Correction of the Gas- Thermometer. 63 



To find the value of the correction dt to be added to the 

 centigrade temperature t on the scale of the gas-thermometer 

 to reduce to temperature centigrade on the thermodynamical 

 scale, since the temperature centigrade on the scale of the 

 gas-thermometer is given by the formula 



t=T-%=(pv~ Po v Q )100l(p lVl - P oVo), • (35) 



we have evidently the simple expression 



dt=(0-e o )-(T-T o )=(q-q o )-(q 1 -q o )t/lOO. (36) 



It may be noticed with regard to the separate terms in this 

 expression that q is the zero-correction, and the second part 

 (Qi~~ Qo)t/100 is the correction for the fundamental interval. 

 The correction at any point of the scale is not simply q — q , 

 as might appear at first sight, because the values of the 

 constants R and R' are different, and the correction must 

 vanish at 100° 0. as well as at 0° C. 



In order to apply formula (36) to the calculation of a table 

 of corrections, we may select any empirical formula which 

 represents satisfactorily the properties of the gas under 

 consideration. The equation is then thrown into the form 

 (32), and the expression for q is simplified as far as possible 

 by rejecting all quantities of the second order, and is ex- 

 pressed in terms of p and T or 0. As a simple example we 

 may take the equation devised by Clausius to represent the 

 deviations of C0 2 from the formula of van der Waals, 



(p-t-a/6(v + {3) 2 )(v-b)=R0. . . (37) 



Neglecting small quantities of the second order, this may be 

 put in the form 



0=pv/R+(a/R0*-b)p/R, . . . (38) 

 whence 



q=(a/R0*-b)p/R=(c-b)p/R. . . (3D) 



Writing p for p we have the value of q for the constant- 

 pressure thermometer. For the constant-volume thermometer 

 we must substitute PqO/Oq for p. The values of the constant- 

 may be immediately calculated (as above, Table II.) from 

 the observations of Joule and Thomson on the cooling-effect, 

 without reference to any other experimental data. A table 

 of corrections calculated in this manner may not be the most 

 accurate possible at the present time, when so many more 

 observations are available, but it is of special interest to 

 compare the results of an investigation made so long ago 

 with those of the latest thermometric researches. For this 

 reason I have calculated the following table of correction- oil 



