94 Prof. L. Boltzmann on some Questions 



his treatise " On the Equilibrium of Potential Energy amongst 

 Gaseous Molecules," * was the first to employ. 



I assume that we have a gas constituted in the usual way 

 entirely of similarly constituted monatomic gaseous molecules, 

 and enclosed in a vessel bounded on all sides by solid walls. 

 For the sake of simplicity we will suppose the form of the 

 vessel unalterable. Let each molecule be a solid absolutely 

 elastic sphere of mass m, which also is infinitely little de- 

 formed upon impact, and whose diameter is vanishingly small 

 in comparison with the mean path. We also suppose the 

 molecules to be reflected against the walls of the vessel as 

 perfectly elastic. 



Besides these elastic forces, now let external forces act upon 

 the gaseous molecules, and let mX, mY, mZ be the compo- 

 nents, estimated along the axes of coordinates of the external 

 force which acts upon a molecule the coordinates of whose 

 centre are x, y, z. Let these external forces be independent 

 of the time, but have a potential, and let them be nearly con- 

 stant within a space of the dimensions of a mean path. We 

 will construct the diagram of velocities by drawing from the 

 centre of coordinates a straight line to represent the velocity 

 of each molecule in direction and magnitude. We will call 

 the end-points of the straight lines thus obtained the "velocity- 

 points " of the corresponding molecules. From all the mole- 

 cules we choose those for which the coordinates of the centre 

 lie between the limits 



at and as + das j ynndy + dy, z and z + dz; . (1) 



and the component-velocities between the limits 



£and£-M£, V and v + dv, £and £+df; . . (2) 



and of these we will say that they lie in the parallelepiped 

 dx dy dz, and their velocity-point in the parallelepiped d% dn d£. 

 The number of these molecules will be denoted by 



/(•*, V, h £ V, £ do dco, . . . . (3) 

 where 



do = dx dy dz, dw = dg dr) d%. 



We write here also the time t under the functional sign in 

 order to include the general case that the gas is in motion 

 under the influence of external forces : for the condition of rest, 

 of course, the function / must be independent of the time. 



Let us now, following Lorentz, imagine a second function 



* H. A. Lorentz, Wien. Sitmtngsber. vol. xcv. p. 117 (1887). 



