94 Proceedings of the Royal Society of Victoria. 



For most bodies Kp is sufficiently nearly a constant between 

 such temperature limits as 0° and lOO'C, and we may replace 

 it in the integral by its mean value ; thus we obtain 



J 4., ^ T, i 



T 

 or <^, - (^1 = K,, log, ^- 



i.e., the change in the entropy during the transformation is 

 proportional to the difference between the napierian logarithms 

 of the final and initial absolute temperatures. 



A perfectly similar calculation shews us that the gain of 

 entropy during a transformation in which the body is kept at 

 constant volume is expressed by 



T 



<^, - <^i = K,. log,— • 



-•-1 

 where K^. denotes the specific heat at constant volume. Here 

 again the change in the entropy is proportional to the difference 

 of the logarithms of the absolute temperatures. 



We may therefore measure these entropy changes by means of 

 the expansion of mercury. If a mercurial thermometer tube be 

 marked off, not into divisions of equal length, but into lengths 

 proportional to the logarithms of the corresponding temperatures 

 reckoned from absolute zero, its indications will give directly the 

 entropy changes of water, reckoned in thermal units, to about the 

 same order of accuracy as its readings, when it is graduated in the 

 usual way, give absolute temperatures if 273° be added to them. 

 For any other substance the readings must be multiplied by the 

 value of the mean specific heat. In this way the first model on 

 the table (Fig. 1) was constructed; I have merely supplied a 

 thermometer with a scale of napierian logarithms placed opposite 

 to the corresponding temperatures reckoned from absolute zero. 



Something more can, however, be done with these instruments 

 than the mere determination of changes of entropy. It may 

 frequently be used to measure the entropy of a body from a fixed 

 zero — ^,just as thermometers measure temperatures above and 

 below 0°C. — provided either its pressure or its volume is supposed 

 to remain constant. The zero of the instrument corresponds to 

 a temperature of 1° absolute, or - 272° Centigrade, since at this 



