244 THE NUMERICAL RELATION 



great a difterence between the true and observed weights as two units could have es- 

 caped detection in the numberless analyses which have been made, by the most expe- 

 rienced chemists, of the Fluorine compounds. It must, therefore, be admitted, and not 

 only in the case of Fluorine, but also in other instances, that there are deviations 

 from the law ; but these deviations are not greater than those from similar numerical 

 laws in astronomy and other sciences, and indeed, judging from the analogy of these 

 sciences, ought to be expected. 



Those who are not familiar with the amounts of probable error in the determination 

 of the different atomic weights would judge, on comparing together the columns of the- 

 oretical and observed values, that the deviations from the law were much greater than 

 they are in reality. It should, therefore, be stated, that, in by far the larger number of 

 instances, the deviations are within the limit of possible errors in the detenninations, 

 leaving only a few exceptional cases to be accounted for. It must be remembered that, 

 other things being equal, the amount of probable error is the greater the greater the 

 atomic weight, so that a difference of 1.9 in the case of Iodine is not a greater actual 

 deviation from the law than only 0.5 in the case of Chloiiue. Indeed, it is very possi- 

 ble that on more accurate determinations the atomic weight of Iodine will be found to 

 correspond to the law, which cannot be expected of that of Chlorine. It is well known 

 that many of the larger atomic weights, especially those of the rarer elements, cannot 

 be regarded as fixed within several units. 



I have calculated, as well as the data I have would permit, the amount of probable 

 error in the determinations of many of the atomic weights, and by comparing together 

 the results from different processes, and by different experimenters, I have endeavored 

 to detect the existence of constant errors, which seem to be the great eiTors in all these 

 determinations, those accidental errors which are made in the repetitions of the same 

 process by equally careful experimenters being comparatively insignificant. The re- 

 sults of this investigation will be published in a subsequent memoir. It is sufficient 

 for the present purpose to state, that, while they show that, in the greater number of 

 cases, the apparent variations from the law are within the limit of probable error, 

 there are yet several instances, where, after allowing for all possible errors of observa- 

 tion, there is a residual difference. I do not therefore look alone to more accurate ob- 

 servations for a confirmation of the law, but, regarding the variations as ascertained 

 facts, hope that future disco-sery will reveal the cause. Whether the variations will be 

 found to be a secondary result of the very cause which has determined the distribution 

 of the atomic weights according to a numerical law, as the perturbations in astronomy 

 are a necessary consequence of the very law they seemed at first to invalidate, or 



