784 SIE B. C. BEODIE ON THE CALCULUS OP CHEMICAL OPERATIONS. 



to be understood as connecting every letter in the symbol, and was suppressed only from 

 motives of brevity and convenience. So that Hg O was an abbreviated expression for 

 H+H+O ; H and O being numbers by which the relative weights of the combining pro- 

 portions of hydrogen and oxygen were expressed. Sir Jonx Heesciiel, in a paper con- 

 tained in the Edinburgh Philosophical Journal for 1819*, and more recently in his intro- 

 ductory address to the Chemical Section of the British Association at Leeds, in the year 

 1858, objected to this system of chemical notation as opposed to algebraic convention, and 

 suggested the replacement of the symbol H2 O, for example, by the expression 2H-f O, 

 arguing that the apposition of letters, being the algebraic sign of multiplication, cannot, 

 consistently with the conventional principles of algebra, be employed to express the sum 

 of two Aveights. Gebhardt, while he admitted the general principles of the atomic 

 mode of representation, ridiculed all attempts to express the grouping and arrangement 

 of atoms. Such, indeed, is the prevailing uncertainty that even in express treatises on 

 chemistry all details on the subject are frequently evaded, and symbols are introduced 

 and employed without any precise meaning being assigned to them. Such latitude is 

 obviously inconsistent with the methods of science, and it has been proposed by more 

 than one chemist, to whose more exact turn of mind it was eminently distasteful, 

 that we should return to the simpler system of Bebzelius. We are not, however, jus- 

 tified in concluding, as some have done, that because these symbols are wanting in pre- 

 cision, therefore they are utterly without reason or utility, mere idle arrangements of 

 letters to which no serious meaning can be attachedf . On the contrary, a more candid 

 appreciation cannot fail to recognize that, notwithstanding many imperfections, they 

 have rendered a most important service, by affording an external and visible image of 



* See Edinburgh Philosophical Journal, vol. i. pp. 8, 18, 28. 



t See Bebthelot, 'Chimie organique, fondee sur la synthese,' 1860, Introduction, p. cxxii, and p. 189. If 

 the principles laid down by M. Berthelot are to be regarded as literally correct, the questions raised in the 

 present memoir are unworthy of any serious consideration whatever. 



" Ce serait meconnaitre etrangement la phUosophie des sciences natureUes et experimentales, que d'attribuer 

 a do semblables mecanismes une portee fondamcntale. En effet, dans I'e'tude des sciences, tout reside dans la 

 decouverte des faits generaux, et dans ceUes des lois qui les rattachent les uns aux autres. Peu importe le 

 langage par Icquol on les exprime ; c'est nne affaire d'exposition, plutot que d'invention veritable : les signes n'ont 

 de valcur que par les faits dont Us sont I'image. Mais les consequences logiques d'une idee ne changent point, 

 quelle que soit la langue dans laqucUo on la traduit." 



It is a fundamental principle of sj-mbolic reasoning, to whatever science it maybe applied, that we cannot by 

 the aid of symbols arrive at any conclusion which is not implicitly contained in them. And it might with equal 

 justice be asserted that it was a matter of verj' little consequence whether we employed for the purposes of 

 calculation Arabic or Roman numerals, the number expressed being in either case precisely the same, and " the 

 language by which it is expressed being of little moment." Or again, that the discovery of the method of 

 denoting the position of points in space by means of the sj-mbols of algebraic geometry was a very unimportant 

 matter. Our conception of a circle is the same as that of the ancient geometricians, and " the logical conse- 

 quences of an idea do not change into whatever language we translate it." Nevertheless our power of following 

 out and appreciating those consequences may be very materially affected by such a method, as experience has 

 amply proved. 



