( 420 ) 
sequence of the electric forces, we should not have found the true con- 
dition. The influence of the collisions may probably not be neglected. 
If the mutual collisions of the molecules took place in a perfectly 
irregular way, they would undoubtedly lessen the degree of regula- 
tion, and render the condition nearer irregular. The way of motion 
is however not only partially regulated with regard to the action 
of the electric forces on the molecules, but also with regard to the 
mutual collisions of the molecules. In order to explain this we 
consider two molecules which have come very near to each other. 
The forces exercised by the surrounding molecules will be about 
the same for both, and will tend to bring their internal motion more 
and more into syntony. Moreover each of the molecules absorbs part 
of the energy emitted by the other. On account of these two causes 
a partial regulation is brought about in the collisions of the mole- 
cules, of which it seems impossible to me to determine the influence 
without special hypotheses on the mechanism and even the form of 
the molecules, for which as yet all data are wanting. 
There is however another difficulty which makes me doubt whether 
the considerations of Prof. BOLTZMANN on the internal motion are 
applicable to the motion which causes radiation. 
For according to Prof. BOLTZMANN the internal energy would 
increase in proportion to that of the progressive motion of the mo- 
lecules, i.e. with the temperature. According to the law of STEFAN 
the emitted energy is proportional to the fourth power of the tem- 
perature. ‘These two results can only be brought into harmony by 
assuming that the absorption decreases strongly with the rise of the 
temperature. 
Properly speaking the law of Sreran holds good for the total 
quantity of emitted light and may perhaps only be applied for cases 
where a continuous spectrum is emitted. The wavelength, which 
has the greatest intensity depends however for a continuous spectrum 
on the temperature, so that for the light of a fixed wave-length 
the law of SrrFAN does not hold good. The displacement of the 
predominating wave-length is however not so great, that the law 
of STEFAN could not be applied with approximation. 
Let us assume that actually the internal energy increases propor- 
tional with the temperature, and so the quantity 01) with the root of 
the temperature. Let us represent two temperatures by 7 and Ty, 
the intensities of light emitted at that temperature by Zj and J, and 
") Proc. Royal Acad. of Sciences, Dec. 1899. Pag. 319. 
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