52 Prof. H. L. Callendar on the Thermody 'mimical 



at constant temperature. The integral W and its variation 

 with temperature cannot be determined for the gas without 

 an exact knowledge of the form of the isothermals, and of 

 the coefficient (dp/d0) v in terms of the absolute scale. 

 Thomson therefore proposed to make an approximate esti- 

 mate by assuming (1) that the gas obe) r ed Boyle's law 

 p'v , =Rll—p // v n , (2) that the degrees on the absolute scale 

 were nearly the same size as on the constant-volume gas- 

 thermometer at the temperature of experiment, or that we 

 may write (dpld0) v =(dp/dT) v =p/T = R/v. Making this 

 approximation, we obtain immediately, 



0-T = $(6'-6 ,/ )IRlog e {u // /i J ). ... (7) 



This approximation is unsatisfactory, because if we knew the 

 absolute value of the pressure-coefficient and the deviations 

 from Boyle's law, the gas-thermometer might be corrected to 

 the absolute scale without performing the porous-plug ex- 

 periment. The quantities neglected are evidently of the 

 same order as the quantity sought. Thomson and Joule 

 clearly realized this, and devised other methods of correction, 

 but unfortunately the first approximate solution is still 

 retained in many text-books *, in a slightly different form, 

 as the final and correct solution of the problem. The method 

 of exposition generally adopted is as follows : — 



Assuming that the degrees on the scale of the constant- 

 pressure gas -thermometer are of the same size as those of the 

 absolute scale at the temperature of the experiment, we may 

 write dv/d6 = dvldT=R/p in equation (4). Rearranging the 

 terms and substituting T for pvjR, we then obtain 



0-T = $pd0/Rdp (8) 



Assuming further that the small difference (6 — T) is inde- 

 pendent of p, the right-hand side is integrated from p' to p n , 

 substituting for dd the actual difference of temperature 

 (0 1 — 6"y observed when the gas expands adiathermally from 

 a pressure p' to a pressure p". This gives again the ex- 

 pression 



6>-T = S(6"-0")/R logp'/p , '=S(0 l -0")/Rlog c"/v'. (9) 



When the experiment was tried, it was found that the fall 

 of temperature (0—0') was not proportional to log (p/p f ), but 

 simply to {p—p f )< so that the second assumption involved 

 in solution (9) is evidently erroneous. As a matter of fact, 



* E. g. Maxwell's ' Heat,' p. 214 (1897) ; Tait's 'Heat/ p. 340 (1895). 



