122 Physical Properties [CH. vi 



It is convenient to classify gases into "ideal" and "real" according as 

 they do or do not accurately satisfy the laws expressed by equation (288). 

 No ideal gas is known to exist : all gases in nature shew deviations from 

 equation (288) for certain temperatures and pressures. At the same time 

 for some other temperatures and pressures, the deviation from equation (288) 

 may be very slight, and in such cases we may say that for these temperatures 

 and pressures the gas differs very little from an ideal gas. From equation (288) 

 it is clear that the Kinetic Theory scale of temperature which we have 

 introduced is the scale of an imaginary gas-thermometer in which an ideal 

 gas is used as thermometric substance. 



142. We proceed to discuss the divergencies from equation (288) which 

 are to be looked for in a gas in which the molecules are not regarded as 

 infinitely small. We shall do this first upon the assumption that it is 

 permissible to use the conception of a "sphere of molecular action," defined 

 in 82. Assuming this, we may use equation (287), calculating v b in the 

 way already explained in Chapter IV. In the notation of 66 (equation (124)) 

 we have 



_m^^ ........................ (2g9) 



I (a, b, c, d ...) 



expressing the value of PI at the point x a , y a , z a . Here / (a, b, c, d ...) is the 

 element of volume integrated throughout the whole of the generalised space 

 except those parts excluded by 33. 



The element of volume integrated through the whole of the generalised 

 space is, as in 65, equal to 11-^. The excluded parts are of two types. 



We have in the first place to exclude the region given by equation (53) 

 in which <$>(x a , y a , z^)<\<r. This exclusion can be represented fully by 

 limiting the size of our vessel, and supposing it to have a layer of thickness 

 \<r removed from the interior. Let the remaining volume be supposed to 

 be fl', then the corrected value of the integral I (a, b, c...) will obviously 

 be fl'*. 



Secondly we must exclude from the generalised space regions of the type 

 given by 



yb? + (ea-*b?<o* ............... (290). 



Let us consider the contribution to the whole integral fl /JV which must be 

 removed on account of this particular exclusion. The whole integral may 

 be taken to represent all possible ways of distributing the centres of the 

 molecules A, B ... throughout a volume 1', each position being equally 

 likely for each molecule. In this case the contribution which satisfies con- 

 dition (290) represents all arrangements for which the centres of A and B 

 lie within a distance cr of one another. 



