286 
NATURE 
[January 17, 1907 
UNIVERSITY AND EDUCATIONAL 
INTELLIGENCE. 
Mr. Evan Spicer, chairman of the London County 
Council, will distribute the prizes and certificates at the 
annual conversazione of the Northampton Institute, 
Clerkenwell, E.C., on Friday, January 25. 
Tue annual general meeting and dinner of the Central 
Technical College Old Students’ Association will be held 
at the Trocadero Restaurant, Piccadilly Circus, W., on 
Saturday, February 23. Applications for tickets should be 
sent to Mr. J. Caldwell, 40 Salehurst Road, Crofton 
Park, London, S.E. 
Tue department of archeology of the University of 
Pennsylvania has received a gift of 80001. from Mr. 
Eckley Brinton Coxe, jun. The donor has specified that 
of the gift 1720l. a year shall be paid for five years to 
the new curator of the department of Egyptology, Dr. 
D. Randall Maclver, who is now in Egypt, where he has 
been instructed to begin excavations. 
Mr. SipnEy WELLS, principal of the Battersea Poly- 
technic, and a member of the consultative committee of 
the Board of Education, has been appointed Director- 
General of the Department of Agriculture and Technical 
Education for Egypt. This department has been created 
in order to develop, organise, and control technical educa- 
tion in Egypt generally. It will be concerned with all the 
Government educational institutions of every kind, and also 
with the non-Government technical institutions. 
A PRIVATE donation has enabled the Meteorological Com- 
mittee to invite applications for an appointment as reader 
in dynamical meteorology. The readership will be of the 
annual value’ of 350l., and will be tenable for three years 
at any British siniversity that may be approved for the 
purpose and affords the required facilities. The duty of 
the reader will be primarily to promote the science of 
meteorology by mathematical investigation, and he will 
be expected to give annually a short course of about twelve 
lectures. Further details may be obtained from the 
Director of the Meteorological Office, 63 Victoria Street, 
London, S.W. 
THE annual report of the council of University College, 
London, has just been issued. The number of students in 
the college for the session 1905-6 was 1396; of these, 134 
were post-graduate and research students. The report 
contains particulars of the benefactions received during 
the year, which include valuable grants from the Drapers’ 
Company, from the Chadwick trustees, and the sum of 
25001. collected by the Jewish Historical Society for the 
maintenance of the Mocatta library. The report also con- 
tains a summary of the research work done during the 
past session; the lists of the publications by professors, 
assistant teachers, and senior students occupy fourteen 
pages. The steps that have been taken for the union of 
the college and the University of London are summarised 
in the report. On January 1 of the present year the 
college ceased to be a school of the University, and became 
incorporated with it, thus realising the aims of those who 
in 1826 founded it. It is the first college to be thus in- 
corporated with the University, and it is understood that 
its example will be followed by King’s College. Important 
additions have been made during the past year to the de- 
partments of physics and chemistry, and a plan has been 
worked out for the rearrangement of many of the college 
departments. This will be possible when the new build- 
ings for the school of advanced medical studies, now in 
course of erection by the generosity of Sir Donald Currie, 
and the new buildings of University College School at 
Hampstead, are completed. 
SOCIETIES AND ACADEMIES. 
Lonpon. 
Mathematical Society. January to.—Prof. W. Burnside, 
president, in the chair.—An exhibition of models of four- 
dimensional figures was made by Mrs. A. Stott. The 
models are sections by three-dimensional flat spaces of the 
six regular hypersolids of a flat space of four dimensions. 
The sections are in general polyhedra ; 
NO. 1942, VOL. 75| 
and corresponding 
faces of different polyhedra, forming a series of sections of 
the same regular hypersolid, are coloured identically in 
order to show the relations between the different sections. 
Other models show the grouping about a point of the 
regular hypersolids which have the space-filling property. 
—The uniform convergence of Fourier’s series: Dr. E. W. 
Hobson. The coefficients of the Fourier’s series deter- 
mined by an assigned function are defined by integrals, 
which may be determinate when the extended definition 
of integration introduced by Lebesgue is used, although 
they have no meaning when integration is interpreted in 
accordance with Riemann’s definition. It is shown in the 
paper that whenever the coefficients of the Fourier’s series, 
determined by a function f(x) in the interval 7>x>—z, 
are, in this sense, determinate, and the function f(x) is 
continuous. throughout a sub-interval included in this 
interval, and this function is of limited total fluctuation 
in the whole interval, the Fourier’s series so determined 
converges uniformly in the sub-interval—Hyper-even 
numbers and Fermat’s numbers: Lieut.-Colonel A. 
Cunningham. The hyper-even numbers are formed in 
on 
sequence as 2”, 2°, 2% , and so on. Fermat’s numbers 
are of the form 27"+1. The numbers £ which are such 
that 2&=1(mod.m) are the Haupt-exponents of 2 for the 
modulus m. The paper is occupied with tracing the re- 
lations which connect together the residues of successive 
hyper-even numbers, the uneven factors of the Hawupt- 
exponents, and the Fermat’s numbers.—Riemann’s hyper- 
geometric function: Dr. E. W. Barnes. It is shown how 
the differential equation of the hypergeometric series, and 
likewise that of Riemann’s function, can be solved re- 
spectively by means of certain contour integrals, and how 
the known solutions can all be obtained by deforming the 
contour. The relations between the various forms of solu- 
tion, which hold in the neighbourhoods of the singular 
points, can be traced very simply by means of the general 
formula. The method is applied to obtain asymptotic 
approximations to zonal harmonics in the case where the 
index increases indefinitely.—Partial differential equations 
of the second order, having integral systems free from 
partial quadratures: Prof. A. R. Fersyth. The integral 
systems discussed are those in which three variables 
x, ¥, S are expressed in terms of two parameters u, v, an 
arbitrary function of u, an arbitrary function of v, and 
differential coefficients of these two functions. The object 
of the paper is to determine the forms of the differential 
equations which possess integrals of the type in question, 
and to construct the integrals of such equations.—The 
singular points of certain classes of functions of several 
variables: G. H. Haydy. The theory of the singularities 
of functions of one variable, defined by Taylor’s series, 
may be said to be tolerably complete, but in the case of 
functions of several variables little advance has been made. 
The purpose of this paper is, by the consideration of a 
few of the simplest cases, to make a beginning with the 
problem of classifying types of power series in two or 
more variables according to the nature of their singulari- 
ties.—The singularities of functions defined by Taylor’s 
series: G. H. Hardy.—Asymptotic approximation to 
integral functions of zero order: J. E. Littlewood.—The 
reducibility of covariants of binary quantics of infinite 
order: P. W. Wood.—The forms of the stream lines due 
to the motion of an ellipsoid in infinite fluid, frictionless 
or viscous: Dr. T. Stuart. 
Geological Society, December 19, 1906.—Sir Archibald 
Geikie, Sec.R.S., president, in the chair.—The post- 
Cretaceous stratigraphy of southern Nigeria: J. Parkin- 
son. In this paper, which is a first attempt to outline 
the sequence of the later deposits of southern Nigeria (now 
including the colony of Lagos), a series of beds is de- 
scribed from four localities—three from the western side 
of the Niger, and one around Calabar near the Kameruns 
frontier. The alluvium of the river-beds and the lower 
terraces are referred to, and the succeeding sediments 
grouped under three heads.—The geology of the Oban 
Hills (southern Nigeria): J. Parkinson. The country de- 
scribed in this paper comprises some 1800 square miles 
of the Eastern Province of southern Nigeria, adjacent to 
