Correction of the Gas-Thermometer. 53 



Joule and Thomson did not make any direct use of the 

 approximate solution in this form. But owing to its frequent 

 repetition, it has proved a stumbling-block to many who 

 have attempted to apply the results of these experiments to 

 the calculation of the difference between the scales. 



In order to calculate the correction for the a^r-thermometer 

 over the whole range, Joule and Thomson proceeded in 1854 

 by a different method. Combining Kegnault's formula for 

 the pressure-coefficient at various constant densities, namely, 



Pressure-coefficient of Air= '00365343 + '000011575 V /r, . (10) 



with his experiments on the deviations from Boyle's law at 

 4° C, and with their own experiments on the cooling-effect, 

 they calculated the following formula (the units being feet 

 and pounds) to satisfy all the available experimental data: — 



^w = R(0- (-0012811- 1-391 8/6> + 353'2/6> 2 )V /?;). (11) 



This is a very simple and direct method provided that the 

 data employed are accurate and consistent. Calculating 

 from this formula they obtained the value of the freezing- 

 point of water on the absolute scale 0° C.= 273*72 Abs., 

 which is still frequently quoted, and was universally accepted 

 for many years. They also calculated a table of corrections 

 for the air-thermometer which has been quoted in many 

 recent books (e. g. Guillaume's Thermometries Paris, 1889) 

 as the final result of their work. It is evident, however, that 

 the value 0° C. = 273"72 Abs. is simply the reciprocal of 

 Kegnault's limiting coefficient at zero initial pressure, namely, 

 '00365343, and does not depend at all on the value of the 

 cooling- effect ; and since Kegnault's formula (7) is well 

 known at the present time to be erroneous, it is not to 

 be wondered at that the values of the thermodynamical 

 correction given in Joule and Thomson's original table should 

 be very greatly in excess of the true difference between the 

 scales. 



Other attempts have been made on similar lines to calculate 

 tables of reduction for the gas-thermometer, notably by Joch- 

 mann (1860), and by Weinstein (1881), whose resultsare quoted 

 in Gruillaume's Thermometrie, p. 261 *. Weinstein quotes 

 Jochmann's equation, and endeavours to adapt the method 

 for calculation of the corrections of the constant-volume 

 thermometer. By a somewhat complicated method, taking 



* Jochmann, Schlomilchs' Zeit. Math. Phys. v. pp. 24 & 96 : Wein- 

 stein, Matron. Beitr. n. o, p. (55. 



