( 316 ) 



and integrate with respect to </ and i>. It is not allowed to change 

 the order of these operations : to integrate first and to differentiate 

 afterwards, as we should do if we calculated the attraction bv 

 differentiating E with respect to /■. This is obvious from mathematical 

 considerations, but it can also easily be shown from physical consi- 

 derations. For we saw that the double points have yielded in a 

 higher degree to the couples they exercise on one another, according 

 as they have approached one another more closely. 



If therefore we make a group of bipoles approach another bipole 

 from a distance i\ to a distance i\ , and if we waul the axes 

 of the bipoles, when they are at the distance i\ to be orientated 

 in the same way as may be expected from the laws of probability, then 

 we must make the bipoles turn in the direction of the couples at 

 the same time as the\ approach to the fixed double point. The loss 

 of potential energy is therefore not equal to the work of the attracting 

 forces but contains also the work of the couples and therefore we 

 cannot find the average force by differentiating the average potential 

 energy with respect to /■. 



The attraction of each pair of molecules is found by differentiating 



— — [/% cos 1 & -j- 1 . cosy with respect to /', i.e. by multiplying this 

 3r s 



quantity by . Therefore we find also the value of the average 



/■ 



force by multiplying the value of the average potential energy by 



3 



; so we find : 



r 



A - M "!»/V |37 + 3W5.I ' 3W7/" 1 """ ( 



where the quantities p have the name signification as on p. 136 I.e. 

 It appears thai the way in which the attraction depends on r is 

 the same as I had indicated 1. c., but that the coefficients have 

 another value than we should find by differentiating K with respect 

 to r. 



