50 THE ROYAL SOCIETY OF CANADA 
abscissæ. It will be seen that the points fall nearly on straight lines 
which are nearly parallel. This is what was to be expected from the 
theory, according to which At — A! should be nearly constant. 
m+1 m 
The mean value of C deduced from the slope of the straight lines is 0-81, 
which gives 8 = 8. Hence the number of electrons per atom comes 
out 8 times the atomic weight in all cases. 
So far all the positive spheres have been supposed to have the same 
density p. This assumption, however, is not necessary for so long as 
each sphere is of uniform density the arrangement of electrons in it 
is easily seen to be independent of the size of the sphere provided its 
total charge is kept constant. 
3 3 
The equation C — A — À gives 
m+1 m 
3 3 
MCA TA NC) 
If we take A, — 1, this gives the following numbers with C — 0-81. 
m A 
m 
1 1 EME 
2 | 6 ENT 
3 18 Na—123 
4 40 169 
5 76 RD — 765 
6 129 Cs —195 
The last column contains the atomic weights of the alkalimetals 
for comparison. The agreement is fair considering that the solution 
is only an approximation to the truth. If we take A, — 9, we get in 
the same way. 
m A 
1 9 Be — 9 
2 24 Mg — 24 
3 51 Ca — 40 
4 92 ST Of 
5 150 Ba = 137 
6 230 Ra = 226 
