123 



in how far may we regard the distance calculated with (1) as the 

 distance of the centres of the molecules? 



As in reality the electrons are the diffracting j)articles, this question 

 may only be answered when the true position of the electrons in 

 the molecule is known for every instant. 



In order however to form us still an oj)inion in this problem we 

 shall consider the case of molecules each consisting of a nucleus 

 (which is supposed not to contribute to the diffraction) and one 

 election that is freely moving in a sphere with radius r (so that 

 it passes in all volume elements equally long times). A system of 

 arbitrarily orientated pairs of such molecules all with the same 

 distance a between the molecule centres gives then in a direction 

 which makes an angle (f> with the direction of the incident light 

 an intensity proportional with 



I sin a r — a r cos a r\* sin a a 

 1+9' — -i-.^- (2) 



« a 



when 



sm— (o) 



k 2 



This expression may be easily deduced by an extension of the 

 calculation given by Ehrenfest for the case of two simple diffraction 

 centres. 



When r is not small compared with a, the first maximum does 

 no longer correspond with the relation (1). In this case an other 

 factor must be substituted for 7,72 in this formula. When f.i. we 



take rt = 4 A, r = l,25A, this factor is 7,42. 



Evidently the influence of the dimensions of the molecule is small. 

 The more will this be the case as the (mean) density of the electrons 

 in the molecule is greater in the central parts than near the periphery. 



When the molecules come so near to each other, that they are 

 in conctact the influence is greater. For the simple molecule models, 

 described above, the factor in (1) would then become 10 7o smaller. 



^ 6. Water. The blackening which is found in the diffraction 

 image for water round the above mentioned diffraction ring seems 

 to point at a rather great number of pairs of molecules with a 

 mutual distance smaller than that wich we shall call here the 

 normal one ^). On this supposition (he limit of this blackening 



1) With the above is in good agreement, that in table I the mean distance 



o o 



(3,6 A) for water is smaller than the normal one (3,75 A). 



