869 



the second power of tlie distance between the attracting or repulsing 

 points), so tliat these forces might be ascribed to an electric agent. ') 

 possibly with multiple points"), 



c. the total quantity of the agent in each molecule = (the 

 molecules behave as electrically neutral).] 



2. No odd power of T—^ occurs, if the following conditions 

 are fulfilled : 



{B) : a, J) and c as above, and besides : 



d. the molecule possesses, as regards its attractive and repulsive 

 forces, at least one axis of ''inverse symmetry", by which expression 

 we mean, that each volume element contains a quantity of the 

 agent (as indicated under b) equal and opposite to that of the volume 

 element with which it coincides after a revolution about that axis 

 through an angle of ^njl-, k being a whole and necessarily even 

 number'). 



In this case B is an even function of the temperature. 

 The proof of these two theorems follows below in § 3 and 4. 

 If in the development of B according to (2) the second term 

 does not occur, the series for B reduces for high temperatures to: 



i? = 5. (i + ~) m 



This dependence of B on the temperature is the same as that 

 which follows from van der Waals' equation by putting b^^r = 

 constant, and assuming for aw with Clausius and D. Berthei.ot : 

 aw -^ T'^ (cf. Suppl. N". 39a). Hence if the molecules satisfy the 

 conditions (^4), then for high temperatures and at densities for which 

 only encounters of two molecules at a time have to be considered, 

 the equation of state in the form accepted by D. Berthelot would hold. 



If the conditions {B) are fulfilled the agreement with Berthelot's 

 equation of state is still closer in consequence of the absence of the 

 term è,/2''. 



') On the supposition that electrodynamic forces (other than magnetic) need 

 not be considered. 



-) In this, if need be, a magnetic agent may be included. 



^) As examples of this we mention the cases, that a molecule contains two 

 positive and two negative charges situated at the corners of a square, the centre 

 of which coincides with that of the molecule. If the homonymous charges lie 

 diametrically opposite to each other, the molecule has one quadruple and two 

 double axes of inverse symmetry . in the other case it has two double axes of 

 inverse symmetry. Wo have another example, where the charges form a figure of 

 revolution about an axis through the centre of the molecule, and the part on one 

 side of the equatorial plane is the "inverse image" of the part on the other side. 



