46 MOLECULAR MOTION AND ITS ENERGY 25 



yfill therefore result from one collision as often as it will be 

 / destroyed by another ; and from this principle, together with 

 ^ the laws of collision, Maxwell's law may be established. 



L. Boltzmann 1 completed and perfected this proof by 

 employing stricter mathematical work, and thus removing 

 just ground for doubt. A further step forward we owe to 

 H. A. Lorentz, 2 who raised a new objection and improved 

 tne calculation, thereby inciting Boltzmann 3 to again 

 /give a new proof, which proof may now be considered as 

 quite free from objection. 



Further, Kirchhof f has given a proof of the law in his 

 Lectures 4 ; buTligairist this, too, according to a remark of 

 Boltzmann, 5 objection may be made. 



In a different way the proof of this law was attempted 



in^the first edition of this book. The weak points of this 



Attempt were removed by N. N. Pirogof f, 6 and a varied 



./form of Pirogoff's proof is given in the second of the 



Mathematical Appendices. 



These mathematical proofs cannot be repeated here, nor 

 > should we attempt here to give them ; I will only indicate a 

 striking point that arises from them. 



Since the law of distribution which we are looking for 

 is concerned with the state which in time results from the 

 encounters between molecules, we might expect that a 

 knowledge of ivhat occurs during the encounters might be 

 necessary in order to find the law. It would seem that we 

 ought to know the law of collision for molecules if we would 

 calculate the final result of the collisions ; and apparently 

 we must therefore know whether the molecules behave 

 during collision as elastic bodies, or whether their collisions 

 occur as those between hard or soft bodies. 7 



1 Wiener Sitzungsber. Iviii. 1868, p. 517 ; Ixvi. 1872, p. 275. 



2 Ibid. xcv. 1887, p. 115. 



3 Ibid. xcv. 1887, p. 153. 



4 Vorlesungen iiber mathematische Physik, iv. (Theorie der Warme, heraus- 

 geg. von Planck), 1894, p. 142 (14th Lecture). 



5 Munchener Sitzungsber. xxiv. 1894, p. 207. Ibid. (Planck) p. 391. 



6 Journal der russ. physik.-chem. Ges. xvii. 1885, pp. 114-135, 281-313. 



7 A discussion of the question how far the laws of elastic collision are 

 applicable to molecules of gas is given in Chapter X. 



