MOLECULES AND ATOMS 307 



The law of Avogadro-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 

 of vapour, according to the law, a volume equal to the molecules of 



other bodies, be indicated by the letters M,, M 2 or, in 



general, M, and if the letters D,, D 2 , or, in general, D, 



stand for the density or weight of a given volume of the gases or 

 vapours of the corresponding substances under certain definite con- 

 ditions of temperature and pressure, then the law requires that 



M 1= M, - M = C 



D! D 2 " "D 



where C is a certain constant. This expression directly shows that the 



volumes corresponding with the weights M l , M 2 M, are equal 



to a certain constant, because the volume is proportional to the weight 

 and inversely proportional to the density. The magnitude of C is 

 naturally conditioned by and dependent on the units taken for the 

 expression of the weights of the molecules and the densities. The 

 weights of the molecules (equal to the sum of the atomic weights of 

 the elements forming a given substance) are usually expressed by 

 taking the weight of an atom of hydrogen as unity, and hydrogen is 

 now also chosen as the unit for the expression of the densities of gases 

 and vapours ; it is therefore only needful to find the magnitude of the 

 constant for any one compound, as it will be the same for all others. 

 Let us take water. Its reacting mass is expressed (conditionally) 

 by the formula or molecule H. 2 O, for which M=18, if H=l, as 

 we already know from the composition of water. Its vapour density, 

 or D, compared to hydrogen =9, and consequently for water 0=2, and 



therefore and in general for the molecules of all substance ^. = 2. 



Consequently, the weight of a molecule is equal to twice its vapour 

 density expressed in relation to hydrogen, and conversely the density of 

 a gas is equal to half the molecular weight referred to hydrogen. 



The truth of this may be seen from an infinitely large number of 



and the law of gravity, &c.), proves to be not an empirical deduction from direct obser- 

 vation and experiment, not a direct result of analysis, but a creation, a penetration of an 

 inquiring mind, which is guided and directed only by experiment and observation a 

 synthesis to which the exact sciences are capable to an equal extent with the highest forms 

 of art. Without such a synthetical process of reasoning, science would only be a 

 collection of the results of arduous labour, and would not be distinguished by that force 

 with which it is really endowed when once it succeeds in attaining a synthesis, or con- 

 cordance of outward form with the inner nature of things, without departing from the 

 analysis of individual parts ; in short, when it discovers by means of outward forms, 

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

 signification of things discovering simplicity in complexity and uniformity in 

 diversity. 



x 2 



