786 sill B. C. BKODIE ON THE CALCULUS OF QIEMICAL OPEEATIONS. 



It is frequently asserted that our present hypothesis affords a clear and simple expla- 

 nation of chemical phenomena, which is the evidence of its truth. Now it may be con- 

 sidered that such an explanation was perhaps afforded of the incomplete system of facts • 

 known to Dalton, but with our present knowledge this account can no longer be 

 regarded as satisfactory. The most important feature in our modem system is the 

 identification of the weight of the chemical molecule with the weight of the unit of 

 g'aseous volume, to which we are brought by physical as well as chemical considerations. 

 This great simplification was practically introduced by Laurext and Gerhaedt, and it 

 is generally allowed that this assumption affords the surest basis of chemical thcorj'. 

 Now the atomic theory of Dalton accounts for the fact that the weight of the chemical 

 molecule may be regarded as consisting of an integral number of the atomic weights of 

 those elemental bodies into which it can finally be decomposed. But this is not the 

 only limitation with which we are acquainted. The chemists before mentioned dis- 

 covered the existence of a peculiar numerical relation between the atomic weights of 

 certain elemental bodies, when combined in the chemical molecule, to which they gave 

 the name of " the law of even numbers." This law may be thus stated : — " The sum 

 of the volumes of the hydrogen, chlorine, bromine, iodine, nitrogen, and generally of that 

 class of elements which goes under the name of the dyad elements, which are formed by 

 the decomposition of two gaseous volumes of any chemical substance, is an even 

 number"*. This statement rests upon evidence quite as satisfactory as that by which 

 the atomic doctrine is supported. A formula containing an uneven number of these 

 elements jointly is rendered as improbable, from our experience, as a formula containing 

 fractions of atoms. But the atomic theory in its present form takes no account of this 

 relation, and so little has this great discovery been appreciated that such formulae are 

 often met with, even in the works of accomplished chemists ; and indeed they are truly 

 admissible, so far as the limitations imposed by our actual theory are concerned. It 

 need not certainly be a matter for surprise or reproach, that the speculations of Dalton' 

 should not apply to a class of facts with which he was unacquainted ; nor even can this 

 be regarded as conclusive evidence against the truth of his system. But nevertheless 

 this omission indicates some profound defect in chemical theory, and if it should be 

 found that another view of the constitution of matter should cover the whole gi-ound, 

 and account by one and the same hypothesis for both numerical relations, there can be 

 but little room for doubt as to which should be preferred. 



Another, although a less important, defect in our method is the singular unit of volume 

 which chemists have been compelled to adopt, for which selection no reason can be 

 assigned except the necessities of the atomic hypothesis. In the so-called " two-volume" 

 and " four-volume" notations the weight of the chemical unit or molecule is assumed as 

 twice or four times the weight of the unit adopted for the purposes of physical measure- 

 ment, the numbers which express the weight of the chemical molecule being propor- 



• See LAxmEirr, Methode de Chimie, Ed. 1854, p. 57, " Sur les nombres pairs d'atomcs ;" ' Chemical Method,' 

 English translation, 1855, p. 46. 



