for) 
The value of @| is equal to that of P| for the corresponding 
s t 
. . . * ge . as . 
interval, as is easily seen if one thinks that — represents the time 
7 
taken by the system to pass through ds. The stationary line-ensemble 
can therefore be used to determine the value of observed quantities. 
I shall now consider another kind ef ensembles. We divide the 
space La in elements in the following manner. Let P be a point 
of this space and £ the trajectory through this point. Put in P 
a space fs, ; perpendicular to ZL and in the section of /,,—; and 
Ro, 1 a (22—1)-dimensional element of volume do, containing P. 
Through the limits of do the lines ZL are drawn and in a point 
P' on L at a distance ds from P a space F's,-) perpendicular to 
L is constructed. This cuts the paths drawn from do; in the space 
(on, Roi) an element of volume is formed, which is equal to 
do (differing only from it in the order of ds). 
The volume of the part of the space’ Zo, limited by the elements 
do and the lines Z amounts to ds do. 
We take the element do so small that v7 may be thought equal for 
all points of it and fill the element with a density — with repres- 
» 
enting points. The number of systems in do ds amounts to 
A 
do ds — , 
5 
or if we put do ds = dw 
A 
dw 
+ 
The mean value in such an ensemble shall be defined by 
| g dw 
Sa et 
á hes dw 
| 5 v 
the integration has to be extended over the whole space Mn. 
as 
=~] 
— 
The definition has been chosen thus because the contribution for a 
strip of the breadth do between P and /” (s, and s,) then amounts to 
