Mr Vincent , On a general numerical connection, etc. 477 
Note on a general numerical connection between the atomic 
weights. By C. A. Vincent, B.A., St John’s College. 
[Read 5 May 1902.] 
If a list of all the atomic weights in ascending order of magni- 
tude be taken and the order in this list be called n, then the nth 
atomic weight, from n = 3 to n = 90 is given by the equation 
W = (n+2f^. 
If the atomic weights are from Clarke’s 1901 list with hydro- 
gen as unit, then the greatest difference between the computed 
and determined value will not exceed 4 units, nor will the error 
ever be greater than 5°/ 0 ; in 36 cases the result will not be a 
unit wrong and in 20 cases will not be l°/ 0 wrong; the mean 
error for the whole 58 elements considered is about 1*005, the 
mean percentage error about 1*6. 
By replacing n + 2 of the above formula by N, and taking N 
as indicating the order in an augmented list of the elements, the 
formula may be made to embrace the whole of the 77 elements 
now definitely known. This necessitates predicting an element 
between hydrogen and helium, and one between helium and 
lithium. No other gaps are left till after samarium, when in 
order to complete the list it is necessary to assume elements in 
various places, making 15 gaps in all. The 18 gaps introduced 
after samarium are in general accord with those predicted by the 
periodic table. 
