amongst the Molecules of a Gas. 87 



the gas. Thus the cooling effect is proportional to 



If T is the absolute temperature of the gas and^> and j/ 

 the pressures corresponding to the densities p and pi ', 



P t is proportional to ^ ^ . 

 os Is 



In the case of air s is practically constant, so that the 

 theoretical cooling is directly proportional to the difference oi 

 pressures and inversely to the absolute temperature. 



Thus the hypothesis of a force attracting according to the 

 law of the inverse fourth power and the product of the masses 

 yields the two results deduced from the experimental data. 



It may be worth while mentioning that if the case is worked 

 out for a very long cylinder of matter, attracting according 

 to the Newtonian law, treated as a very prolate spheroid and 

 expanded into another cylinder of the same section treated also 

 as a spheroid, results in accordance with the above experimental 

 results may be obtained, but with a third result, that the 

 cooling effect would be proportional to the sectional area of 

 the cylinder. Thus if the time ever comes when it will be 

 practicable to look for the part of the cooling effect due to the 

 mutual gravitation of the molecules, it will be found as a 

 small fraction of the whole cooling effect, varying with the 

 sectional area of the plug. 



The only other gas on which Thomson and Joule conducted 

 a sufficiently extended series of experiments to obtain definite 

 results was C0 2 . They were able to enunciate the same two 

 general results as for air, only the total cooling effects were 

 not so accurately proportional to the inverse square of the 

 temperature. To evaluate the thermal equivalent oi jpv—jp'v' 

 at different temperatures for C0 2 , Clausius' formula is used, 



^—10.070 T 5533 



t LJ * iD v _ -000426 TO + -000494) 2 * 



The unit of pressure is that of a kilogramme per square 

 metre, and v is the volume in cubic metres of a kilogramme 

 of C0 2 . 



But, in the first place, the formula shows how at a given 

 temperature the value ofpv —jp'v' is very nearly proportional to 

 p—]d, so that, as in the case of air, we can assert that the 

 cooling effect due to increase of molecular potential energy is 

 proportional to the difference of pressure on the two sides of 

 the plug. 



