Mr. J. C. Maxwell on the Dynamical Theory of Gases. 137 



tions of matter can coincide in the same place, being deductions 

 from our experiments with bodies sensible to us, have no ap- 

 plication to the theory of molecules. 



The actual energy of a moving body consists of two parts, 

 one due to the motion of its centre of gravity, and the other due 

 to the motions of its parts relative to the centre of gravity. If 

 the body is of invariable form, the motions of its parts relative 

 to the centre of gravity consist entirely of rotation ; but if the 

 parts of the body are not rigidly connected, their motions may 

 consist of oscillations of various kinds, as well as rotation of the 

 whole body. 



The mutual interference of the molecules in their courses will 

 cause their energy of motion to be distributed in a certain ratio 

 between that due to the motion of the centre of gravity and that 

 due to the rotation or other internal motion. If the molecules 

 are pure centres of force, there can be no energy of rotation, 

 and the whole energy is reduced to that of translation ; but in 

 all other cases the whole energy of the molecule may be repre- 

 sented by |Mi> 2 /3, where /3 is the ratio of the total energy to the 

 energy of translation. The ratio (3 will be different for every 

 molecule, and will be different for the same molecule after every 

 encounter with another molecule, but it will have an average 

 value depending on the nature of the molecules, as has been 

 shown by Clausius. The value of /3 can be determined if we 

 know either of the specific heats of the gas, or the ratio between 

 them. 



The method of investigation which I shall adopt in the fol- 

 lowing paper is to determine the mean values of the following- 

 functions of the velocity of all the molecules of a given kind 

 within an element of volume : — 



(a) the mean velocity resolved parallel to each of the coordi- 

 nate axes ; 



(/3) the mean values of functions of two dimensions of these 

 component velocities; 



(7) the mean values of functions of three dimensions of these 

 velocities. 



The rate of translation of the gas, whether by itself or by 

 diffusion through another gas, is given by (a), the pressure of 

 the gas on any plane, whether normal or tangential to the plane, 

 is given by (/3), and the rate of conduction of heat through the 

 gas is given by (y) . 



I propose to determine the variations of these quantities, due, 

 1st, to the encounters of the molecules with others of the same 

 system or of a different system ; 2nd, to the action of external 

 forces such as gravity; and 3rd, to the passage of molecules 

 through the boundary of the element of volume. 



