24 J. E. Moore — Electrical Discharge from the point 



tion for the flow of heat in an infinite cylinder, to the problem 

 of the variable electric flow in submarine cables. 



The mathematical theories of heat and electricity are identi- 

 cal in form, so that one can pass from a given theorem in the 

 theory of heat to the corresponding theorem in electricity, by 

 merely changing such quantities as temperature to potential, 

 thermal conductivity to electrical conductivity, etc. 



The comment that has always been made on this remarkable 

 correspondence is, that it seems highly probable that these 

 analogies are consequences of hitherto undiscovered relations 

 existing between the two classes of phenomena. 



The kinetic theory of gases rests upon two fundamental 

 hypotheses. First, that matter is not a continuous plenum, 

 but that it is made up of minute, discrete parts, which are in 

 constant agitation. Throughout the kinetic theory, these parts 

 are called molecules ; but it is clearly stated that they are not 

 necessarily u chemical molecules." Second, that these mole- 

 cules repel one another with a force, acting in the line of their 

 centers of gravity, whose magnitude depends upon the mass of 

 the molecules, and on some function of the distance between 

 their centers. In some cases, the equivalent of this last 

 hypothesis, viz : that molecules are hard, perfectly elastic 

 spheres, has been used to establish theorems in the kinetic 

 theory. 



From these two hypotheses, Clausius, Maxwell, Beynolds, 

 and others, have deduced, by ordinary processes of rational 

 mechanics, almost all the known properties of gases. Thus, 

 according to the kinetic theory, the pressure in a homogeneous 

 gas, at uniform temperature, is ipv 2 , while its temperature is 

 kmv* ; where p is the gas density, v the mean velocity of the 

 gas molecules, m the mass of the molecules (supposed all the 

 same), and Tc a constant depending on the gas. 



§ 3. Maxwell has considered, in his paper, " On the 

 Dynamical Theory of Gases,"* the pressures due to the motion 

 of a medium composed of moving molecules. His argument 

 is briefly as follows : 



Let the medium move, with reference to a fixed system of 

 rectangular coordinates, so that the velocity of flow referred 

 to the three axes shall be u, v, and w. Let a second system of 

 rectangular coordinates move with the medium, with velocity, 

 u, v, and w. Call f, 77, and f the component velocities of the 

 motions of agitation of any molecule, when referred to this 

 second system. The actual velocity of any molecule at any 

 instant will then be w+f, v+rj, and w + %. The pressures in 

 the moving medium will then be, as Maxwell has shown, 



* Phil. Trans. Roy. Soc, vol. clvii, p. 49. 



