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 + 2) 1 - 21 . 



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°/ ; in 36 cases the result will not be a 

 unit wrong and in 20 cases will not be l°/ wrong; the mean 

 error for the whole 58 elements considered is about 1005, the 

 mean percentage error about 16. 



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 13 gaps introduced 

 after samarium are in general accord with those predicted by the 

 periodic table. 



