103 CONDUCTION OF BEAT 279 



the transmission having themselves to move in the direction 

 of the motion of the heat. 



But this instance in illustration of the objections contains 

 in itself its own refutation, for it does not correspond in all 

 points to actuality. In the collision-apparatus the trans- 

 mission of energy takes place at all the collisions in the 

 same direction, and travels therefore over a wide stretch in 

 a short time. But in the gaseous medium in which the 

 molecules collide now in this direction and now in that, the 

 energy is carried over now here and now there, and is 

 jerked about in the same zigzags as the molecules. The 

 transmission of heat therefore goes on in a fixed direction 

 with slowness similar to that of the forward motion of the 

 molecules. 



104. Kinetic Theory of Conduction 



Starting from this conception Clausius, 1 a short time 

 after Maxwell, 2 who first treated the problem, gave a 

 detailed analysis of the process of the conduction of heat, 

 by which he has removed the last doubts before men- 

 tioned regarding his hypothesis. Stefan 3 and von Lang 4 

 have later given elementary demonstrations of this theory. 

 The same question has been mathematically treated by 

 Boltzmann 5 on the basis of a later hypothesis of 

 Maxwell's, according to which the molecules of gases 

 repel each other with forces that are inversely as the fifth 

 power of the distance. The theory given in the Mathe- 

 matical Appendices of this book starts from Maxwell's 

 older view and rests on Maxwell's law of distribution of 

 speeds. 



1 Pogg. Ann. 1862, cxv. p. 1 ; Abhandl. U. Warmetheorie, 1867, Abth. 2, 

 p. 277 ; Mechanische Warmetheorie, iii. p. 105. 



2 Phil. Mag. 1860 [4] xx. p. 31 ; 1868, xxxv. p. 214. Scient. Papers, i. 

 p. 403 ; ii. p. 74. 



3 Wien. Sitzungsber. 1863, xlvii. Abth. 2, p. 81. 



4 Ibid. Abth. 2, 1871, Ixiv. p. 485 ; 1872, Ixv. p. 415 ; Pogg. Ann. 1871, 

 cxlv. p. 290 ; 1872, cxlviii. p. 157 ; Einleitung in die theor. Physik, 1867, 

 p. 529. 



5 Wien. Sitzungsber. 1872, Ixvi. Abth. 2, p. 330 ; 1875, Ixxii. Abth. 2, p. 458. 



