NovVEMBER 6, 1913]| 
WAT ORE 395 
consequence the papers and discussions were of a 
very high order of excellence. 
The address of Sir Oliver Lodge was of special 
interest, as in it he touched on the main subjects 
of discussion in the section. The address has been 
published in full in an earlier number of NaturE, so 
that there is no need for further remark here. The 
sectional president’s address has also appeared in full 
in Nature, and there is similarly no call to deal with 
it further in this place. It was listened to by a 
crowded audience, and formed a fitting opening to a 
meeting that proved itself of great importance, and 
in which the interest was kept up till the last day. 
The address of Dr. Baker, after a vote of thanks 
proposed by Sir Oliver Lodge and seconded by Lord 
Rayleigh, was followed by a paper by Prof. Barkla 
on the nature of X-rays. This subject has practically 
ceased to be controversial except as it has passed 
over into the general subject of radiation. Prof. 
Barkla gave an outline of the evidence in favour of 
the undulatory theory, of which he has always been 
a keen exponent, and which is now accepted by all 
physicists. Sir J. J. Thomson and Prof. Rutherford 
spoke in the following discussion, the former paying 
a well-deserved compliment to Prof. Barkla on the 
large amount of our knowledge of X-rays which is 
due to him. Prof. Rutherford laid stress on some of 
the still outstanding difficulties in the subject. The 
discussion was not so interesting as it would have 
been a year ago, when the supporters of the cor- 
puscular theory would have been in force. This paper 
was followed by one from Sir J. J. Thomson on the 
structure of the atom. This was a brilliant attempt 
to construct an atom which would account for some 
of the evidence for the quantum theory of energy. 
The paper was delivered with the clearness and bold- 
ness now always expected from Sir J. J. Thomson, 
and it will be long before his illustration of the 
quantum theory by pint-pots is forgotten. 
The next paper was by Prof. H. A. Lorentz. Prof. 
Lorentz is known to all physicists as the leading 
exponent of all questions involving the interactions 
of zther and matter. His presence at the Birming- 
ham meeting added greatly to the interest and value 
of the discussions. His command of English, his 
extraordinary capacity for exposition, and his quiet 
humour made his paper and his speeches in discus- 
sion one of the most enjoyable features of the pro- 
ceedings of Section A. The subject of the paper 
was, “The Relation between Entropy and Prob- 
ability.” The entropy of a body in a certain state is 
intimately connected with the probability of that 
state. Boltzmann has deduced the expression of the 
relation in his well-known formula, in which the 
entropy is proportional to the logarithm of the prob- 
ability of the state. Prof Lorentz’s paper was to 
investigate how the probability is to be evaluated. 
The method of calculation, closely connected with 
Gibbs’s microcosmical ensembles, gives the entropy 
of Boltzmann’s formula as the thermodynamical 
entropy. On account of the enormous number of 
molecules contained in a body, Boltzmann’s formula 
thas the remarkable property that great changes in 
the value assigned to the probability have no ap- 
preciable effect on the entropy. 
A special case considered was that of a monatomic 
gas. If the number of molecules is n, P the prob- 
3n 
ability=Cune2’, C being a determinate constant 
factor; hence if we omit the corresponding term in 
: 3 R : 5 ; 
the entropy S, this=nv loz (vet), which since n 
- R : E Ries 
is very large=7—log(ve*), an expression which is 
NO. 2297, VOL. 92] 
neither very large nor very small when the mass of 
the gas is comparable with a gram-molecule. Now 
it is clear if P be multiplied by n, or even a high 
power of n, say n’®*°, this produces no appreciable 
effect on S, for logn is very small compared with n 
for large numbers. Boltzmann’s formula is there- 
fore insensible to such factors as n'°* in the value of 
P. Again, if the nm molecules be supposed distributed 
at random over a volume v, the probability that they 
all lie in one half of it is +, whereas it is 1 if all 
possible distributions are considered. The correspond- 
ing difference in the entropy is no more than 
we log2. The result of this property is that we are 
to a large extent free in the choice of a value of P. 
Thus, in order to calculate the entropy, we may as 
well take the probability of the most probable state 
of things as the much higher value that is obtained 
if all possible states are included. 
After Prof. Lorentz, another paper on the structure 
of the atom was read by Prof. Rutherford. The 
author took the opposite view to that represented by 
Sir J. J. Thomson’s atom. The Rutherford atom con- 
sists of a charged nucleus of minute dimensions, in 
which most of the mass is concentrated. This 
nucleus is surrounded by a distribution of electrons. 
The evidence for this structure of atom lies in the 
large angle scattering of high-speed particles like the 
a and 8 particles from radio-active matter. New 
experiments were described by Prof. Rutherford on 
the scattering of « particles by the simple gases. It 
was unfortunate that there was no time for a fuller 
discussion of the interesting points raised by this 
paper and that of Sir J. J. Thomsor. 
The last communication, taken on Thursday, was 
one by Dr. Swann—who has just left Sheffield for 
America—-on the resistances of thin metallic films. 
Some of the hitherto unexplained facts in connection 
with the conductivity of thin films were explained on 
the hypothesis that the film deposited by the electric 
discharge does not consist of a continuous and homo- 
geneous distribution of molecules, but of patches or 
groups of molecules more or less definitely separated 
from each other. This distribution was taken account 
of in the paper, and a formula calculated to allow for 
the resulting alteration in the mean free path of elec- 
trons concerned in conduction. ‘fhe agreement of 
the theory with experimental results is as close as 
could be hoped for. : ‘ 
On Friday morning the most important discussion 
of Section A, if not of the whole meeting, took place. 
The subject was radiation, and it was opened by 
Mr. J. H. Jeans in a masterly and concise manner. 
The discussion turned on the question of the validity 
of the laws which have hitherto been believed to be 
the ultimate laws of nature. The problem at its 
simplest occurs in the case of black body radiation. 
Mr. Jeans regarded the work of Poincaré as con- 
clusive when starting with the mean energy of each 
vibration of specified wave-length he deduces the quite 
definite result that the exchange of energy must take 
place by finite jumps. This leads directly to the 
quantum hypothesis which the opener assumed in its 
entirety. He went on to consider what other pheno- 
mena bear witness to its truth. The most important 
is the photoelectric effect: the energy imparted to 
an electron appears to be exactly the right amount 
required by the quantum hypothesis. Mr. Jeans 
quoted in this connection the recent work of Dr. 
Bohr, who has arrived at a convincing and brilliant 
explanation of the laws of spectral series. 
Against the quantum theory seem to be arranged 
