48 THE ROYAL SOCIETY OF CANADA 
tend to contract so that when the electrons are in equilibrium the 
tubes will all be as short as is possible consistent with their volumes 
remaining constant. It is easy to see that this requires the field of 
each electron to be as nearly spherical as possible with the electron 
in the middle. It appears, therefore, that to obtain an approximate 
solution of the distribution of electrons in a neutral atom it is only 
necessary to divide the positive sphere into n equal volumes all approxi- 
mately spherical and put an electron at the centre of each one. The 
electrons will therefore arrange themselves approximately like the 
centres of the shot in a pile of equal shot. The arrangement of the 
electrons will also be symmetrical about the centre of the positive 
sphere, so that they must be approximately in concentric spherical 
layers. 
The fields of the electrons in each layer will form a layer of thick- 
ness approximately equal to the diameter of the nearly spherical field 
of each electron. 
Consequently, if r,, r,, r,;, ete., denote the radii of the positive 
spheres of the atoms of a series of similar elements, we have approxi- 
mately 
To — Yr, = lg — Ty — I, — I, — ete. 
Let n,, n,, Ny, ete., denote the numbers of electrons per atom in such a 
series, and A,, A,, Ay, etc., the atomic weights. 
Also let BA, — n,, BA, — n, and so on where B is a constant. If 
v denotes the volume of the field of each electron we have 
EE Te Wn VN 
m m m 
TI =n v= /6vA 
m+1 m +1 m+1 
Hence 
Cay eerie ia 
3 By pt * m+1 m 
where C is a constant which can be found from the atomic weights. 
MT Ree EL been 
Also ( mir mj) = V approximately, so that 3B 4—C 
AT 
oT B= 36 
In the figure the values of A* for series of similar elements are 
plotted as ordinates and the order of the elements in the series as 
