SIE B. C. BEODIE ON TIIE CALCULUS OF CHEMICAL OPERATIONS. 809 



knowledge as to the identical relations of ponderable matter is implicitly comprised 

 in it. Indeed it may readily be shown that, however numerous may be our experiments, 

 we can never arrive at any greater number of independent equations without effecting 

 the decomposition of the elements. For if such an independent equation were discovered, 

 it either would be an equation connecting the symbols of the elements themselves, or 

 if it contamed the symbols of other substances we might elimmate between it and the 

 other equations of the system, and thus derive such an equation. It is possible that the 

 limited range of physical conditions under which we necessarily operate, or other 

 obstacles equally insuperable, may for ever preclude such an addition to our knowledge, 

 but nevertheless we can form a conception of another and a wider -chemistry, of which 

 our actual system should be but an imperfect fragment, and in which we should have 

 n independent equations containing n-\-l symbols admitting of a solution of the form 



when we should recognize but one primary elemental form of ponderable matter, and the 

 gi'eat problem of analysis would be completely and finally resolved. 



Every chemical equation is necessarily the expression of a hypothesis ; for even the 

 most accurate experiments arc attended with error, and can only be regarded as affording 

 a certain approximation to that true result at which it is our object to arrive. Even the 

 assertion that two gaseous volumes of water consist of the same ponderable matter as 

 two volumes of hydrogen and one volume of oxygen involves hypotheses as to the gaseous 

 densities of those substances, and the relations of absolute weight before and after 

 chemical change, which go beyond our actual experience. Experiment proves this pro- 

 position to be true within certain limits of error, but in the equation 



an assertion is made in which the errors of observation are not included. Regard being 

 had to the total evidence on which it rests, no statement of the kind is perhaps more 

 credible than this ; and the above equation may serve to mark the extreme limit to 

 which chemical certainty has attained. Such equations form the true basis of the science. 



It is, however, only in comparatively few instances that we are able to ascertain by 

 direct observation the gaseous densities of all the chemical substances which enter into 

 a reaction ; and where this cannot be effected we are compelled to have recourse to 

 indirect methods of a less satisfactory character, to attain the desired end. 



There are many admirable examples of such chemical reasoning*, which, divested of 

 the theoretical considerations with which they are unnecessarily complicated, may be 

 regarded as arguments based upon actual observation of the laws of chemical change, 

 by which certain forms of these equations are established with superior probability, to 



* For example, Odlino " On the Atomic 'Weight of Oxygen and Water," Journal of the Chemical Society, 

 vol. xi. p. 107. Also the article in Watts's Dictionarj' of Chemistry by the same awthor on the atomic weights 

 of the metds ; and Wttrtz, " On the Oxide of Ethylene considered as a link between Organic and Inorganic 

 Chemistrj-," Journal of the Chemical Society, vol. xv. p. 337. 



