10G Dr. J. H. Vincent on a Numerical 



This is a very strong argument in favour of the formula 

 with which Stoney worked, but it is perhaps a stronger 

 argument in favour of the treatment of the periodic law by 

 graphic methods. The prejudice against such methods enter- 

 tained by Mendeleeff is very surprising. In his book already 

 referred to, he says he has never expressed, " and will never 

 express, the periodic relations of the elements by any geome- 

 trical figures/" 



Carnelley (Phil. Mag. [5] xxix. p. 97) founded his method 

 of computing the atomic weights on the periodic law. He 

 mentions that he had made frequent attempts to find a simple 

 numerical expression for the periodic law during seventeen 

 years previous to the publication of this paper, but without 

 marked success. 



The atomic weight A is given by the formula 



A = 6'6(m+N/v), 



where m is a constant for each of MendeleefFs "series," 

 while v is equal to the order of each element in its series. 

 The values chosen for m were 0, 2£, 5, 8£, and thence by 

 differences of 3^ to 33, for the successive series II., III., . . . X\l. 

 Thus " for any element in series IV. or upwards 



A=6'6(3-5a-9 + \/v), 



where a = the number of series to which the element belongs, 

 and v the numerical order of the element in its own series." 

 A table of determined and computed atomic weights with 

 their differences is given, from which it is at once evident 

 that the rule is capable of calculating the atomic weights 

 with a considerable degree of accuracy. The greatest varia- 

 tion is for iodine, in which the computed atomic weight falls 

 short of the real atomic weight by 6*7 units. The difference 

 in the same direction for tellurium is given as 6*5; but if we 

 substitute the value now accepted for the atomic weight of 

 tellurium, the difference becomes greater. The mean differ- 

 ence for the 54 elements considered is only 1*9. 



If, on the other hand, we examine the results from a 

 percentage point of view, they do not appear so satisfactory. 

 Thus the computed value for the atomic weight of carbon is 

 10 per cent, too high, that of selenium is 8*2 per cent, too low, 

 that of lithium is 5*7 per cent, too low, and that of nitrogen 

 is 5*7 per cent, too high. 



The nearness of the constant 6'6 to the 6*4 of Dulong and 



