THE KINETIC THEORY OF MATTER. 143 



is at the best merely an approximate representation, by supposing that 

 the centres of the molecules approach till they are, on an average, a dis- 

 tance s from each other, and that then they recede. It is often con- 

 venient, for calculation, to think of a sphere of action surrounding one 

 molecule of a colliding pair, and to concentrate our attention on the 

 centre only of the other molecule. We then regard the centre of the 

 first molecule as surrounded by a sphere of radius s, within which the 

 centre of the second molecule cannot penetrate, and we term the 

 radius of molecular action. We ought really to picture two spheres of 

 action, one round each molecule, and each of radius s/2, but the result is 

 the same. Since the molecular centres do not get within distance s, we 

 may regard s as the diameter of each molecular system. If the gas is 

 reduced to the liquid or the solid condition, we think of each molecule as 

 being just within the spheres of action of its neighbours all the time, and 

 we therefore regard s as indicating approximately the distance of a solid 

 or liquid molecule from its immediate neighbours. 



Dependence of the M.F.P. on Molecular Dimensions and on 



the Density Of the Gas. If the molecules were mere points, and if 

 they exerted forces upon each other only at infinitely small range, the 

 M.F.P. would be infinitely great so long as the number of molecules in 

 a finite space was finite. For consider a single molecule projected from 

 a point. The spheres of action of the surrounding molecules within any 

 finite distance would fill up an infinitely small fraction of what we may 

 term its field of vision, since the total solid angle subtended by any finite 

 number of molecules at the point would be infinitely small. If then 

 a line were drawn in any assigned direction the chance that it went 

 through another molecular point within a finite distance would be in- 

 finitely small. But if we assign a finite value to the radius of molecular 

 action and now think of a molecule as projected from a point, in what- 

 ever direction we draw the line of projection it is practically certain that 

 within some finite distance it will impinge on the sphere of action of 

 another molecule. This is illustrated by a shower of rain which has only 

 to be of sufficient breadth to hide entirely objects beyond it. 



We may form a mental picture of the M.F.P. by imagining that all 

 the molecules but one are fixed in the configuration which they have at 

 a given instant. We may then project the one from its position in turn 

 in all directions till it comes into collision with another molecule, and 

 take the average distance traversed before collision as equal to the M.F.P. 

 The fixing of the molecules, which we have assumed for simplicity, gives 

 us, as Clausius and Maxwell showed, too great a value for the M.F.P. 

 It is easy to see that the motion of the molecules increases the chance of 

 collision, for imagine a spherical shell 2s thick drawn at a distance from 

 the point of projection. The projected molecule will travel through this 

 in time 2s/V, and meanwhile a molecule within the shell, and having the 

 same velocity, will travel a distance V x 2s/V = 2s, and sweep out an area 

 4s 2 . The effective area subtended at the centre of projection by the 

 molecule will be ?rs 2 + a fraction of 4s 2 , the fraction depending on the 

 inclination of the motion to the direction of travel of the projected mole- 

 cule. Thus the chance of collision is increased. It can be shown to be 

 \/2 times as great as the chance when only one molecule moves. 



If the number of molecules per c.c. remains the same, while the cross 



