
when the body is strained, we should not be able to deduce that SC© was even approxi¬ 
mately zero. In this case, the adjustments brought about in a steady field of the 
kind just contemplated by reason of the equations (25), would probably be mainly 
strain adjustments that would not cause C and © to vary much, if at all, from paral¬ 
lelism. These strains, of course, might very well have hitherto escaped detection. 
These difficulties are, however, sufficiently serious to make it necessary to consider 
the results of assuming P independent of the strain. The most important of these 
results are easily seen to be (1) that, although the connections between the Peltier 
effect and the electromotive forces in a circuit of different metals whose junctions are 
at different temperatures would on the theory of reversibility be the same as is usually 
supposed, yet there would on that theory, taken alone, be no Thomson effect [equa¬ 
tion (19)], and (2) that there would be no thermoelectric effects in a circuit of a single 
metal whose various parts were variously stressed. These two, then, would have to 
be explained on the theory of irreversibility, and no quantitative connection need be 
expected between the Thomson effect and the main thermoelectric effects. 
92. These difficulties seem to me not to be confined to the particular form of theory 
developed in this paper. For instance, there seems as much reason to suppose 
Professor J. J. Thomson’s cr x , <x ;/ , cr~ (‘ Applications,’ 1st ed., §53) to be independent 
of the strain as the present P. And I may remark in passing that similar statements 
may be made with regard to the Cf {ibid., § 43) introduced to explain the Hall 
effect. [By §84 above, it is obvious that on the present theory it is impossible to 
explain the Hall effect by such a term owing to the results other than the Hall 
effect that would ensue from the term.] 
93. Our chief conclusions, so far, may be thus summarised:— 
