34 THE DYNAMICAL THEORY OF GASES. 



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 parta of the body are not rigidly connected, their motions may consist 

 tit' 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 represented by ^Mifft, 

 where is the ratio of the total energy to the energy of translation. The 

 ratio /8 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 ft 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 following 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 coordinate axes; 



() the mean values of functions of two dimensions of these component 

 velocities ; 



(y) 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. 



I shall then apply these calculations to the determination of the statical 

 cases of the final distribution of two gases under the action of gravity, the 



