APRIL 21, 1904] 
NATORE 
399 
Mathematical Society, April 14.—Dr. E. W. Hobson, | 
vice-president, in the chair.—Mr. G. B. Mathews communi- 
cated a paper by Prof. F. Morley on a plane quintic curve. 
The curve is the locus of the points of contact of tangents 
from a fixed point to a pencil of cubics. It is of maximum 
genus (deficiency), viz. 6, and the 45 tangents at points of 
inflexion pass by nines through 5 points.—Mr. H. M. 
| 
Macdonaid gave an account of his recent researches con- | 
cerning the singularities of functions determined by Taylor’s 
series. Unless special relations hold among the coefficients 
of the series every point on the circle of convergence is a 
singularity, and attention has been directed to the problem 
of determining the coefficients in order that the function 
may have singularities at prescribed points on the circle 
only.—The following papers also were communicated :— 
Note on a system of linear congruences: Rev. J. Cullen. 
—The tile theorem: Dr. W. H. Young.—Note in addition 
to a former paper on conditionally convergent multiple 
series: G. H. Hardy.—On functions generated by linear 
difference equations of the first order: Rev. E.-W. Barnes. 
The simplest solutions of linear difference equations with 
meromorphic functional coefficients are one-valued func- 
tions with sequences of poles tending to infinity. When the 
coefficients are one-valued functions with essential singu- 
larities the solutions generally have sequences of such 
singularities. These functions cannot in general arise as 
the integrals of differential equations of any finite order and 
dimensions with coefficients which are not derived from the 
function itself. Thus linear difference equations give rise 
to classes of transcendental functions which cannot be 
generated by differential equations.—Mathematical analysis 
of wave-propagation in isotropic space of p dimensions : 
T. H. Havelock. In the case of three dimensions certain 
methods of integration of the equation of wave-propagation 
were found by Poisson and Kirchhoff. ‘These are connected 
with the analytic expression of Huygens’s principle. In 
two dimensions the corresponding integrals are more com- 
plicated, and the interpretation of them shows that in 
general the waves generated at a temporary source have 
no definite rear surface, but leave a trail behind. Corre- 
sponding integrals are obtained in the paper in the case of 
any number of dimensions, and it is shown that this dis- 
tinction of properties extends to all cases of uneven and 
even numbers of dimensions.—On spherical curves, part ii. : 
H. Hilton.—Perpetuant syzygies of degree four: P. w. 
Wood. 
—(1) Transformation of the function F([a] [8] [y]x); (2) 
The extension of Neumann’s addition theorem for Bessel 
functions: Rev. F. H. Jackson.—The following informal 
communications were made :—Behaviour of a power series 
near a point on the circle of convergence at which the series 
diverges: Dr. H. F. Baker.—Transvectant operators in 
connection with binary forms: R. J. Datlas.—Factorisation 
of 13°°—1: Lieut.-Colonel A. Cunningham. The factors 
are 4.3; 3-61; 1803647: 53.264031; 57745124662681" : 
79.1093.4603.21841, where the semicolons separate the 
algebraic factors and the colons separate the Aurifeuillian 
factors. The factor marked with an asterisk has not been 
resolved. 
MANCHESTER. 
Literary and Philosophical Society, January 5.—Prof. 
W. Boyd Dawkins, F.R.S., president, in the chair.—Note 
on a method of preparing hydrobromic acid: R. L. Taylor. 
January 19.—Prof. W. Boyd Dawkins, F.R.S., president, 
in the chair.—The specific heats and specific volumes of 
certain alloys: H. E. Sehmitz. The calculated and 
observed values in the cases examined agreed very closely. 
—On phenomena due to repetitions of stress, and on a new 
testing machine: F. Foster. When a metal is strained by 
a steady stress, the crystals of which it is composed undergo 
no change until the elastic limit is passed, but then an 
internal slipping tales place, which is permanent. The 
same slipping takes place if a stress much less than the 
elastic limit is applied and removed repeatedly, and is due 
probably to hysteresis in the extension of the metal. In 
order further to study these phenomena, the author has 
designed a new testing machine capable of subjecting the 
metal under test to a great variety of conditions. 
February 2.—Prof. W. Boyd Dawkins, F.R.S., president, 
in the chair.—A diagnostic key for the genera of recent 
dibranchiate Cephalopoda: Dr. Hoyle. 
NO. 1799, VOL. 69] 
Extension of Sylow’s theorem: Prof. G. A. Miller. | 
February 16.—Mr. Charles Bailey in the chair—On a 
suitable arrangement for determining the capacities of con- 
densers by the successive discharge method: H. Morris- 
Airey and E. D. Spencer. The rotating commutator 
generally employed in this method was replaced by an 
electrically excited tuning fork, the prongs of which carried 
aluminium riders making contact in mercury cups. By 
this means it was possible to obtain perfectly regular dis- 
charges at a much bigger rate than is usually possible 
with rotating commutators.—Note on the spectrum of the 
glow discharge at atmospheric pressure: Dr. G. A. 
Hemsalech. With an alternating discharge the spark 
spectrum between metallic terminals is affected by heating 
them, the glow then being obtainable at either pole. 
Special Meeting, February 23.—Prof. W. Boyd Dawkins, 
F.R.S., president, in the chair.—The Wilde lecture, on 
the evolution of matter as revealed by the radio-active 
elements, was delivered by Mr. F. Soddy (see p. 418). 
March 1.—Prof. H. B. Dixon, F.R.S., in the chair.— 
The ionisation of air: Prof. A. Schuster, F.R.S. The 
author described a method of observation which allowed 
him to determine the number of ions which are constantly 
being formed in the atmosphere. All experiments which 
have hitherto been made only determined the total number 
of ions present, but not the rate at which they re-combined 
or formed. Some experiments made in a field near Roch- 
dale on February 28 gave 2400 for the number of ions in 
each cubic centimetre of air, and a formation of 18 new 
ones in each second, while on the roof of the physical 
laboratory at the Owens College on February 29 the 
numbers were 3600, with a formation of 38 fresh ones each 
second. 
March 15.—Prof. W. Boyd Dawkins, F.R.S., president, 
in the chair.—The Falkland Islands revisited: Rupert 
Vallentin. The principal zoological, botanical and geo- 
logical features of the district were described.—Mendel’s 
principles of heredity: A. D. Darbishire.—On_ photo- 
chemically active chlorine: D. L. Chapman. 
Paris. 
Academy of Sciences, April 11.—M. Mascart in the 
chair.—Theory of the quadrifilar azimuth balance: 
H. Poincaré. An investigation of the equations of sensi- 
bility and stability of the quadrifilar balance described by 
M. Crémieu.—Note on the graphical method applied to 
human pathology: M. Lannelongue. The graphical 
method, the use of which is described in detail in the paper, 
can be applied with advantage in a number of cases where 
photography or radiography would not give the same 
results.—A new general theorem in the theory of analytical 
functions: G. Mittag-Leffer.—Remarks on the com- 
munications of M. A. Charpentier, and the questions of 
priority to which they have given rise: M. d’Arsonval. 
The results of Charpentier are held to be new, since it is 
one of the characteristics of the radiations which he has 
discovered that they are without effect on a photographic 
plate, whilst the work of others claiming priority in this 
matter has been mostly carried out by means of photo- 
graphy.—On a_ particular of persistent conjugate 
systems: D. Th. Egorov.—On groups of operations: G. A. 
Miller.—On the equations of geometry and the theory of 
substitutions : Ed. Maillet.—A quadrifilar azimuth balance : 
\. Crémieu. A description of an entirely new form of 
balance, in which the beam is supported by a plunger float- 
ing in mercury, and in which the pointer of the ordinary 
balance is replaced by a system supported by four wires in 
torsion attached to the beam. The theory of this balance 
is worked out by M. Poincaré in a previous paper. Instead 
of using a rider, differences below a centigram are measured 
by means of the electrodynamie repulsion produced between 
two bobbins, the current being adjusted by means of a 
resistance until the point of equilibrium is reached.—On the 
penetrating power of the n,-rays emitted by certain sources, 
and their storage by different substances: Julien Meyer. 
The n,-rays, discovered by Blondlot, the effects of which 
are the inverse of the n-rays, are given off by vacuous glass 
tubes, and possess a greater penetrating power than the 
similar rays given off by a Nernst lamp. Certain substances 
appear to possess the power of storing up these rays, 
aluminium being a notable example, and then emit them 
for as long as twenty-four hours afterwards.—On the earth- 
class 
