810 SIR B. C. BUODIE ON THE CALCULUS OF CILCMICAL OPERATIONS. 



the exclusion of other forms. The conclusions thus arrived at must obviously have very 

 different values, and while some arc in the highest degree probable, others can only be 

 regarded as tentative and conjectural. But, nevertheless, uncertain as such results may 

 often appear, a profound distinction is to be drawn between this order of hypothesis and 

 those molecular speculations which can neither be confirmed nor disproved by facts. 

 In the former case experiment is constantly controlling our conclusions, and we have 

 the most positive evidence that the methods pursued by the chemist are in the main 

 coiTect; since in numerous cases he has been able to anticipate the results of direct 

 observation, and in others even to correct by theory the erroneous results which obser- 

 vation apparently afforded. 



It is essential to have clear ideas upon this point, that Ave may not over-estimate the 

 value of our results, since any uncertainty attached to the data must undoubtedly attend 

 the conclusions which are derived from them ; but nevertheless the question does not 

 fall within the scope of a deductive and symbolic method, the province of which com- 

 mences only where the task of experiment terminates; and in the consideration of 

 chemical equations I have not, in uncertain cases, attempted any full discussion of the 

 evidence on which they rest, but have limited myself to arguments, in regard to which 

 the application of symbolic reasoning afforded some peculiarity or advantage. 



Section VII.— ON THE SYMBOLS OF THE UNITS OF CHEMICAL SUBSTANCES. 



Group 1. — Symbols of Hydrogen, Oxygen, Sulphur, Selenium, Chlorine, Iodine, 

 Bromine, Nitrogen, Phosphorus, Arsenic, and Mercury. 



(1) Symbol of Hydrogen. — I am about to show by the aid of the principles which 

 Iiave been established in the previous pages that the imits of chemical substances are 

 composed of an integral number of simple weights; that is to say, according to the 

 definition previously given (Sec. I. Def. 9 & 10), that these units are "integral com- 

 pound weights." The point will be demonstrated if it be found possible to express the 

 symbols of these units in the actual system of chemical equations by means of an integral 

 number of prime factors, these factors being the symbols of real weights (Sec. V. (9 & 10)). 

 Now it will be found that such an expression is not only possible, but possible in a great 

 variety of ways ; in other words, many assumptions may be made as to the composition 

 of ponderable matter which are consistent with the above fundamental hypothesis. From 

 these possible expressions, that one will in each case be selected, as the correct inference 

 from the facts, in which the symbol is expressed by the smallest possible number of such 

 factors ; since any other expression, as has before been indicated, must involve hypo- 

 theses which are unnecessary. 



The problem is not dissimilar to that of the determination of the density or relative 

 weight of the same units. We are about to estimate the number and the absolute 

 weight of the simple weights of which the units (Sec. I. Def 8 & 10) of ponderable 

 matter are composed ; and, as in the former case the problem is unmeaning unless the 



