ix 



The papers to which we liave called attention by no means exhaust 

 the list of Maxwell's contributions to electrical science, but they are 

 the most important. Most of what he wrote found its proper 

 place in the treatise on Electricity and Magnetism, which is in a 

 great measure the outcome and product of his study of Faraday's 

 researches and of his own speculations and labours. 



The theory that the properties of a gas are due to the action of 

 invisible molecules in rapid motion was propounded by several writers 

 before Maxwell, and an explanation had been given of Boyle's law 

 that the product of the pressure and volume of a gas is constant for 

 the same temperature; 



Herapath had also given an explanation of diffusion, and Joule had 

 calculated the mean velocity of the molecules of various gases. The 

 most important advance was, however, made by Clausius, whose first 

 memoir " On the kind of motion which we call heat " contains a very 

 clear exposition of the theory, and establishes that the vis viva of the 

 translatory motion of the gas does not represent the whole of the 

 heat in it. His second memoir treats of the mean length of path 

 described by a molecule, and an expression is obtained for it in terms 

 of the average distance of the particles, and the distance between their 

 centres at collision. The paper is valuable not so much on account 

 of this result, which in fact is different from that subsequently obtained 

 when the subject was more fully developed, but because it led the 

 way in bringing the kinetic theory fairly under the domain of mathe- 

 matics. 



Maxwell perceived the importance of Clausius' work, and his first 

 paper contains an attempt to complete the investigation of the mean 

 path. This paper, entitled " Illustrations of the Dynamical Theory 

 of Gases," was read before the British Association in 1859, and pub- 

 lished in the " Philosophical Magazine " of the following year. 

 Theories, mathematically developed, are here given of the internal 

 friction of gases, the conduction of heat through a gas, and the 

 diffusion of one gas through another* One or other of these phe- 

 nomena, he thought, ought to yield an accurate expression for the 

 length of the mean path. 



He supposes the molecules to be hard perfectly elastic spheres, and 

 investigates the laws of motion of a system of such molecules acting 

 on one another, only during impact. His method is first of all to 

 discuss the motion of two molecules under their mutual action, and 

 having discovered the changes in their velocities and directions due 

 to an encounter, to apply what he has happily termed the statistical 

 method to determine the mutual action of two systems. The methods 

 he employs for this purpose, founded on the mathematical theory of 

 probabilities, are remarkable for their elegance and for greater 

 generality than had been attempted by previous writers. 



