i291 



If for two (lifferen( elements of space llie xaliies for L were 

 always 'mdepemJenl of each oilier, A^A' would be = 0, except when 

 we make the element dui coincide with c/w,. When we then mad^e 

 the value of (/to, approach zero, the righthand member of (21 A) 

 would become zero. The A's for different elements of s|)ace are, 

 however, not independent, but when A, is e.g. positive, the A's in 

 the adjacent elements will probably also be positive, so that the 

 product A, A'(/to, t/(o' will be positive on an average not only for 

 iUo = (/a»2, but also for a finite region round din^. In this region 1 

 shall assign to A' not only the same sign, but also the same value 

 as to Aj, and I shall assume that the size of the region is equal to the 

 sphere of attraction of a molecule ^). I shall furthei- assume that we 

 get a sufficient approximation for p^^ — p, when we assign the 



value n to n^, and I shall write v for I ?Zj r/cti', in which we extend 



the integration over the just-mentioned region, v then represents the 

 mean number of molecules in a sphere of attraction. At the critical 

 density I should then be inclined to ascribe to r a value between 

 5 and 25, though not much is to be said with certainty about this 

 value. In consequence of these assumptions (216) passes into. 



V^av err örp(^-§,)»-(S-sj-^ 



V^ènav err ^ör/)(i 

 ,,,_, = - -^-jjj A, ^- 



1 ^ip{%-%S- 



dio dio^doj^ {2\f) 



In order to find the sign of this expression, we transport the 

 origin to the point C, i;, ^^, and first determine the sign of 



the quantity v ^ Q. Ihe bisexfrices of the angles 



Or, r, 



between the displaced ^ and ^-axes, divide the plane into four 

 quadrants; two of them contain the ^-axis, and two the ?-axis. In 

 the two quadrants that contain the §-axis, Q will be ^ 0, in the 

 others Q will be <[ 0. If we next inquire into the sign of 



JQ dio = I, this sign will depend on the situation of the point 



If this point lies in the quadrants where ^^^0, / will also be 



') Not improbably it is greater; but as the elements d'jj' and cZwo, the mutual 

 distance of which is much greater, do not appreciably contribute to the value of 

 the lighthand member of (21^), the restriction to this value may be justified. 



