260 On the Theory of the Constant-volume Gas-thermometer. 



The quantity t( -j- ) — p is therefore proved to be zero in so 



far as we can treat Joule's result as free from experimental 

 error. 



The great flaw in Joule's method is that it is not sufficiently 

 delicate, and a sensible deviation from Mayer's hypothesis 

 might occur without being detected. Lord Kelvin consi- 

 derably improved Joule's apparatus as regards delicacy, but 

 he also changed the theory of the experiment. The equation 

 given in his writings as applying to his form of the experiment 

 is 



«©.— JK I ; 



so that when no change of temperature is observed we should 

 have 



•(J),—* 



This condition is not necessarily the same as 



The precise manner in which the fall of temperature 

 occurring in Lord Kelvin's form of the experiment may be 

 made to test Mayer's hypothesis, is easily deduced from the 

 formula obtained in the first section. Since 



we see that for Mayer's hypothesis to be true it is necessary 

 and sufficient that 



JK ! + (?H - *---«(3&* 



Boyle's law is not rigorously fulfilled by any actual sub- 

 stance ; hence we see that Mayer's hypothesis would be 

 actually disproved by finding no change of temperature in 

 the gas which had come through the porous plug. 



