xvm THE CLASSIFICATION OF THE ELEMENTS 485 



Prout's hypothesis and the law of probabilities, 



Although it is universally admitted that the atomic weights 

 do not conform to Prout's hypothesis, and cannot be 

 calculated or corrected by means of that hypothesis, the 

 frequent approximation of the atomic weights towards 

 integral numbers shows clearly that, as Stas admitted in 

 1887, "there must be something in it" (Mallet, loc. at. 

 p. 35). Marignac, in reviewing Stas's paper, pointed out 

 that the average difference between Stas's nine atomic 

 weights and those required by Prout's hypothesis (as modified 

 by Pelouze and by himself ) was only 0*056 (Geneva Archives, 

 1860, 9, 105). He concluded that the law of Prout, like 

 the laws of Boyle and of Charles, had been proved to be 

 inexact, but that such laws had still a practical value in 

 supplying useful approximations for everyday use, and were 

 theoretically important as affording an ideal standard or rule, 

 the deviations from which demanded very careful study. 



The same idea has been expressed in a mathematical 

 form by Strutt in a paper " On the Tendency of the Atomic 

 weights to approximate to Whole Numbers " (Phil. Mag., 

 1901, [vi], 1, 311-314). Taking a series of eight atomic 

 weights given by Richards to three decimal places, he 

 showed that the sum of the differences from integral 

 numbers was 0*809, three-fourths of this difference being 

 due to the two elements chlorine and potassium. The 

 probability of this total deviation is o - ooii59, or about i 

 chance in 1000, so that "the atomic weights tend to 

 approximate to whole numbers far more closely than can 

 reasonably be accounted for by any accidental coincidence." 



Newlands on atomic numbers (1864 to 1878). Prout's 

 hypothesis is perhaps responsible for the introduction of the 

 idea of ATOMIC NUMBERS, i.e. of representing the elements 

 by a series of integral numbers. The publication by New- 

 lands, in 1864, of a table showing the elements in the order 

 of their atomic weights (Periodic Law, p. 7) was followed 



