TRANSACTIONS OF SECTION A. 385 
consider, say, only the first 1010! terms: we have a finite series of terms, 
and until millions of years have elapsed the physical problem is perfectly well 
represented by this finite series, for which questions of convergence have no 
meaning. 
Professor Lorentz: In reply to Professor Love’s interesting remarks, I should 
like to say that it is precisely one of the objects of the physical theory of radiation 
to explain why the energy of the black radiation can be represented by a conver- 
gent series. The old theories lead to a different result, but this in itself would 
not be a physical contradiction or impossibility; it would simply mean that all 
energy will in the end be transferred to the ether and that it will continually 
take the form of shorter waves, a really final state never being reached. Our 
aim must be to account for a true state of equilibrium, in which there is a finite 
ratio between the parts of the energy that are found in a ponderable body 
enclosed in an envelope and in the surrounding ether. We shall also have to 
assign a physical meaning to the universal constant 4 occurring in the formula 
by which Planck calculates this ratio. 
Sir J. Larmor derived the impression from the trend of the discussion that it 
would turn out that in the new low-temperature determinations there was nothing 
in direct conflict with the classical dynamical principles. The essential argu- 
ment for equipartition among vibrational types of energy is, briefly, that these 
types enter similarly into the total energy, and thus, other things being in- 
different, there is no reason that can be assigned to the contrary. They enter 
similarly merely because the energy is a sum of squares of their ‘momentoids.’ 
But ‘other things may not be indifferent ; for example, in the kinetics of a rotating 
atmosphere the distribution of energy must be modified so as to maintain con- 
stancy of the angular momentum as well as of the energy, giving as the result 
equipartition relative to the rotation instead of absolutely. Moreover, in an 
isolated region of xther there is no way open for any interchange of energy at 
all between one type of vibration and another; here also other things are not 
indifferent. The exchange must be effected through the mediation of material 
molecules. It is true that a single electron, moving erratically between com- 
plete reflections from the ideal impervious walls of the chamber, would suffice. 
But the structure of an electron, including the mechanisms by which it exchanges 
energy with the ether, is totally unknown. Such a fundamental fact as the 
pressure of radiation is involved in that structure; we can only establish it 
theoretically as pressure on systems of electrons; it must be transmitted by the 
ether in some way, but we do not know how, except by speculating, for it is a 
second-order phenomenon not involved in the Maxwellian linear scheme of equa- 
tions. In the very intense kinetic: phenomena in the mechanism of the electrons 
or molecules, by which they serve to transfer energy from one type of ethereal 
vibration to other types, the energy must be expressible as a sum of squares of 
definite momentoids if the transfer is to lead ultimately to equipartition. This 
restriction in its form is unlikely; the transfer may even be of a discontinuous 
character, involving release of electrons into freedom. The Planck formula for 
the constitution of natural free radiation may be obtained by statistical reason- 
ing, strictly on the lines of Boltzmann’s entropy theory for gases, in which atoms 
or vibrators are not considered at all, but the pressure of radiation is introduced 
instead, as I have tried to show (Proc. Roy. Soc. 1906); the only implication is 
that the process of interchange of ethereal energy between different vibrational 
types, by the mediation of matter, though unknown, must be such as to provide 
a pressure of radiation. If, then, there is no reason to press equipartition as 
regards free natural radiation, the atomic vibrations, which are set up by its 
agency and must be in equilibrium with it, are also absolved therefrom. 
The new knowledge relating to specific heats at very low temperatures has 
already suggested most interesting speculations and tentative adjustments, and 
will certainly lead to definite expansion of our theoretical schemes; but it can 
be held that there is nothing in it that is destructive to the principles of physics 
which have led to so rich a harvest of discovery and synthesis in the past. 
Mr. Jeans: As the time is so short, I must only touch on a very few of the 
many interesting points that have been raised. 
With regard to Professor Love’s suggestion that the radiation formula might 
be obtained by the old mechanics from an analysis of electron orbits, two remarks 
19S, Cc ¢ 
