191 1.] WILSON— CONSTITUTION OF THE ATOM. 371 



denote the radii of the atoms in the series we should expect to have 



To — i\ = Tg — r„ =:r r^ — Tj = etc. 



Let A^, A.^, A^, etc., denote the atomic weights and suppose 

 /SA^^u^, ^A.^^n.-,, etc.. where ^ is a constant. Then we have 



Hence 



m 



(r ,. — r ) = A ,,'- — A 3 = C, 



\ m+l m/ m + 1 m ' 



3^r 



where C is a constant which should be the same for all series of 

 similar elements. 



Also ('',„+^ — r„i)^^t' approximately, so that 



According to the theory therefore we ought to be able to find the 

 number of electrons per atom from the atomic weights. 



In the figure the values of Ai for series of similar elements are 

 plotted against the order of the elements in the series. For some 

 series a constant has been added to the values of Ai to prevent the 

 different lines falling too close together. It will be seen that 

 the values of Ah for each series fall nearly on straight lines 

 and that the different lines are nearly parallel. This shows that 

 Am+^i — A,ni = C is nearly constant, as was to be expected from the 

 theory. The mean value of C is o.8i. Hence w'e get ^ = 8 so that 

 the number of electrons per atom conies out 8 times the atomic 

 weight in all cases. 



This estimate agrees as well as could be expected with the num- 

 bers deduced from the optical properties of the elements which 

 might be expected to be too low. 



We have assumed that the electrical density of the positive 

 spheres is uniform so that the approximate agreement of the atomic 

 weights with the theory confirms this assumption. It is easy to 

 see that the arrangement of the electrons in the positive sphere is 

 not afifected by a change in the size of the sphere provided its density 

 remains uniform and its total charge the same as before. It is 



