HALL AND CAMPBELL. — MAGNETIC EFFECTS IN SOFT IRON. 651 



7^ to T + dT is SidT, or rather, since St is essentially — , the mechan- 

 ical equivalent of the heat given out in this change is — StdT, and this 

 is represented by the area between the two adjacent vertical lines of 

 our diagram. Evidently this area is equal to the area between the 

 two adjacent horizontiil lines from /' to /, that is, to (a< + 0'<) dl] and 

 so we get 



— Si= ©'< + a<, or 0', + Si = —a J. (18) 



That is, the sum of Voigt's &\ a-^d the .% which Moreau uses in place 

 of 0'j, is a constant, represented in Figure 1 1 by the line 7\Jo taken as 

 a negative quantity. As we have already identified 0'j numerically 

 with the line TI, taken as a negative quantity, we see that Sf is repre- 

 sented by the line //' taken as a negative quantity. 



It must be remembered that this simple relation between St and 0'< 

 results from the assumption made, for the time, in drawing Figure 

 11, and made also by Voigt, that the iron line is straight. The actual 

 relation between St and 0'^ is, according to our experiments, more 

 complex. 



The argument for Voigt's proposition, as expressed in equation (13), 

 ■we shall not undertake to give ; and even when we try to put it to an 

 empirical test by means of our data, we do so with a serious a priori doubt 

 as to its value. What real significance can we attach to the formula 

 of Voigt 1 His — 0', the " thermo-electric height " of iron with respect 

 to lead, cannot be taken as a fundamental datum for iron. We have, 

 to be sure, identified — 0' with our S; but this S does not profess to be 

 the absolute value of the thermo-electric entropy for iron. It is merely 

 what we get for iron when we arbitrarily take the thermo-electric en- 

 tropy of lead to be zero. 



We have proceeded as follows : Assuming the " thermo-electric 

 height" of " galvanoplastic " copper relative to lead to be 380 X 10~® 

 microvolts, or 380 absolute, at 20° C, from the observations of Matthi- 

 essen, and taking the thermo-electric height of our iron with respect to 

 modern commercial copper wire (assumed to be thermo-electrically like 

 Matthiessen's copper) to be 1049 absolute at 20° C, according to our 

 own observations, we get 1429 absolute as the thermo-electric height of 

 our iron with respect to lead at 20° C. But " thermo-electric heights " 

 are merely isothermal entropy-differences, if we reckon entropy, as we 

 do, in ergs -r- T. Accordingly in Figure 12 we take the 7^-axis as the 

 lead line and at 20° C. lay off from this axis a distance 380 to give us 

 the 20°-point on our copper line, and a distance of 1429 to give us the 

 20°-point on the iron line. The other points of the iron line must be 

 found by means of our formula (9) for the Thomson eflect in iron. 



