TRANSACTIONS OF SECTION A. 905 
4, On a Law concerning Radiation. By Professor Scuuster, Ph.D., F.R.S. 
5. On Boltzmann’s Theorem. By Professor W. M. Hicks, M.A., E.R.S. 
It has always seemed to me that one of the strongest objections to Boltzmann’s 
theorem lay in the supposition that the mean energy of any kind of vibration of 
any atom must be equal to that of translation in any direction, and therefore 
capable of unlimited increase. It is not difficult to conceive of systems where this 
cannot be true, as, for instance, a rigid spherical shell with a vortex ring inside. In 
this system the internal energy may be made to vary within certain limits, but 
cannot possibly be increased beyond a certain amount. The fact seems to be that 
Maxwell’s theorem and Boltzmann’s extension do not necessarily correspond to the 
actual state, but are only proved to give possible distributions of energy which are 
permanent. In any case, however, even if we assume the law of distribution of 
momenta given by them to be true, I can see no reason to justify us in assuming, 
either that all values of any momentum from — o to + © are possible, as is done 
in Watson’s proof, or even that all values consistent with the equation of energy 
are possible, as is done in Maxwell’s proof. If in Watson's proof all the non- 
existent states are left out of account, the form of solution is unaltered, but the 
energy will no longer be equally distributed amongst the co-ordinates. In this 
case, therefore, there is no difficulty in accounting for the ratio of the two specific 
heats in different cases, although it is not possible to predict it until the general 
constitution of the atom is known. Maxwell’s proof takes account of the whole 
history of a molecule, and not merely of what happens at a collision as in 
Watson’s. But it cannot be generally true that all states consistent with the 
equation of energy are possible. For instance there may be geometrical relations 
which prevent it, but which do not appear in that equation; as for example in a 
system of mutually attracting spheres. The equation of energy would permit of 
the infinite velocities due to an infinitely near approach of the centres of two 
spheres, a state which cannot exist owing to the finite size of the spheres. Another 
ease is where the integrals of the equations of motion of the atom introduce 
relations between different momenta, as, for example, where part of the system 
consists of connected gyrostats. 
6. The Rate of Explosion of Hydrogen and Oxygen. By H. B. Dixon, M.A. 
The author has continued his experiments on the velocity of explosion of electro- 
lytic gas. His results confirm those of Berthelot that the explosion is propagated 
at a constant velocity which is independent of the diameter of the tube. With a 
tube 100 metres long the mean of ten experiments gave a velocity of 2,819 metres 
per second, with a probable error of four metres. This velocity is in close agree- 
ment with the mean velocity of translation of the steam molecules produced in 
the reaction calculated on the supposition that all the heat produced is retained in 
the steam. The calculated velocity is 2,831 metres per second. 
7. Report of the Committee for constructing and issuing practical Standards 
for use in Electrical Measurements.—See Reports, p. 31. 
8. Report on Hlectrical Theories. By Professor J. J. THomson, M.A., 
F-.R.S.—See Reports, p. 97. 
9. On Constant Gravitational Instruments for measuring Electric Currents 
and Potentials. By Professor Sir W. THomson, LL.D., F.R.S. 
‘These instruments, the author stated, were parts of two series of electric mea- 
suring instruments, for current and potential, which he was now working out. In 
the two current instruments—the milliamperemeter and the hecto-amperemeter— 
