the Constant-vohime Gas-thermometer. %b5 



we "treat the substance as a perfect gas ; iil the case of 

 hydrogen at an initial pressure of 1 metre of mercury we 

 have already seen that its numerical value is 273 , 034. The 



term (h~ to) gives us the thermodynamic correction 



P\ ~Po _ 



necessary on account of the deviation of the behaviour of the 

 substance from the laws of a perfect gas : it can be calculated 

 when p u p , M, and N are known. 



In order to discover the values of the mean quantities M and N 

 accurately, we require to know in what way the two quantities 



JK ?tt/ay\ and (d±\ 

 ~dp\do )t L \dv J i 



respectively vary with the temperature ; such knowledge we 

 do not at present possess. It is certain, however, that M 

 must be less than the largest value of 



which occurs between t and t' x , and similarly N must be less 



than the largest value of l-^- which occurs between t and 



t x . We are thereby enabled to calculate a superior limit to 

 each of the corrections corresponding to M and N re- 

 spectively ; and in the case of hydrogen we find that these 

 corrections must be very small— so small that we may safely 

 employ some rough method of finding the mean in order to 

 reach the values of M and N. The errors introduced by 

 taking an approximate mean instead of the true mean 

 would not exceed the uncertainty involved in the value of 



Po 



(t 1 — 1 ) owing to the ordinary errors of experiment. 



P\ —Po 



For the purpose of calculating M we must employ the 



measurements, made by Joule and Kelvin, of the heating- 

 effect which occurs when hydrogen is passed through a porous 

 plug. The heating-effect amounted, at temperatures from 

 4° C. to 5° C, to 0°-100 C. per 100 inches of mercury; and 

 at temperatures from 89° C. to 93° C. it amounted to C '155 C. 

 per 100 inches of mercury (Reprinted Papers, vol. iii. 

 p. 175). If the heating-effect had been constant and equal to 

 the smaller of the two values quoted above, the value of 

 M would have been '000505 of a metre of mercury; if the 

 hea ting- effect had been constant and equal to the larger .of 

 the two values, then M would have been '001025 of a metre 



