829 
If we suppose that the condition is stationary : 
do 
= 
it follows that: @ is a function of those integrals which do not 
contain ¢ explicitly, ie. of (2n—1) integrals, if only, as we shall 
suppose all the time, H does not depend on ¢ explicitly. 
We are at liberty to understand by o the density of probability 
a posteriori or a priori. When applied to the theory of quanta our 
result expresses the fact, that the quanta-quantities are functions of the 
(2n—1) integrals of equations (1) which are independent of t. 
Replacing the 2n-dimensional phase-space (pi,q;) by the corrre- 
sponding integral space (c;,t;)*) the “‘path” of the system is a straight 
line parallel to the t-axis. We can describe these lines either by 
making ¢ increase, i.e. by following a definite system in its motion, 
or by keeping ¢ constant and varying r, i.e. considering together 
all the systems with given c,...cn?f,....t» and all possible values 
Ott. 
fo ee 3) 
§ 2. H contains a variable parameter. 
If H contains a parameter which may either have a constant 
value as in the case just considered or vary slowly ®), the quantities 
c, and ¢, are no longer constant, but variable; they have to satisfy 
the following “equations of motion’’*): 
A 0K : Ook 
SS SS = —j . . . . . . 3 
Bi at, ; t de. ( ) 
where: 
Vv. 
K = €, + & i), ep an oh tere (4) 
0a 
1) As in a previous communication we write the integrals of equations (1) 
in the form: 
Cg = Coach oe ee 
and 
“OV OV OV 
a zet rt, ao = ae ae de 
2 n 
where c,...,¢n,T,h,...,¢ represent the 2m integration-constants and V 
Jacosi’s. characteristic function. Comp. Proc. XXI, p. 1112, 1919. 
*) The slowness is expressed in the fact, that H contains only a, not the 
correspondiug momentum. 
3) Proc. le. 
ET tny 
