22 A. W. Witkowski on the 



The shape of these curves leads forcibly to the conclusion 



"d 2 v 

 that for small pressures (p = l atm.) ^ cannot be zero 



throughout the whole range of temperatures. It is very 

 small indeed for temperatures above —100°; but near the 

 critical temperature its values cannot be neglected. This is, 

 of course, an inference obtained by extrapolation (dotted parts 

 of the curves on PL I.), since no experiments are available 

 on expansion of air at low temperatures under atmospheric 

 pressure. 



Although this extrapolation does not seem to be doubtful, 

 and, moreover, anv errors in it do not influence the final 



. c p yv 



result, namely the integral 1 — dp, in a marked degree, yet 



it seemed desirable to test its probability in an indirect way. 

 For that purpose I integrated twice the extrapolated values of 



^-Y (for p = l atm.), with respect to temperature, by mecha- 



. 6 



nical quadratures, adding to the result 1 + ^jk in lieu of 



constant of integration. It appears from this calculation 

 that at a temperature 6= —140° (hydrogen scale), a constant 

 pressure (1 atm.) air-thermometer would indicate — 140 0, 76. 

 I know of no experiments to corroborate this result. From 

 Olszewski's experiments on constant volume gas-thermo- 

 meters*") there may be quoted the following results: at a 

 temperature of — 143°* 7 (hydrogen scale) a constant volume 

 nitrogen thermometer indicated — 144°*4, a similar oxygen 

 thermometer — 145 0, 5. This is not inconsistent with the 

 above extrapolation. 



§ 12. In order to obtain the values of the specific heat c p , 

 according to equation (4) it remains to calculate the integrals 

 C p h 2 v (V 2 u 



^T dPi a l on g t ne isothermals „, p and dp being ex- 

 pressed in atmospheres. These integrals multiplied by the 

 respective absolute temperatures t and by the constant factor 

 18'714 represent the difference between the specific heat c p 

 and the specific heat c u under atmospheric pressure, which is 

 very nearly a constant, =0*2372. 



The integrations have been performed by Simpson's formula, 



~& 2 v 

 with the help of a large diagram of ^ , a reduced reproduction 



of which will be found on PI. I. The results are embodied 

 in the following tables : — 



* •' Rozprawy " of Cracow Acad. vol. xiv. (Math. Class). 



