833 
Let us further consider the c-space. If a varies slowly, the fixed 
points in it begin to move. Since in this motion the points do not 
disappear nor new points are formed, the density gw must satisfy 
the equation of continuity, i. e. our fundamental equation. As 
@ = const. is certainly a possible solution, w itself must satisfy the 
equation 
dw k doc, 
<= > ee — 0 . . . . . Ld . 13 
where 
zt De 
Ct 
in Da 
Or with the notation 
Dw dw k Qw De. 
Da E da i=l de, Da É 
in the equivalent forms 
Dw k de’. 
= 
— See ee cea oe CLS 
Da a ae dc. pee) 
or 
kde! 1D 
iol Me ore (13") 
i=1 00, w Da 
For the quantity on the left side — the “divergence” — we 
shall deduce another expression. 
The essential adiabatic invariants — & in number — satisfy the 
equations 
Dv. ov. as) 
SN Ch EN RPL ee omnes) 
Das | tape Terdege 
We shall suppose that the quantities vi can be expressed in the 
quantities c,(2= 1,2...) or . 
0(v,,.-+5%)) 
Ee oen Be 
Ò(e‚,-.-,C) 7 ed 
The properties of our system can be equally well described by 
the quantities v; as by the quantities c;. The (v, .. . vz)-space has the 
advantage over the c-space of being static, also with respect to the 
action of adiabatic influences. Let us now examine the mutual 
relation of the two spaces. 
To this end we shall consider the D-derivative of the determi- 
nant T: 
(16) 
