Dr. Schroeder van der Kolk on Gases, 187 



Hence 



dw a /9 



dh h {y—h)h 

 from which is obtained, by integration, 



w 



= la jlognat AH log nat (7 — h) + const.; 



or between the pressures h x and h , changing the natural loga- 

 rithms into common ones, 



M\ 7/ B h ^My & y-h Q 



in which M = 0*43 42 gives the modulus. The introduction of 

 the coefficients gives 



i<; = 00806 log ^ + 1-7564 log ^|— ^ 



/Iq L<£*0 — /Iq 



where h x denotes the lower, and h Q the higher pressure. 

 For h Y ~\ and h = 2 metres, we have 



w= —0-0243 + 0-0693 = 0-0450 thermal unit. 



Hence with two equal globes, one of which is exhausted and the 

 other filled with 1 kilogramme of air at 5° and 2 metres pressure, if 

 the latter is allowed to now into the former, 0'045 thermal unit 

 must be added in order to keep the temperature at 5°. If this 

 is not the case, the gas is cooled; and if the specific heat under 

 constant volume =0*1681, the cooling amounts to 



00450 



0-1681 



0°-27 C. 



In like manner this may be calculated for the other gases. I 

 have not, however, repeated this more complete calculation, 

 since the value for present use may be obtained with sufficient 

 accuracy by means of simple interpolation. Calculating in the 

 above case the value from the first column 



= 0-0035 + £(0-0070 -0-0035) = 0-0046, 



and dividing this by the corresponding value of the second column 



= 0-0001 7 -f £(0000384— 0-0001 7) = 0-00026, 



we obtain 0-0449, which is almost exactly equal to the value cal- 

 culated directly. 



The following numbers were calculated in this way. They always 

 refer to the case in which a vessel containing a kilogramme of 

 gas under 2 metres pressure is placed in connexion with an ex- 

 hausted one of the same capacity. The first column gives the 



