1202 
the one case (96) being 77° in the second (9a) even 84°. The corres- 
ponding ranges are exceedingly much smaller than for the H-atoms 
emitted in the direction of the primary @-particles. 
These results agree with the result of RurHerrorD’s experiments’), 
who found al! the H-atoms to be propelled in the direction of the 
primary rays. The range of this secondary radiation was 28 cms, 
which gives R, = 0.028 em. or R, = 0.3) em. according as we use 
(9a) or (95). These values are too small for experimental verification, 
and were bound to escape detection. 
§ 7. Transition to the stationary orbits. Up to the present time 
the quantum theory has only been applied to systems whose members 
permanently move round each other at a finite distance, i.e. systems 
which in the LAPLACE-sense are stable. My attempt of 1916 (lc.) to 
apply the theory to the single passage of a particle through the 
sphere of action of a nucleus has not met with much sympathy 
among physicists. lt therefore seems necessary to submit the difference 
between the two cases to a careful conceptual analysis. 
The hypothesis of the theory as established by Bour consists of 
two parts: 1. There are certain preferential or stationary orbits in 
which the system moves without radiation. 2. If the initial state is 
not a stationary one, the system passes into a stationary state with 
the emission of energy in the form of radiation. It is quite possible, 
that the real process is only formally represented by this division, 
but it has been confirmed in:several cases and it forms for the 
present the only basis on which we can erect our further structures. 
As regards the existence of stationary orbits, there does not seem 
to be any reason, why the quantum conditions shouid be solely 
applicable to finite orbits. Our views on this point have been ex- 
pounded in $$ 3 and 4; but we shall try to strengthen them from 
a fresh point of view. The difference between motions which are 
finite and those which reach to infinity is expressed analytically by 
the fact, that for the former each cartesian co-ordinate may be 
represented as a Fourter-series according to angular variables, 
whereas this is impossible for the latter. Bonr has established a 
relation between the terms of this Fourimr-series and the transitions 
which on the quantum-theory are possible from one stationary orbit 
to another. 
In the case of the relativistie Kepler-motion the Cartesian co- 
ordinates are e= rcosp, y=rsing. For shortness putting 
1) E. RUTHERFORD, l.c. 
