Correction of the Gas- Thermometer. 57 



from which, since SQ is small, we have the approximate 

 value of the correction, 



0„-T o =l-163S^„Q/E (19) 



This is equivalent in effect to the method adopted by Lehfeldt 

 (Phil. Mag. April 1898, p. 363), who takes for Q the value 

 of the "proper mean cooling-effect" given by Thomson. 

 Applying the correction to the value of the pressure-coefficient 

 for COo found by Chappuis at p =100 cms., namely, 

 •0037251, T =268°-45, he finds o =274°-83, which 'is 

 evidently much too large. The error is chiefly due to the 

 neglect of the term d(pv). He also applies formula (18) 

 to evaluate the scale-correction between 0° and 100° for 

 comparison with Chappuis' observations. His results for 

 the scale-difference between the nitrogen and hydrogen 

 thermometers are given in Table VI. (p. 67), and indicated by 

 the dotted curve in fig. 1 (p. 69) . They appear to be somewhat 

 in excess of the true values, partly in consequence of the 

 assumption SQ = constant, which cannot be made in deducing 

 the scale-correction. 



There is a much simpler method of deducing the absolute 

 zero correction directly from the differential equation, without 

 integrating on the assumption SQ = constant, which, so far as 

 I am aware, has not been previously noticed. 



For the constant-pressure thermometer, we take the 

 equation in the form (4), and substitute dv/d6 = ~R/p, and 

 T=jt?r/R, which gives the simple result, 



0-T = SpQ(R, (20) 



which is accurately true at a point in the neighbourhood of 

 50° C, where the degrees on the scale of the gas-thermometer 

 are of the same size as those on the absolute scale. To find 

 the value of the zero correction 6 — T , we have merely to 

 subtract the value of the scale-correction at this point. But 

 the latter must be very small compared with the zero cor- 

 rection, since the whole number of degrees between 0° and 

 100° C. is the same by definition for both thermometers. 

 If, therefore, we substitute the proper mean value of SQ, 

 which corresponds to the point where the degrees are of 

 equal size, we shall obtain a very good approximation to the 

 absolute zero correction, which is in fact seen to be the 

 same as that given by Thomson for the constant^pressure 

 thermometer. 



To make a similar estimate for the constant-volume ther- 



