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which have to be quanticized'). A new proof will be given by 
establishing a connection between the adiabatic invarianis and the 
phase-space (below 18’). 
This connection, which will be found to arise in a natural way, 
with a concept derived from statistical mechanics, strengthens the bond 
between it and the theory of quanta, a bond which, as it seems to 
me, has gone into the background in the latest development of the 
theory or at least has not been sufficiently emphasized, although in my 
opinion it is of great importance. In view of this connection I think 
that the only justification of the expression ‘‘action-quantum” is the 
fact that it recalls to our mind the dimensions of the phase-extension. 
Another conception of great importance to the theory of quanta 
which will find a place in our classification is PLANCK’s*) coherence 
of degrees of freedom. To me it seems of fundamental importance. 
Its meaning will be found to appear very clearly by a juxtaposition 
of the properties of a conditionally periodic system and a BOLTZMANN 
“ergode’’. 
This coherence of degrees of freedom must be very clearly distin- 
guished from what is called ‘degeneration’ *). For instance from our 
point of view an ergodic system is to the highest degree coherent, 
but could in no case be called degenerated. For a degenerated system 
the number of essential adiabatic invariants is greater than that of 
the degrees of freedom, for a coherent system it is smaller. 
The question arises: must the supernumerary adiabatic invariants 
of a degenerated system be quanticised or, as suspected by Scnwarz- 
SCHILD *), is the number of quanta-conditions smaller for such a 
system for the normal case without degeneration? 
For the solution of these questions the three steps which have 
been taken viz. (1) establishment of the adiabatic invariants (2) 
selection of the essential ones and (3) “normalisation” of the latter 
are insufficient. In order to get nearer to the solution we must, I 
think, take into account, that the quanta-functions must have a 
meaning which is independent of the system of co-ordinates. We may 
undoubtedly postulate this: if the quanta-laws are really physical 
laws, they must necessarily satisfy this condition. The question is, 
how to formulate this new invariance of the quanta-functions? I 
shall not try to discuss it here in general; but only remark that 
1) M. PLANCK. Ann. d. Phys. 50 (1916) p. 392. 
*) M. PLANCK, l.c. 
8) K. SCHWARZSCHILD. Sitzungsber. Berlin 1916. P. Epstein Ann. d. Phys. 
51 (1916). p. 168. 
*) K. SCHWARZSCHILD, l.c. 
54* 
