1259 



seems arbitrary at lirst siglit, but it seems to me that it will not 

 be thought so arbitrarjs when it is full)' realized what the friction 

 given by Stokes's formula, really is. 



Let us imagine a particle suspended in a gas which is made to 

 fall under the influence of gravitation, in order to determine its 

 radius in the usual way. Here too there is a measurable movement 

 (here the motion of falling), and a thermal movement. Now we get 

 a correct formula for the measurable motion by assuming that a 

 force of viscosity — Qji^az opposes this movement. And as we 

 demonstrated that also in the Brownian movement a force: a con- 

 stant X the measurable velocity, opposes the measurable movement, 

 it is very natural to assign the value — Qnï^a to this constant. 

 This becomes still more plausible when we think of equation (C) 



It contains that if there is a velocity x, this will try to bring 



about a force in opposite sense; hence to cause the product force 



X velocity to become negative. It is counteracted in this by the 



fact that the force tries to develop a velocity in its own sense ; 



hence to make the product in question positive. If .v is the thermal 



velocity, the two tendencies counterbalance each other: the product 



remains zero on an average. The thermal velocity varies its sign 



repeatedly. If, however, there is a velocity in the same sense for a 



dS: . , . 



longer time, — continues to keep the same sign all this time, and 

 dt 



a force opposite to that velocity will be developed. And this will 



take place independent whether this velocity of longer duration is 



owing to gravity, or whether it represents a measurable velocity of 



the Brownian movement. 



When we assign this value to r', (7) yields: 



— 1 



A'nrQ -t 



Q is defined by equation (5). It would, however, not be possible 



to derive its value from it without introducing further, perhaps 



pretty uncertain, hypotheses. Fortunately, however, it is possible to 



find a value for A' in another way, namely by multiplying (6) by A, 



dA ■ 1 d'A 



bearing in mind that ==r.ran(l ir{t)^= . We then find: 



dt m dt'' 



^ d'A d'A' /dAy ] ^ ^ A' 



dt' dt' V ''« J n> t 



