391 
electric variables a change in the character of the centres of light- 
emission takes place. 
After J. Srark had already derived this theoretically for slight 
optical thickness (Ann. d. Phys. (4) 14, 506, (1904) ), C. D. Cuup 
has returned to this subject in some papers (Phil. Mag. (6) 27, 278 
(14); Phys. Rev. (2) 15, 33 (’20) ). 
From the fact itself that the quantity of emitted light 1s approxi- 
mately proportional to the current strength, follows that in principle 
the emission of light is owing neither to ionisation, nor to recombina- 
tion (after previous ionisation). It is known that it has been made 
experimentally probable, that emission of light can take place also 
without ionisation. It is, indeed, in agreement with the theory of 
Bour c.s, which states that radiation takes place when an electron 
crosses from a path that lies more on the outside to one that lies 
more on the inside of the atom, to which the supposition may be added 
that in most cases of electric discharge the electron that changes from 
one path to another, bas never been entirely separated from the nucleus. 
Cuip shows that if the emission of light were owing to the 
recombination of ions, this emission would have to be approximately 
proportional to the second power of the current strength, and the 
same thing would hold, when ionisation was considered as the 
cause of the light emission. While the number of recombinations 
resulting from complete ionisation depends on the product of positive 
_ and negative ions, and is, therefore, proportional to the second power 
of the electrons present, the number of partial ionisations’) depends 
only on the number of electrons present that gives rise to the partial 
ionisation. Consequently this is proportional to the first power of 
the electrons present. 
The previous calculations’) have taught that free electrons are really 
present in the luminous column in great numbers, and that they 
bring about the current conveyance in a preponderating degree. This 
proves that the current is approximately proportional to the number 
of electrons present. The number of partial ionisations is proportional 
to the latter, from which the proportionality of the light-emission 
to the current strength follows directly. For it will readily be seen 
that the number of recombinations ensuing from partial ionisation 
is in direct ratio to the number of partial ionisations. 
6. It is clear that a more accurate knowledge of what takes place 
with mixtures of gases, can give us a clearer insight with regard to 
') Let by partial ionisation be understood the increase of the distance of one 
of the electrons from the atomic nucleus, without it breaking away from it. 
2) Cf § 5c. note and § 6. 
