MOLECULES AND ATOMS 313 



equal volumes, although, in this case, it is often possible to discover* a 

 preceding reaction between equal volumes. 11 



The law of Avogadrb-Gerhardt may also be^easily expressed in an 

 algebraical form. If the weight of a molecule, or of that quantity of a 

 substance which enters into chemical reaction and occupies in a state 



11 The possibility of reactions between unequal volumes, notwithstanding the general 

 pplication of the law of Avogadro-Gerhardt, may, in addition to what has been said 

 abo^e, depend on the fact that the participating substances, at the moment of reaction, 

 undergo a preliminary modification, decomposition, isomeric (polymeric) transformation, 

 &c. Thus, if NO 2 seems to proceed from N 2 04,,if O 2 is formed from O 3 , and the converse, 

 then it cannot be denied that the production of molecules containing only one atom is 

 also possible for instance, of oxygen as also of higher polymeric forms as the 

 molecule N from N 2 , or H 3 from H 2 . In this manner it is obviously possible, by means 

 of a series of hypotheses, to explain the cases of the formation of ammonia, NH 3 , from 

 3 vols. of hydrogen and 1 vol. of nitrogen. But it must be observed that perhaps our 

 information in similar instances is, as yet, far from being complete. If hydrazine 

 or diamide N 2 H 4 (Chapter VI. Note 20 bls ) is formed and the imide N 2 H 2 in which 2 vols. 

 of hydrogen are combined with 2 vols. of nitrogen, then the reaction here perhaps first 

 takes place between equal volumes. If it be shown that diamide gives nitrogen and 

 ammonia (3N 2 H 4 = N 2 + 4NH 5 ) under the action of sparks, heat, or the silent discharge,, 

 &c., then it will be possible to admit that it is formed before ammonia. And perhaps 

 the still less stable imide N 2 H 2 , which may also decompose with the formation of 

 ammonia, is produced before the amide N 2 H4- 



I mention this to show that the fact of apparent exceptions existing to the law of 

 reactions between equal volumes does not prove the impossibility of their being included 

 under the law on further study of the subject. Having put forward a certain law or hypo- 

 thesis, consequences must be deduced from it, and if by their means clearness and con- 

 sistency are attained and especially, if by their means that which could not otherwise be 

 known can be predicted then the consequences verify the hypothesis. This was the' case 

 with the law now under discussion. The mere simplicity of the deduction of the weights 

 proper to the atoms of the elements, or the mere fact that having admitted the law it 

 follows (as will afterwards be shown) that the vis viva of the' molecules of all gases is 

 a constant quantity, is quite sufficient reason for retaining the hypothesis, if not for 

 believing in it as a fact beyond doubt. And such, is the whole doctrine of atoms. And 

 since by the acceptance of the law it became possible to foretell even the properties and 

 atomic weights of elements which had not yet been discovered, and these predictions 

 afterwards proved to be in agreement with the actual facts, it is evident that the law of 

 Avogadro-Gerhardt penetrates deeply into the nature of the chemical relation of sub- 

 stances. This being granted, it is possible at the present time to exhibit and deduce the 

 "truth under consideration in many ways, and in every case, like all that is highest in 

 science (for example, the laws of the indestructibility of matter, of the conservation of 

 energy, of gravity, &c.), it proves to be not an empirical conclusion from direct observation, 

 and experiment, not a direct result of analysis,. but a creation, or instinctive penetration, 

 of the inquiring mind, guided and directed by experiment and observation a synthesis 

 of which the exact sciences are capable equally with the .highest forms of art. Without 

 such a synthetical process of reasoning, science would only be a mass of disconnected 

 results of arduous labour, and would not be distinguished by that vitality with which 

 it is really endowed when once it succeeds in attaining a synthesis, or concordance of 

 outward form with the inner nature of things, without losing sight of the diversities, 

 of individual parts ; in short, when it discovers by means of outward phenomena, which 

 are apparent to the sense of touch, to observation, and to the common mind, the internal 

 signification of things discovering simplicity in complexity and uniformity in diversity. 

 And this is the highest problem of science. 



