481 
One of these methods, viz. that of introducing as kinematical relation 
the condition that the moment of momentum of each electron must 
NAN 
preserve the same value (==) is only touched upon in that paper ') 
Jt 
and not fully worked out. [t seems to me, however, that this may 
be done in the following way. 
The equations expressing these conditions can be written as follows: 
] 
mr ay, = ay dt | 
ua | 
Be Solna AE SPP Mee ete 
D 
mr,” dy, =~ dt 
JT 
Al 
~ 
(m: mass of the electron; 
r: radius of the orbit; 
y: angle of position). 
By their form they recall the equations between infinitesimal 
changes of the coordinates in a non-holonomic system; only 
dt also appears here. Now we may try to form the equations of 
motion in a way analogous to the treatment of non-holonomic 
systems by introducing into the formula of p’ALEMBERT’s principle 
auxiliary forces Q, which do not come into play in any virtual 
displacement. A virtual displacement will be defined as an arbitrary 
variation of the coordinates, subjected to the relations: 
mr, OP, = 05) 
mr? dp, = 0 | 
Or: 
der = dpc 0, 
which are derived from (1) by taking df= 0. It appears that in a 
virtual displacement the position angles of the electrons must not be 
varied; from this it follows easily that only tangential auxiliary 
forces Q, and Q, may be introduced (i.e. forces which act upon the 
coordinates wp, and w,), which have the task of ensuring the constancy 
of the moment of momentum. 
Deduction of the equations of motion. 
A. Free vibrations. 
Notation. Distance of the nuclei: 2a (this is regarded as a 
constant). 
Radius of the orbit of the electrons in the normal state: /. (For 
H,: R=avs3; He, to which the calculation likewise applies, has 
1) Le. p. 1081. 
od 
Proceedings Royal Acad. Amsterdam Vol. XIX. 
