1331 
path on an average passed over by a molecule in a definite direction. 
After it has been passed over, a new velocity will have arisen, 
and a new path / will begin, which is independent of the preceding 
one. During the time that the path / is covered, the direction of 
the velocity will therefore on an average turn 90°. Whether this 
change of velocity is then the result of the impact against a single 
other molecule, or of forces of attraction exerted by several sur- 
rounding molecules, is immaterial. In the same way we shall under- 
stand by r the Ame required on an average by the velocity to 
change its direction 90°. The / and r defined in this way we shall 
call the effective free path and the effective collision time. And it 
is this effective collision time whieh occurs in equation (3), as 
appears from the derivation, 
If we assign this meaning to / and rt, we think that the consi- 
derations on which Maxwerr’s derivation of the equations (4) are 
based, will also continue to be valid for liquids to a certain extent, 
and that it is to be expected that the + calculated in this way will 
be approximately equal to the quantity + occurring in equation (3). 
It is clear that this can only be the case to a certain extent. 
Thus in case of diffusion we always have to do with two substances, 
e.g. alcohol and water. We can, therefore, derive from the value 
of D eg. the / for alcohol molecules in water. But it is by no means 
sure that we may also use this /, when we want to know the / 
for alcohol molecules in alcohol or water molecules in water. 
Sut also the formulae for $ and x are open to objections. In his 
derivation MaxwerL took, namely, only convection of quantity of 
motion and energy into consideration. In a collision these quantities 
are, however, also ceded by one molecule to another. And it is 
clear that in consequence of this a correction must be applied, 
which will be mueb greater for liquids than for gases. 
We shall now examine in how far, in spite of the objections 
mentioned, the quantities + calculated from the equations (4) yield 
a value which can be used for the calculation of A“. We then 
find for some substances : 
Tt ie tp in water 
methylaleohol 1,0.10—!! 0,9.10—" ethylaleohol 1,6 .10—'4 
ethylaleohol 2,8  ,, |t ocr glycerine 1,6 „ 
water 0,7 os 0,7 - canesugar 5,4 ,, 
glycerine Dt DES ae ureum Dak ek. 
The index of + indicates from what quantity it has been calculated. 
86 
Proceedings Royal Acad. Amsterdam. Vol. XVIII. 
