Correction of the Gas- Thermometer. 89 



method, though troublesome, is evidently capable of great 

 accuracy. It avoids or minimizes the effects of surface- 

 condensation, which are so great an objection to the more 

 convenient capillary-tube method. Witkowski observes in 

 fact that his method always gave lower measurements of 

 compressibility than the capillary-tube method, amounting to 

 about 0'5 per cent, at 15° and 90 atmos, which may probably 

 be explained as due to surface condensation in the capillary- 

 tube method. For our purpose it will suffice to take one of 

 Witkowski's isothermals for air, namely that at — 78°"3 C, 

 which appears to have been determined with especial care, and 

 which is so nearly straight up to high pressures that it is 

 easy to make an estimate of the initial value of dpv/dp, 

 which gives: — 



Air at -78°-3C, c-5 = l'47 c. c; at 0° C., c-b = 0'50 c. c. 



The values of c and b for air calculated from the cooling- 

 effect alone, assuming % = 2, namely, c = 0'90, b =—'002, 

 give c — b at 0° C. = 0*92 c. c, whereas the value should be 

 0*50 c. c. to agree with Amagat's observations. The value at 

 — 78°* 3 C. would be 1*79 c. c, which is also greater than that 

 found by Witkowski. Moreover the negative value of b 

 cannot be interpreted, and would make the error of the cal- 

 culated compressibility much greater at higher temperatures. 

 It is clear that the value of b requires emendation. If we 

 retain the same type of formula with w = 2, and calculate the 

 values of c and b to satisfy the observed values of c — b above 

 given, we find : — 



n=2, c =i-01c.c, 6 = 0-52 c-c, Q = 0°-250, Q 100 =0 c vll0. 



The value of b thus found is still too small ; the values of the 

 cooling-effect deduced are also smaller than the observed 

 values, namely, o, 271 and 0°\147, and the air would not 

 become "pluperfect " till 105° C. 



A much better agreement between the cooling-effect and 

 the compressibility is obtained by taking «=1*5 in the 

 formula. This is not improbable theoretically, as the number 

 of degrees of freedom lost by two diatomic molecules (each 

 possessing five degrees of freedom) in coaggregating should be 

 less than for triatomic molecules like C0 2 . It is most un- 

 likely that the tetratomic aggregate would possess only 

 six degrees of freedom. The value n=l'h implies the loss of 

 three degrees of freedom, which is more likely, if we suppose 

 for simplicity that the number lost must be an integer. We 

 then obtain 



n=l-5, ^=1-48, 6 = 0-98, Q =0°'271, Qioo=0°135. 



