246 



SCIENCE, 



[N. S. Vol. IV. No. 87. 



less the hypothesis has not been neglected. 

 As was said, if it is true, we may expect 

 from it new insight into the nature of 

 atoms. Accordingly, an immense amount 

 of labor has been expended in attempting 

 to determine whether the atomic weights 

 of certain elements are or are not divisible 

 without remainder by the atomic weight of 

 hydrogen. ISTow since our last meeting in 

 this city results have been attained which 

 show that further effort in this direction is 

 not justified by the hope of any theoretic 

 advantage. The chapter has come to an 

 end. Front's hypothesis cannot be proved 

 by experiment. 



When we attempt to decide by experi- 

 ment whether Front's hypothesis is true, 

 the nature of the problem, and the limita- 

 tions of our present knowledge and of our 

 available manipulative skill, impose three 

 conditions to which we must conform. 



In the first place, we can more readily 

 test the correctness of Front's hypothesis 

 by determinations of the smaller atomic 

 weights. The reason is obvious. All an- 

 alytical work is affected with some acciden- 

 tal error or uncertainty. When Herschel 

 wrote his admirable ' Discourse on the 

 Study of Natural Fhilosophy' he said that 

 it was doubtful whether we could depend 

 on the result of a chemical analysis as hav- 

 ing an uncertainty less than one part in 

 four hundred. Work of much greater ac- 

 curacy has been done since this statement 

 was made ; but, for the moment, let us as- 

 sume that, even now, the uncertainty of a 

 determination of an atomic weight is a 

 four-hundredth part. This uncertainty af- 

 fects a large atomic weight much more un- 

 favorably for our purpose than it affects a 

 small atomic weight. For instance, Stas 

 found the atomic weight of lead to be 206.91, 

 if we take the atomic weight of oxygen as 

 16.00. The assumed uncertainty, one four- 

 hundredth part of this, is 0.53 ; so that, on 

 our assumption, the true value is some- 



where between 206.38 and 207.44. These 

 numbers differ more than a unit ; no one 

 has a right, on this showing, to assert that 

 true value is the whole number 207.00, nor 

 that it is not so. 



But a small atomic weight may be much 

 less unfavorably affected by the same pro- 

 portionate uncertainty. For instance, re- 

 cent determinations show that the atomic 

 weight is 15.88 when the atomic weight of 

 hydrogen is taken as unity. The assumed 

 uncertainty, one four-hundredth part of 

 this, is 0.04; so that, on our assumption, 

 the true value is between the limits 15.84 

 and 15.92. These numbers differ by only 

 one twelfth of a unit ; and both of them 

 differ much from the nearest whole number, 

 16.00. It is, therefore, by determinations 

 of small atomic weights that we may hope 

 to decide the truth of Front's hypothesis. 



But among the smaller atomic weights, 

 some, in the present state of our knowledge, 

 can be more accurately determined than 

 others. Accordingly a second condition 

 imposed on us by the limitations of our 

 knowledge is that we must determine, with 

 what precision we can, those small atomic 

 weights which admit of the maximum of 

 precision. There are eight atomic weights 

 upon which, with the experimental data 

 now available, the decision of the matter 

 may be fairly made to depend. These ele- 

 ments are lithium, carbon, nitrogen, oxy- 

 gen, sodium, sulphur, chlorine and potas- 

 sium ; the atomic weights are, in round 

 numbers, 7, 12, 14, 16, 23, 32, 35.50 and 39. 

 If numerous and careful experiments show ■ 

 that these atomic weights are whole numbers f i 

 Front's hypothesis has a solid basis in fact ; 

 if seven are whole numbers and the other 

 is 35.50, then Dumas's modified statement 

 of the hypothesis has a solid basis in fact, 

 for 35.50 is divisible without a remainder 

 by half the atomic weight of hydrogen. 



One niore condition is imposed on us by 

 the limitations of our knowledge and 



