I9I0.] OF OXYGEN AND SILVER. 361 



— • 1 20, while for the element oxygen in all reactions and in all 

 determinations made by all chemists at all times and under all con- 

 ditions the departure was zero always. 



But is this introduction of the departure for the entire atomic 

 weight not merely a formal matter? Not to the man versed in 

 higher mathematics ; for he knows that even the most complex func- 

 tions permit a simple solution by proportional parts for all cases in 

 which the increment of the variable is sufficiently small. Thus this 

 solution would even hold true, with fair approximation, for the 

 departure of 120 thousandths of a unit, above indicated. We may 

 therefore express the difference between the Berzelian reduction 

 maintained to the present day by the dominant school of chemistry 

 and our own as corresponding to the difference between common 

 algebra and higher mathematics. 



While we have worked with the departures instead of the entire 

 atomic weight for over twenty years, we had not been able to deter- 

 mine the relation between the different departures of the different 

 elements in a given chemical reaction until we discovered the equa- 

 tion of condition in 1907. Since then we have determined the depar- 

 tures for each element in all the three hundred chemical reactions 

 that have been used for the determination of atomic weights during 

 the entire century. The results have been put into five tables, each 

 giving sixty reactions. The first two of these tables have been pub- 

 lished, the other three have been ready for publication since the 

 close of 1909. 



Now we may return to the point at issue, the value of the atomic 

 weight of silver: is it 107.88 or is it 108, on the scale of 16 for 

 oxygen ? 



Our tables show that oxygen occurs in 158 of the reactions used 

 for the determination of atomic weights, while silver occurs 115 

 times. Consequently the atomic weight of oxygen has been deter- 

 mined 158 times and that of silver 115 times. Of course, the domi- 

 nant school will declare that they have done no such thing ; but that 

 will not prevent us from using the data they have published although 

 we will accept their declaration as made in good faith. 



The following table gives the results obtained, as stated repeat- 



