1333 
; 3 RTtt 
Je es TA ee . . : s ‘ z 3 (6) 
2 Nm 
This expression is in perfect agreement with a formula, which 
has been derived by a purely kinetic method by one of us. ') 
With Maxwerr. we may Sad for tv’ 
1 Mm 
2 oe on Mm RT 
in which 6 is equal to the sum of the radii of the particle and of 
the molecule, hence practically ee to a. 
' 
— 
On account of this equation (4) finally becomes : 
La Pan t 
—- — Ce ea er AZ) 
GT N oa” 
§ 5. The invalidity of Sroxes’ formula for particles with dimen- 
sions of the order of the lengths of free patb of the medium or 
smaller, has been pointed out by CUNNINGHAM *). STOKES supposes 
that the surrounding molecules are carried along by the moving 
particle, so that on the surface of the particle they have on an 
average the same velocity as the particle itself. CUNNINGHAM takes 
the sliding into account and supposes that the particle moving with 
a velocity v imparts to the surrounding molecules a velocity of mass 
kk, an interaction through collisions being added to this, in which 
the velocities of the molecules are independent of that of the particle. 
The value % can be calculated from the condition that under the 
action of a constant force the velocity v will be constant, and 
3 pee 1\- 
k={ 1+ — - ) 
( 4 IN 
is found, in which / represents the mean free path of the molecules. 
In this way CUNNINGHAM derives a force of friction : 
X = 62abv | 1 : ae an 8 
ASO v 5 = . : e e 
A 7 4 a, (8) 
If we now calculate A* in the way originally indicated by Erysrrin, 
substituting, however, expression (8) for the value Y = 67a%y, which 
the force of friction according to Stokes’ formula would possess, we 
8 6 l , 
get an expression which for — — small, of course passes again into 
a 
EINsTEIN’s formula. For — = large it yields, however, a formula 
a 
}) A, SNETHLAGE. This kinetic derivation will probably shortly be published in 
another paper. 
2) CUNNINGHAM. Proc. Roy. Soc. Serie A Vol. 83 p. 357. 1910. 
86* 
