the Constant-volume Gas-thermometer. 257 



that the quantity in curly brackets should vary inversely as 

 the absolute temperature. An examination of the experi- 

 mental results obtained with such gases shows us that 



JK^ — Y \~j ) * s a P os ^ive quantity which decreases as the 



temperature increases ; and it is quite consistent with the 



experimental evidence to assume that JK =r- + I ~ | actuallv 



OP \ dp Jt 



varies as the inverse temperature, making due allowance for 



the unavoidable errors of experiment. At the same time the 



measurements that have been made do not enable us to assert 



that the proposed law has been proved ; it is conceivable that 



JK^ — (- I i ) decreases rather more rapidly than the inverse 



temperature. 



The simplicity of the proposed law, and its close approxi- 

 mation to the truth, render it interesting to examine what 

 further deductions can be made therefrom. We start with 

 the equation 



and then suppose that the right-hand side of the equation is 



found by experiment to be equal to -g, where \ is a constant. 



We thus have 



dp\ _ \ 



\dt ) v 



j. v - 



Integrating this we obtain 



p=Mt-~ 2 , 



V 



where f(v) is a function of the volume only. Multiply by v, 

 and then differentiate with regard to v keeping t constant ; 

 we get 



Also since 



we mav write 



_(*fc\_j K |L(£)-?i. 



\ dv J t OP \dv J t ir 



*©),+*s®,-<>w- + *w 



