Law of Molecular Force. 181 



If, for the moment, we set apart the results for 15° and — 25°, 

 on account of the large sources of experimental error incident 

 to the employment of the very high excess of pressure 

 (38591 millim., or 50 atmospheres) in the one set and the 

 low temperature in the other, we find the agreement to be 

 excellent, except in the case of the high excess (7921) at 

 100°, where Regnault found a cooling of 9°*88, and the 

 equation gives 7 o, 30; but here the experiment is evidently at 

 fault, because, while the pressure -excess is not much more 

 than |- of 4682, the cooling-effect is more than double 4°*72 — 

 a result in complete disaccord with all Thomson and Joule's 

 and Regnault's general results. 



With regard to Regnault's number for 15°, obtained from 

 capillary-tube experiments, we can see at once how the expe- 

 riments are certain to yield too great a cooling-effect ; for it 

 is certain that the gas at the high-pressure end of the capillary 

 tube, which is assumed to be all at the temperature 15° of the 

 bath surrounding it, cannot be at that temperature quite close 

 to the capillary tube, where the gas is doing work at the great 

 rate due to the excess of pressure of 50 atmospheres ; thus it 

 is certain that the gas is cooled before it enters the capillary 

 tube. Under these circumstances we may consider the agree- 

 ment between the experimental cooling-effect 81° # 96 and the 

 theoretical one of 73°'8 to be all that could be expected. The 

 same sort of remarks apply to the experimental determination 

 at —25° (the number given above is the mean of five deter- 

 minations made by Regnault). 



Thus, then, the experiments of Regnault, which the great 

 experimenter lamented as having cost him all too dear in 

 thought, effort, and time for the results achieved, no less than 

 those which cost the great English experimenters so much 

 time valuable to science, are of fundamental value to molecular 

 physics, if it is allowed that the agreement between them and 

 the results deduced from the characteristic equation for C0 2 

 is such as to justify the statement that the potential energy 

 of the molecules of a kilogramme of C0 2 occupying a volume v 



is — , and is equal to § of the virial of the molecular attraction. 



As Thomson and Joule and Regnault conducted expansion 

 experiments on air, further light may be obtained by a brief 

 discussion of them. 



In constructing a characteristic equation for air I used 

 Amagat's data for 16° (Comptes Eenclus, xcix.), and his 

 general result that, at 100° and up to 8-atmospheres' pressure, 

 the departures of air from the Boyle-Mariotte law were too 

 small to be measurable. These, with Regnault's value for the 



