6J8 



molecules by the irregular, accelerating forces into molar energy of 

 (lie particle, and of this again by the resisting forces into molecular 



energy. 



Also I he molecular velocities are <is a whole independent of 

 those of the particle, but the molecules can be dixided into a large 

 majority the mean velocity of which differs too little from that of the 

 particle, and into smallercomplexes whose velocities dilFei- too much from 

 that. The first gi'oup Joins the motion of the particle, the second 

 causes the accelerating forces. These forces, however, are not only 

 caused by accidental deviations of the velocity, but also by accidental 

 deviations of density. The relative dimensions of the molecules, 

 the particles and the free path agree with the above considerations. 

 While the order of magnitiule of the molecules is 1 ()"'', we generally 

 find for that of the particles about J0~^, the free path in the fluid 

 being of the order 10~^. We thus can represent the dimensions of 

 the molecules and the particles on a scale by I mm and J dm, 

 while then the free path would become 1 cm. As a rough approxi- 

 mation we may assume that in a fluid 10^ molecules are acting at 

 the same time on the particle (of the same order of magnitude as 

 the ruimber that can cover the whole surface) and in a gas lü\ 

 The collisions which keep the particle in motion are therefore due 

 to accidentally arising complexes of these molecules. 



§ 2. Now we find for (he mean distance travelled by a particle 



/?7' 1 



Einstein's formula A'' = — .t, when we take for the friclional 



resistance n^=6.-rCr/r. This value has been deduced by Stokes on 

 the assumption that the fluid is incompressible and that there is not 

 any sliding at the surface, while the velocity may not be too great. 

 It is however questionable, whether it is a allowed to assume this 

 absence of sliding. 



Cunningham has tried the supposition that the velocity of the fluid 

 at the surface of the particle is kv, so that the relative velocity of 

 the particle with respect to the adjoining fluid would be v — kv. 

 Stokes' formula would then give for the resistance W ^=:Q:i^akv. 

 Cunningham now calculated this k in the following way. 



As has been mentioned above he found for the resistance by 



II- -1 ^ I X fiMm 



purely kinetic considerations the value - a^vn I / ; where 



3 1/ {M-\rm)h 



V represents the relative velocity. This would now become 



