196 
Again, by multiplying in like manner the atomic weight 
of the second member of the alkaline earth and cadmium 
group of metals, the products, minus the atomic weight of 
the first member (Gl=8), are the atomic weights of all the 
elements of this group. 
III. 
0.0 . 8 = G1 = 8 
1x24.0 = Mg= 24 
2 x 24-8= Ca = 40 
3 x 24 - 8 = Zn = 64 
4 x 24 - 8 = Sr = 88 
5 x 24-8 - Cd = 112 
6 X 24-8= Ba= 136 
7x24-8= — = 160 
8 x 24-8 = — = 184 
9 x 24-8 = Pb = 208 
The further relations observable between interplanetary 
voids and atomic condensations of the natural groups of 
elements in tables II. III., are as follows : — 
1. The regular geometric series of the planetary distances 
commences at the second member of the system, and the 
regular arithmetical series of atomic weights commences at 
the second and corresponding member of each group. 
2. As the atomic weight of the second element in each 
group is half the sum of the atomic weights of the first and 
third elements, so is the distance of the second member of 
the solar system an arithmetical mean, or half the sum of 
the distances of the first and third members. 
3. The atomic weight of the fourth member in each group 
of elements is equal to the sum of the atomic weights of the 
second and the third ; and the distance of the fourth member 
of the solar system is also equal, within a unit, to the sum 
of the distances of the second and third members. 
4. As the smallest planetary distance is a constant func- 
tion of the distances of the outer planetary bodies, so is the 
smallest atomic weight in each group a similar function of 
all the higher members of tine series to which it belongs. 
It will also be observed that the plus and minus signs of 
