May 5, 1904] 



NATURE 



19 



/lie physihalische Chemic and in the Annalen der Nalur- 

 philosopliie. 



In the foregoing considerations, Franz Wald has played 

 a great part. To him I owe first the idea that the definition 

 of substances and elements i^ in a certain sense arbitrary, 

 thouijh very helpful and convenient. This definition is a 

 condensed expression of our methods of separating and 

 purifying these bodies. While, generally speaking, every 

 solution has the same claim to be investigated as these 

 bodies, the latter soon distinguish themselves as standards 

 to which all other cases may be referred. To Franz Wald 

 I owe further the idea that the conception of a phase ',-■ a 

 far more general one than that of a substance, and that the 

 deduction of the idea of a substance, and, further, the 

 deduction of the laws governing the nature of substances, 

 must start from the conception of the phase. I do not 

 know whether Wald will agree with the way I have 

 manipulated his ideas, but I feel it imperatively necessary 

 to express my deep respect for, and my thankful obligation 

 to, this solitary philosopher, who has prosecuted his work 

 during a long series of years almost wholly without en- 

 couragement or sympathy from others. 



No%v there are still two stoichiometrical laws to be de- 

 duced, namely, the law of multiple proportions and the 

 law of combining weights. I prefer to invert the order, and 

 first to deduce the second law. It expresses the fact that 

 it is possible to ascribe to each element a certain relative 

 weight in such a way that every combination between the 

 elements c.in be expressed by these weights or their 

 multiples. 



We suppose three elements, .A, B, and C, given, which 

 may form binary combinations, .\B, BC, and /VC, and 

 besides these a ternary combination, .\BC ; there shall be 

 but one combination of every kind. Now we begin by 

 forming the combination ."^B ; for this purpose, we must 

 take a certain invariable ratio between the weights of A 

 and B, according to the already proved law of constant 

 proportions. Now we combine AB with C and get the 

 ternary compound, ABC. There will be a certain ratio, 

 too, between AB and C, and we can, if we put A as unity, 

 assign to B and C certain numbers describing their com- 

 bining weights relatively to A. 



Now we begin to combine A with C forming AC, and 

 then we form the ternary combination, ACB from AC and 

 B. .According to our law of a relation between elements 

 and compounds, which can be interpreted only in one way, 

 ACB cannot be different from ABC, and, in particular, it 

 must show the same ratio between the relative weights of 

 its elements. Therefore, the ratio of the weights of A and 

 C in forming the combination .AC cannot be other than 

 that expressed by the relative combining weights already 

 found in the first way. In other words, it is possible to 

 compute the composition of the hitherto unknown combin- 

 ation .AC, from analyses of the combinations AB and .ABC. 

 In the same way, we can compute the composition of the 

 unknown combination BC, by help of the numbers obtained 

 by the analyses of two other combinations of the same 

 elements. To resume : the combining weights relatively 

 to A regulate all other possible compounds between the 

 elements concerned. But this is nothing else than the 

 general stoichiometrical law of combining weights, for we 

 can extend our considerations without difficulty to any 

 number of elements. 



Lastly, it is easy to deduce the law of multiple propor- 

 tions from the law of combining weights. If no com- 

 pounds can be formed except according to their combining 

 weights, then, if there are two different compounds between 

 A and B, we can form the one containing more of B either 

 directly from A and B, or indirectly, combining first A and 

 B to form the lower compound and then combining this 

 with more of B. In applying the law of combining weights, 

 we conceive that the weight of B in the higher compound 

 must be twice its weight in the lower. The same consider- 

 ation may be repeated, and finally we get the result, that 

 instead of double the combining weight, any midtiple of it 

 may occur in combinations, but no other ratio. 



If we cast a backward glance on the mental operations 

 we have performed in the last two deductions, we recognise 

 the method, the application of which has made the two 

 laws of energetics so fruitful. In the same manner as the 

 difference between the whole and the available energy is 



independent of the nature of the path between the same 

 limiting points, the product of the chemical action between 

 a number of given elements is independent of the way in 

 which they are combined. If we compare two different 

 ways, we get an equation bet%veen the characteristics of 

 the two ways, and this is equivalent to a new law. In 

 our case, this new law is the law of combining weights. 



I will put the same idea into somewhat different words. 

 By stating the equation between any two ways, we can get 

 any number of different equations, each representing a new 

 way as an experimental fact. Now, in order that all these 

 equations shall be consistent, there must be some general 

 law regulating the characteristics of the equations. For 

 the consistency of the several equations in the case under 

 discussion, the existence of specific combining weights, in- 

 depender.l of the several combinations, is the necessary 

 condition. 



This is the main point of the considerations I wish to 

 lay before you this evening. There are some secondary 

 questions as to isomerides or allotropic states of substances, 

 and there are other similar questions, but it would lead us 

 too far to consider them one by one. I have investigated 

 them on the same basis, and I can assure you that 1 have 

 nowhere found an insurmountable difficulty or an impassable 

 contradiction. All these facts find their proper place in the 

 frame of the same general ideas. 



Let me still add some words about the nature oj the 

 elements, as considered from my point of view. I wish to 

 lay great stress on the fact that here, too, I find myself on 

 the same ground as that on which Faraday built his 

 general concepts during his whole scientific career. There 

 is only one difference, due to the development of science. 

 Faraday ever held up the idea that we know matter only 

 by its forces, and that if we take the forces away, there will 

 remain no inert carrier, but really nothing at all. As 

 Faraday still clung to the atomic hypothesis, he was forced 

 to express this idea by the conception that the atoms are 

 only mathematical points whence the forces emerge, or 

 where the directions of the several forces intersect ; here 

 his view coincided with that of Boscovich. 



In the language of modern science I express these ideas 

 by stating : what uw call matter is only a complex of 

 energies ivhich we find together in the same place. We 

 are still perfectly free, if we like, to suppose either that the 

 energy fills the space homogeneously, or in a periodic or 

 o-rained way ; the latter assumption would be a substitute 

 for the atomic hvpothesis. The decision between these 

 possibilities is a purely experimental question. Evidently 

 there exist a great number of facts — and I count the 

 chemical facts among them— which can be completely de- 

 scribed by a homogeneous or non-periodic distribution of 

 energy in space. Whether there exist facts which cannot 

 be described without the periodic assumption, I dare not 

 decide for want of know^ledge ; only I am bound to say 

 that I know of none. 



Taking this general point of view, in w-hat light do we 

 regard the question of the elements? We will find the 

 answer, if we remember that the only difference between 

 element's and compounds consists in the supposed impossi- 

 bility of proving the so-called elements to be compounds. 

 We are therefore led to ask for the general energetic proper- 

 ties underlying the concept of a chemical individual, whether 

 element or compound. 



The answer is most simple. The reason why it is possible 

 to isolate a substance from a solution is that the available 

 energy of the substance is a minimum, compared with that 

 of all adjacent bodies. I will not develop this thesis at 

 length, for it is a well known theorem in energetics or 

 thermodynamics. I will only recall the fact that a mini- 

 mum of vapour pressure is always accompanied by a 

 minimum of available energy ; and we have already seen 

 that a minimum of vapour pressure or a maximum of boil- 

 ing point is the characteristic of a hylotropic body or 

 chemical individual. 



This granted, we proceed to the question regardmg the 

 differences between the several substances. Expressed in the 

 most general way, we find these differences connected with 

 differences in their specific energy content. Temperature 

 and pressure are not specific, for we can change them at 

 will. .Specific volume and specific entropy, on the contrary, 

 are not changeable at will ; every substance has its own 



NO- 1801, VOL 70] 



