458 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES .VOL. 11, NO. 19 



During the first transition H remains constant, but I changes from 

 kiHtohH. Hence the total work during the transition is 7/2(^^2 — ki). 

 During the transfer from t and H to t + dr and H + dH, the sus- 

 ceptibility remains constant, but H changes by dH. The work 

 during this stage is k^HdH. Similar expressions give the work during 

 the other two stages of the cycle. The total work of the cycle is 

 HdHiki — ko), and the equation for which we are searching is there- 

 fore 



dr (^2 - k,)HdH 



Under ordinary conditions the change of transition temperature 

 in a magnetic field is very small, but at low temperatures the effect 

 may become large. For the energy content of a body decreases as 

 the fourth power of the absolute temperature, so that X varies as r^ 

 and if Curie's law is true, the susceptibility varies inversely as the 

 temperature, so that, other things being equal, the change of transi- 

 tion temperature in a magnetic field varies inversely as the fourth 

 power of the temperature. 



The formula as given above applies to an infinitesimal tempera- 

 ture range. When approaching zero, the actual change of tempera- 

 ture in a finite field must be found by an integration of this equation. 

 If we make the assumptions of the last paragraph, we have 



tMt = Const. Hd/f 

 which on integration goes into 



r^ - ro' = Const. H\ 



The data by which this equation may be checked are meager, but 

 they are at least consistent with it. In default of measurements of 

 energy content and susceptibility at low temperatures, the equation 

 could be checked from measurements of the normal temperature of 

 discontinuity and the corresponding temperature in two different 

 magnetic fields. The only metal for which Onnes gives the effect of 

 two different magnetic fields on the temperature of discontinuity 

 is lead, and we have already mentioned that the normal temperature 

 for this substance has not been accurately measured. However it 

 is interesting to show that the data for lead are at least consistent 

 with this point of view. From a diagram given by Onnes'' (he does 

 not publish the values numerically) I deduce that the temperature 

 of discontinuity in a field H = 930 is 4.25°, and in a field 1130 is 



• H. KamBRUNch Onnes. Proc. Amst. Acad. Sci. 16: (2) 991. 1914. 



