Chemistri/ and Physios. L49 



facts supposed to be well established ; and the Legitimacy of the 

 law, as a deduction from verified facts, has been proved by the 

 completeness with which this requirement has been met. Peri- 

 odic functions have long been known and have long been used 

 for the purpose of expressing ohangea which are dependent, on 

 variations of time and apace. " A like period io function became 

 evident in the case of the elements, depending on the mass of the 

 atom. The primary conception of the masses of hodies or of the 

 masses of atoms belongs to a category which the present state of 

 science forbids us to discuss because as yet we have no means of 

 dissecting or analyzing the conception. All that was known of 

 functions dependent on masses derived its origin from Galileo and 

 Newton ami indicated that such functions either decrease or in- 

 crease with the increase of mass like the attraction of celestial 

 bodies. The numerical expression of the phenomena was always 

 found to be proportional to the mass and in no case was an in- 

 crease of mass followed by a recurrence of properties such as is 

 disclosed by the periodic law of the elements. This constituted 

 such a novelty in the study of the phenomena of nature that 

 although it did not lift the evil which conceals the true concep- 

 tion of mass, it nevertheless indicated that the explanation of that 

 conception must be searched for in the masses of the atoms; the 

 more so as all masses are nothing but aggregations or additions 

 of chemical atoms which would be best described as chemical in- 

 dividuals." " The periodic law has shown that our chemical 

 individuals display a harmonic periodicity of properties depen- 

 dent on their masses." " If we mark on the axis of abscissas a 

 series of lengths proportional to angles and then lay offordinates 

 proportional to sines or other trigonometrical functions, we get 

 periodic curves of a harmonic character. So it might seem at 

 first sight that with the increase of atomic masses the function of 

 the properties of the elements should also vary iu the same har- 

 monic way. But in this case there is no such continuous change 

 as in the curves just referred to because the periods do not con- 

 tain the infinite number of points constituting a curve, but only 

 & finite number of such points. An example will better illustrate 

 this view. The atomic masses — 



Ag 108 Cdll2 In 113 Snll8 Sb 120 Te 125 1127 



steadily increase and their increase is accompanied by a modifi- 

 cation of many properties which constitute the essence of the 

 periodic law. Thus for example the densities of the above ele- 

 ments decrease steadily being respectively 



10-5 8-6 7-4 7'2 G'7 6'4 4-9 



while their oxides contain an increasing quantity of oxygen : — 



Ag,0 Cd 2 2 lu 2 0, Sn 2 4 Sb 2 6 Te 2 O fl I 2 7 



But to connect by a curve the summits of the ordinates ex- 

 pressing any of these properties would involve the rejection of 

 Daltou's law of multiple proportions. Not only are there no in- 



