48 Messrs. A. C. and A. E. Jessup on the 
These may be expressed in the form —0*8 + 0'6, — 44 + 2*2, 
— 18 + 18, and may thus be regarded as a growth, or recovery 
from the values given above for the devolution of the elements 
of group II. To be more explicit, we may say that alternate 
members of group II. are subject first to a period of evolution, 
and then of devolution, and that the remaining elements of 
this group are subject to both these influences and, in addition, 
a further return of evolution. 
A close approximation for the two series — 08, —4*4, —18, 
and 0*6, 2*2, 18, may be written as follows : — 
Loss. Recovery. 
2° (1-1) 2° 2 (1-1) 
2 2 (1-1) 2 12 (1-1) 
2 4 (1-1) 2 22 (1-1) 
The general expression for the loss if written as above is 
jq 2^~ 2) where p = 2, 4, or 6 ; 
or, in other words, is the position of the corresponding element 
in the original series. 
The general expression for the loss and recovery of the 
odd members is 
1(5 2( ^" 3) - Icj ^~ r) wliere P = X > 3 > 5 > or 7 > 
these numbers denoting position in the series as above. 
Returning to the original series for the evolution, viz., 6, 
16, 52, the general term may be written in the form 
n — l n — \ n — \ 
(2 + 2)(2 + 3)(2 + 4) - 4 ! 
3! ; 
where n = 1 for the first row of the table, 2 for the next two 
rows, and 3 for the last four. 
Thus the complete formula for the evolution and devolution 
of group II. is 
n— 1 n— 1 ti— 1 
( 2 + 2)(2 + 3) (2 + 4) - 4 ! _ 11 
3! 10 * 
for the even members, and 
(2*+2)(2 ,> +3) (2 > +4) -4! 11 ( ,_ 3) , 11 J^f 
3 ! " 10 2 + TO l 
for the odd. 
If we employ this formula, reckoning differences from 
calcium as standard, we obtain the following values for the 
