590 
In the case of anisotropy on the other hand PranrcK’s hypothesis 
of the energy steps is usually applied to each of the principal 
vibrations separately : 
Only those motions are steady for which the energy belonging to 
the two principal vibrations (¢, and ¢,) satisfies the equations: 
& 
es = == he sert liel 
Vv, Yr, 
Let », and r, approach infinitely slowly to the common value r, 
then the quotients (35), being adiabatic invariants, remain constant 
and the total energy e of the system satisfies finally the equation: 
é a 
aa a Ce ae Se. © oy ae ee (36) 
which is in good agreement with (34). *) 
On the other hand it is not evident, why in this way only one 
of the discrete values (33) for the moment of momentum would be 
obtained. 
When rv, and », have already become nearly equal to each other 
the motion takes place in a figure of Lissasous, which ‘‘densely”’ 
covers a rectangle, (with sides parallel to the axes &, and &, pro- 
portional to We, and We). 
During this motion the moment of momentum does not remain 
constant, but oscillates slowly to and fro between zero (at the moments 
when the motion takes place nearly exactly along the diagonals of 
the rectangle) and certain maximal positive and negative limits *) 
(at those moments in which the motion takes place on the largest 
ellipse described in the rectangle). 
The more vr, and rv, approach to each other, the slower these 
oscillations of the moment of momentum are. Which value of the 
moment of momentum is reached after an infinitely slow adiabatic 
change in the case of 1sotropy depends therefore on a double 
boundary passage. 
It is thus evident, that the adiabatic hypothesis needs a specia 
completion to render the result in this case (and in analogous cases 
of the passage of singular motions) quite definite. It is to be hoped 
that a plausible completion will be found, which leads us to Som- 
MERFELD's values (33) of the moment of momentum. 
As we can pass adiabatically from the elastic central force to 
each arbitrary central force (comp. $ 7), the quanta might be 
1) [Remark at the correction]. P. Epstein drew my attention to the fact, that 
there is no good agreement between (36) and (34), for the circular motion 7’ must 
be equal to O, 2 arbitrary ; in (36) however 7, = #3, therefore ,-+ 7 even. 
i 
*)) as Serra ah. 
