64 MOLECULAR MOTION AND ITS ENERGY 31 



Although the considerations by which Avogadro 1 arrived 

 at it are closely bound up with views which were then 

 universally accepted, but are now rejected, viz. with the as- 

 sumption of a material caloric, yet the experimental results 

 from which he. started, and the conclusions he founded on 

 them, agree substantially with those which we have here 

 employed. ' He relied especially on the law of Gay-Lussac, 

 which was discussed in the last paragraph, and from which, 

 even without this special theory of gases, Avogadro's law 

 can be easily deduced with at least very great probability. 



On this ground Clausius, who had already pointed 

 out the significance of this law for theoretical chemistry in 

 his jftrst .memoir 2 on the kinetic theory of gases, was able to 

 proceed the reverse way. From the laws of Gay-Lussac 

 and Avogadro he inferred the law, first given by him, 

 that two gases have the same temperature when the mean 

 kinetic energy of their molecular motion is the same, a law 

 which, aided by Maxwell's later researches, we have 

 deduced from the mechanics of molecules. 



Avogadro's law forms one of the most important 

 foundations of theoretical cEemistry ; for by its aid we are in 

 a position to calculate the molecular mass of a substance from 

 its density in the state of gas. For if in the formula 



p = Nm 



N is a number which is the same for all gases and vapours, 

 we can express the values of the molecular mass for all gases 

 in terms of any arbitrary unit, such, for instance, as the 

 molecular mass of hydrogen. The values of the molecular 

 masses so found do not all agree with the atomic masses, 

 but are in cases multiples of them. A molecule, therefore, 

 must in general consist of several atoms, as we have already 

 assumed to be possible. 



Further inquiry into this interesting subject, which is 

 more concerned with chemistry than with physics, I must 



1 Journ. dePhys.parDclamttherie, Ixxiii. 1811, p. 58 ; Ixxviii. 1814, p. 131 ; 

 Mem. cli Torino, xxvi. 1821, p. 440. 



2 Pogg. Ann. c. 1857, p. 353 ; Abhandl. iiber W&rmetheorie, 2. Abth. 1867, 

 p. 229 ; transl. Phil. Mag. [4] xiv. 1857, p. 108. 



