FOUNDATIONS OF THE KINETIC THEORY OF GASES. 259 



diagram as to be far more readily available for calculation than are those of Andrews. 

 I have not, however, the leisure requisite for anything like an exhaustive treatment of 

 them ; and all that I have attempted is to obtain values of the constants in my formula 

 which make it a fair representation of the phenomena in the experimentally investigated 

 range of the gas region of the diagram ; and, more especially, that portion of it 

 where the volume exceeds the critical volume. It appears to me that to try to push the 

 approximation further at present would be waste of time ; it cannot be attempted with 

 any hope of much improvement until certain points, referred to below, have been 

 properly investigated. These may lead to modifications of parts of the formula which, 

 though unimportant in the regions now treated, may greatly improve its agreement 

 with the facts, in the remaining portions of the diagram. Besides, there is in the data 

 the uncertainty due to the presence of air, which was not wholly removed (though 

 reduced to 1/2500) even in Amagat's experiments. This, as above remarked, begins to 

 tell especially when the volume is small. 



It is very much to be regretted that Clausius did not avail himself of Amagat's 

 data in reducing Andrews' scale of pressures. He expressly says he rejected them 

 because they were not consistent with those of Cailletet. Hence the formula which he 

 obtained after great arithmetical labour, though it is in close, sometimes in almost start- 

 ling, agreement with the data through the range of Andrews' work, is not properly a 

 relation among p, v, and t. If we make it such, by putting in the correction (in terms 

 of v) for the pressures as measured by the air-manometer, a new v-factor is introduced into 

 the equation, and its simplicity (which is one of its most important characteristics) is lost. 

 I tried to obtain hints for the values of the constants in my own formula by making this 

 change in that of Clausius. But I found that the factor l/t which Clausius introduced 

 into the virial term (in order to approximate to the effect of the aggregation of particles 

 into groups at the lower ranges of temperature), made his formula inapplicable to the 

 wide regions of the diagram which Andrews did not attack, but which have been so 

 efficiently explored by Amagat. There are, no doubt, traces of this systematic divergence 

 even in the special Andrews region, but they become much more obvious in the outlying 

 parts. 



It is certainly remarkable that my simple formula, based entirely on the behaviour of 

 smooth spheres, should be capable of so close an adjustment to the observed facts ; and I 

 think that the agreement affords at least very strong testimony in favour of the proposed 

 mode of reckoning the temperature of a group of particles. When this is introduced, it 

 appears at once that the term of Van der Waals' equation, which he took to represent 

 Laplace's K, is not the statical pressure due to molecular forces, but (approximately) its 

 excess over the repulsion due to the speed of the particles. And hence the (external) 

 pressure is not, as Clausius put it, ultimately the difference between two very large 

 quantities, but the excess of one very large quantity over the very large difference between 

 two enormously great quantities ; and thus the whole phenomena of a highly-compressed 

 gas, or a liquid, are to be regarded as singular examples of kinetic stability. 28/5/91.] 



