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TRANSACTIONS OF SECTION A. 383 
sure that this would be of no use at all, and that, whatever be the motion of the 
electrons, we shall always fall back on Lord Rayleigh’s formula, so long as we 
apply the old electro-magnetic equations. This is a most serious difficulty, and 
we cannot escape from it by saying that perhaps the free electrons contribute 
but a small part to the total radiation. It is inadmissible that, in addition 
to a mechanism leading to Planck’s formula, there should be another, however 
feeble be its influence, that would give us a different law. Moreover, it must 
be kept in mind that the explanation of an electric current by the theory of 
electrons requires at all events some free mobility of these particles, and that 
we come across the same difficulty when we consider an electrolytic substance 
partly filling an enclosed space. The motion of the ions would produce a field 
of radiation that would certainly be determined by Lord Rayleigh’s formula if 
the old theories were true. 
It will, therefore, not suffice to introduce the notion of quanta into the 
theory of vibrators, but, as Mr. Jeans has suggested, we shall most probably 
have to modify Maxwell’s equations for those parts of space where there is an 
electric charge. 
(Added after the discussion.) Even if we confine ourselves to the equilibrium 
between the radiation and a vibrator, there is one problem in which the old 
theory encounters a difficulty. It is that of the motion of translation, the 
Brownian movement, as we may call it, which the vibrator will take under the 
influence of a field of radiation corresponding to a definite temperature. One 
would expect its kinetic energy to be equal to that of a gaseous molecule at the 
same temperature. Einstein and Hopf have found, however, a much smaller 
value. 
Professor E. PrinesHemm: It is very satisfactory that Mr. Jeans now has 
abandoned his former doubts of the results found by experiment. So this dis- 
cussion on radiation seems to have great importance in showing that on the 
general question there is an agreement between all physicists who work in this 
matter, although opinions may differ in the details. The theoretical difficulties 
and the chief points where theory requires improvement have been pointed out 
by Messrs. Jeans and Lorentz. I wish to draw attention to the problems which 
are to be solved by experiments. First of all, there is still a remarkable dis- 
agreement between the different measurements of the universal constants of 
radiation, as well of the constant o of Stefan’s law as of the constant h of 
Planck’s law. Here new experiments are necessary. Further, the laws of 
black radiation must be examined through a larger range of temperature and 
wave-length than has been done at present. Finally, the radiation of bodies 
other than black must be studied more and more. Here the metals have the 
greatest theoretical interest, since Aschkinass has shown how the distribution of 
energy in the spectrum of metals can be calculated by means of the laws of black 
radiation and Maxwell’s electro-magnetic theory. And as the metals are the 
material used in modern types of incandescent lamps this question is also of 
great practical importance. The chief difficulty of these experiments consists 
in the determination of the true temperature of the radiating metals. Recently 
my friend, Professor 0. Lummer, in Breslau, has suggested a method which 
seems to solve this problem in a very elegant way. 
Professor A. E. H, Love: I am unable to accept the view that, in order to 
account for the facts about radiation, existing theories of dynamics and electro- 
dynamics need to be supplemented by the theory of quanta. Part of the 
evidence in favour of this view has been derived from an application of the 
principle of equipartition of energy to a system consisting of ether and matter 
in an enclosure bounded by perfectly reflecting walls. Such a system has an 
infinite number of degrees of freedom, and the principle of equipartition cannot 
be applied without modification to any such system. The ethereal kinetic energy 
would be expressed by an infinite series of the form 
Uy + Uy + ug +... ad inf., 
in which there is one term answering to each degree of freedom, and the order 
of the terms is that of increase of the corresponding frequencies. In order that 
an infinite series may represent ethereal kinetic energy, or anything else, it is 
necessary that it should be convergent. In order that it may be convergent, it is 
