the Constant-volume Gas-thermometer. 253 



air they are both found to be very small. Consequently their 

 sum JK^- + \-f-) is also a small quantity ; and if we use 



an approximate equation in finding the value of (-/■) w © 



shall only be introducing errors corresponding to squares of 

 small quantities. 



Now if pv — Rt 



Ave have 



idp\ _ __ R« 



\dvj f t> 2 * 



Employing this approximate value for ( — ) we obtain 



It is further shown by experiment that for hydrogen, 

 nitrogen, and air, the quantities 



JK^ and (p) 



0f> \dp J t 



are nearly independent of the pressure, and depend on the 

 temperature only. Consequently to our present degree of 

 approximation, the quantity 



dp \ap Jt 



may be taken as a function of the temperature only ; and in 

 order that the constant- volume thermometer may give readings 

 in accordance with the thermodynamic scale we must have 

 the values of 



op \ap ) t 

 varying inversely as the absolute temperature. 



The Absolute Value of the Freezing-point of Water. 



We may apply the formula obtained in the last section to 

 the determination of the absolute value of the freezing-point 

 of water. Estimates of the value of this important physical 

 constant have already been given by Lord Kelvin (Reprinted 

 Papers, vol. iii. p. 177), but his figures are based on the 

 ■results of experiments with the constant-pressure gas-ther- 

 mometer. 



