Law of Molecular Force. 185 



The calculated numbers are all larger than the observed ; 

 but we must take account of the smallness of the quantities 

 and the magnitude of the possible experimental errors : thus, 

 the experimental cooling for 17°, namely '86°, is the mean of 

 the results of seven series of experiments, the extremes being 

 '806° and *958°. Moreover, Regnault's determinations seem 

 to show that Thomson and Joule's results for air are perhaps 

 somewhat too small. Thus, as the mean of six series of expe- 

 riments at about 16° C, in which air expanded twelve times 

 in succession through the fine hole between the successive 

 chambers of a calorimeter before it passed from the high- 

 pressure to the low-pressure states, Eegnault found the cool- 

 ing-effect due to a pressure-excess of 1 metre of mercury to 

 be '3548°, which corresponds to a cooling-effect of '9012° for 

 a pressure excess of 100 English inches. Again, Eegnault, 

 by expanding air through a silver capillary tube 2*5 metres 

 long, found the cooling-effect at about 16° to be *377° for a 

 pressure-excess of 1 metre of mercury — that is, '9576° for an 

 excess of 100 English inches. These are the only two definite 

 determinations made by Eegnault for air ; and we find that 

 their mean, *93°, is identical with the number given by the 

 equation for 17°. 



Van de Waals (Wiedemann Beibldtter, i.), with an equation 

 founded on Regnault's determinations, obtains a cooling-effect 

 at 17° almost identical with Thomson and Joule's result; but 



in his equation for the cooling-effect, the term aA log — , 



v i 

 arising from the difference between the absolute thermody- 

 namic and absolute air-thermometric scales, is omitted ; if 

 included, it would increase his theoretical effect by about *3 

 of its own amount. 



As far, then, as the experiments on the cooling of air by 

 expansion are available as evidence, they go to show that the 



potential energy of the molecules of a kilogramme of air is -, 



and is equal to § of the virial of the molecular attractions. 



Thomson and Joule and Eegnault also conducted experi- 

 ments on the cooling of hydrogen by expansion ; but its 

 amount was too small for satisfactory measurement. Eeg- 

 nault obtained a slight cooling-effect ; so also did Thomson 

 and Joule in their researches (part ii.) ; but in their re- 

 searches (part iv.) they found a slight heating-effect. The 

 only conclusion possible is that the real effect for hydrogen is 

 smaller than the possible experimental errors. 



From Amagat's experiments on hydrogen I obtained the 



