Atomic Weights to approximate to Whole JS umbers. 313 



case exceed 90°, any more than the deviation of an atomic 

 weight from the nearest whole number can exceed *5. 



To calculate a numerical result, I shall take the table of 

 atomic weights published by Prof. T. W. Richards ( 4 American 

 Chemical Journal/ vol. xx. p. 545). This table, in common 

 with most others, adopts oxygen as the standard atomic weight, 

 taking its value as exactly 16. For the purpose of the present 

 paper, there does not seem to be any special reason why 

 hydrogen should be preferred. The numbers will therefore 

 be used as they stand. The table gives nine of the best- 

 known atomic weights to three decimal places. These are 

 as follows : — 



Bromine 79*955 



Carbon 12*001 



Chlorine 35*455 



Hydrogen .... 1*0075 



Nitrogen 14*045 



Oxygen 16*000 



Potassium .... 39*140 



Sodium 23*050 



Sulphur 32*065 



If we take the difference between each of these and the 

 nearest whole number and add the results, we get as the 

 sum of the differences *809. In the application of the formula, 

 i=8, since oxygen, as the standard assumed, must be omitted 

 from the reckoning. 



Thus the probability of the total deviation *809 will be 



I ((-)•.,(■»_,)•} _. TO115 , 



or about 1 chance in 1000. 



The table referred to gives the atomic weights of 18 other 

 elements to two decimal places. These are no doubt less 

 well determined than those considered above, Taking the 

 whole 27 elements, the sum of the deviations is 4*37 units. 

 In this case 9 terms of the series are involved. An approxi- 

 mate computation showed that the probability of the sum of 

 deviations being so low by accident was about *00174, about 

 one-half as large again as when only the best known atomic 

 weights were considered. It seems not unreasonable to 

 suppose that if the experimental numbers had been perfectly 

 accurate, the larger number of atomic weights would have 

 presented stronger evidence for a law than the smaller. 



It appears, then, that a calculation of the probabilities 

 involved fully confirms the verdict of commonsense, that the 



Phil. Mag. SL 6. Vol. 1. No. 3. March 1901. Y 



