Connexion between the Atomic Weights. 107 



Petit's law suggested to Carnelley the trial of the rule 



1 



Specific heat 



m 



+ y/ v 



and he found " that in almost all cases the numbers agree 

 very closely with the experimental specific heats." 



A New Rule for Computing Atomic Weights, 



If a list of all the atomic weights in ascending order of 

 magnitude be taken and the order in this list be called ?i, then 

 the nth atomic weight, from n = 3 to n = 60, is given by the 

 equation 



W=(n + 2) 1,21 . 



In the table (p. 108) headed "Augmented List of the 

 Elements/' the numbers standing under n give the actual 

 order of the elements in such a list as the above. The deter- 

 mined atomic weights are given under w, the computed 

 atomic weights under W. 



The atomic weights are Clarke's with hydrogen as unit 

 (Journ. Am. Chem. Soc. March 1902). 



The difference between the determined and the calculated 

 atomic weight is given in another column. Confining our 

 attention for the present to that part of the table from lithium 

 to samarium inclosed by the large bracket, we see that fcr 

 the 58 elements considered, the difference between the expe- 

 rimentally determined atomic weight and that calculated by 

 the rule is less than unity in 36 cases. It is greater than 1 

 and less than 2 in 13 cases ; is between 2 and 3 in 7 cases ; 

 while in only two cases does the computed value differ from 

 the determined value by more than three units, in both of 

 which the difference is Jess than 4. The mean difference for 

 the whole of the 58 elements with which we are now dealing 

 is about l'Ol. 



The percentage differences are given also in the table. In 

 19 instances the difference is less than 1 per cent., in 19 it is 

 either 1 per cent, or greater than 1 per cent, and less than 

 2 per cent. ; in 1 1 cases it is greater than 2 but less than 3, 

 and in 6 it is either equal to or greater than 3 and less than 4, 

 in two instances the percentage difference exceeds 4, and 

 in one case the error is 5*8 per cent. The mean percentage 

 error for the 58 elements is about 1*6. 



