DECEMBER 17, 1903] 
NATURE 
165 
a model to illustrate various properties of wave-motion. 
The model consists of a series of brass balls suspended in 
a line by spiral springs and capable of transverse or up 
and down motion. The balls can be set in vibration by 
releasing them from extreme positions by means of triggers, 
one set of triggers controlling the up and down motion, and 
another set the pendular. 
Chemical Society, December 3.—Prof. W. A. Tilden, 
F.R.S., president, in the chair.—The molecular formule 
of some fused salts as determined by their molecular surface 
energy, by Mr. J. F. Bottomley. Measurements of the 
variation of capillary rise of fused sodium and potassium 
nitrates with temperature have shown that these salts prob- 
ably exist in a fused state in the form of complex molecules 
containing nine or ten of the molecules represented by the 
simple formule NaNO, and KNO,.—The atmospheric 
corrosion of zinc, by Mr. G. T. Moody. It is shown that 
the semi-crystalline scale formed on the surface of the metal 
when zinc is exposed to the atmosphere consists of a hydrated 
carbonate. The same compound is formed when zinc is dis- 
solved in a solution of carbon dioxide and the resulting 
solution is exposed to the air. From these experiments the 
author concludes that carbon dioxide is the principal agent 
in the atmospheric corrosion of zinc, as he has already 
shown it to be in the case of iron.—The formation of urea 
by the direct hydrolysis of lead cyanate, by Mr. A. C. 
Cumming. When lead cyanate is boiled with water it is 
decomposed with the formation of urea and lead carbonate. 
—Acid salts of monobasic acids, by Mr. R. C. Farmer. 
An account of the physical properties of some acid salts of 
benzoic acid and their derivatives is given.—The solubility 
curves of the hydrates of nickel sulphate, by Messrs. B. D. 
Steele and F. M. G. Johnson. Solubility curves are 
given for the heptahydrate, a- and B-hexahydrates, and for the 
dihydrate.—Action of malt diastase on potato starch paste, by 
Messrs. B. F. Davis and A. R. Ling. When malt diastase 
is heated in aqueous solution at temperatures in the neigh- 
bourhood of 60° C, its action upon starch paste is weakened, 
and dextroglucose appears among the products of hydro- 
lysis—The formation of phloroglucinol by the interaction 
of ethyl malonate with its sodium derivative, by Mr. C. W. 
Moore. It is shown that the condensation product formed 
in this reaction is ethyl phloroglucinoldicarboxylate, and not 
the tricarboxylate as stated by von Baeyer. 
Mathematical Society, December 10.—Prof. H. Lamb, 
president, in the chair.—The following papers were com- 
municated:—Mr. R. J. Dallas, Proof of a formula in 
elliptic functions.—Dr. E. W. Hobson, On modes of con- 
vergence of an infinite series of functions of a real variable. 
The condition of uniformity of convergence is known to be 
sufficient to secure the continuity of the function expressed 
by the sum of an infinite series the terms of which are 
continuous functions, but the function may be continuous 
without the convergence being uniform. The necessary 
and sufficient conditions have recently been made out, and 
new proofs of them are given in the paper. Another matter 
discussed is the nature of the conditions which are necessary 
and sufficient to secure that, when the terms of the series 
are integrable without being continuous, the function ex- 
pressed by the sum of the series is integrable. The methods 
of proof depend upon applications of the Heine-Borel theorem 
in the theory of aggregates.—Mr. W. H. Young, On the 
distribution of the points of uniform convergence of a series 
of functions. It is proved that the points in question form 
an ‘‘inner limiting set,’’ and that, conversely, given any 
such set of points, a series of functions can be constructed 
having these points, and these points only, as points of 
uniform convergence.—Rev. F, H. Jackson, A generalisa- 
tion of Neumann’s expansion of an arbitrary function in a 
series of Bessel’s functions.—Prof. A. C. Dixon, On many- 
valued Newtonian potentials. The paper deals with a theory 
on the lines of Riemann’s theory of the Abelian functions, 
but relating to space of three dimensions. The various 
values of the potential function become different one-valued 
functions in a bounded simply-connected region, and these 
various values must be supposed to exist in different co- 
extensive: examples of this region. The chief question is 
that of the existence of a potential one-valued throughout 
all the coextensive examples of the region, and having a 
NO. 1781, VOL. 69] 
simple pole at an assigned point in a particular example. 
Lwo values of a many-valued potential, which are permuted 
by description of an irreducible circuit, may differ by a con- 
stant or by a variable function.—Mr. P. E. B. Jourdain, 
On functions all of whose singularities are non- 
essential.—Prof. J. D. Everett, On normal and _ anti- 
normal piling. The object of the paper is to exemplify a 
convenient method of dealing with systematic assemblages 
of points. Normal piling denotes a particular homogeneous 
assemblage, whereas the arrangement in anti-normal piling 
is made up of two homogeneous assemblages. Both 
arrangements give the maximum of compactness.—Lieut.- 
Colonel Allan Cunningham made a preliminary com- 
munication On some properties of Fermat’s numbers. _ If 
Fn=2*"" + 1 and P is a product of F’s, the smallest suffix 
(a) exceeding unity and the highest not exceeding 2¢—1, 
then 2?—1=y (mod P) and 2"("—-Vv/=y_ (mod P?). 
Entomological Society, November 18.—Frof.E.B. Poulton, 
F.R.S., president, in the chair.—Mr. G. C. Champion 
exhibited numerous specimens of both sexes of Xyleborus 
dispar, from Moncayo, Spain, taken out of beech-stumps. 
—Mr. F. B. Jennings exhibited (1) on behalf of Mr. H. 
Britten, of Great Salkeld, Cumberland, a specimen of Tropi- 
phorus tomentosus, Marsh., from Great Salkeld, showing 
the deciduous false mandibles intact ; (2) a Q specimen of 
Anchomenus parumpunctatus, F., from the same locality, 
showing a malformation of the middle right tibia which 
was abnormally thin, and bent in the centre, but thickened 
at the base; the right antenna also had the last seven joints 
flattened and dilated. Mr. Jennings also exhibited, on his 
own behalf, Apion sanguineum, De G., taken at Brandon, 
Suffolk, in August last, on Rumex.—Mr. H. St. J. K. 
Donisthorpe exhibited Apium sorbi, 3, taken this year 
at Freshwater, Isle of Wight, and said that the ¢ of this 
species was extremely rare.—Mr. M. Burr exhibited two 
Qs and two Qs of the largest known earwig, Anisolobis 
colossea, Dohrn., from New South Wales, representing the 
extremes of size, the average size being between these two 
extremes.—Mr. A. J. Chitty exhibited a specimen of the 
beetle Homalium testaceum, taken in Blean Wood in 1900, 
and a pair of bees, Nomada guttulata, of which the G has 
never been recorded hitherto in Britain, taken by him at 
Huntingford, Kent, in May last.—Dr. Norman Joey ex- 
hibited (1) Euconnus mdklini, Mannerh., taken at Brad- 
field in July, 1901, new to the British list of Coleoptera ; 
and (2) a series of beetles taken at Bradfield at the exuding 
sap of trees attacked by Cossus ligniperda.—Colonel J. W. 
Yerbury exhibited specimens of rare British Diptera, in- 
cluding Leptopa filiformis, Lett., Thyreophora furcata, 
Pelidnoptera nigripennis, and Lucina fasciata.—Dr. T. A. 
Chapman exhibited specimens of Chrysophanus phlaeas 
captured at Reigate, Locarno, and in Spain, showing the 
apparent effects of temperature on the coloration and wing 
markings.—Mr. G. J. Arrow showed specimens and 
diagrams illustrating a remarkable kind of variability 
noticed in beetles of the Trogid genus Acanthocerus. 
These beetles have the faculty of rolling themselves into a 
ball, in the interior of which all the vulnerable parts are 
enclosed. The head forms a large triangular plate in 
which the eyes appear half on the upper and half on the 
lower surface. In some examples of the species exhibited 
(Acanthocerus relucens, Bates) the upper division of the eyes 
forms a large, nearly circular mass, while in others it is 
reduced to a mere thin vestige, and in extreme examples of 
another species of the genus it was found to vanish 
altogether.—Prof. Poulton showed an exhibit sent by Mr. 
A. H. Thayer, of Monadnock, N.H., U.S.A. The greyish 
silhouettes of two butterflies were represented in a tint 
nearly the same as the background, but sufficiently dis- 
tinct to be easily recognisable. On one side of one 
silhouette a row of white spots had been placed in a sub- 
marginal position. It was evident that the adjacent border 
was thereby rendered far less distinct than that of the 
opposite side of the silhouette, or of both sides of the other 
silhouette. The spots in position and shape were approxi- 
mately as in Papilio asterias, and Mr. Thayer considered 
they possessed a similar significance in this butterfly. Prof. 
Poulton also exhibited specimens of Drurya antimachus, 
together with the butterflies which he suggested as form- 
ing a group synaposematic with it. The central species 
