382 
NATORE 
[Fepruary 18, 1904 
found to contain PH, and AsH,. The former was in the 
greater proportion, and to that probably the explosions were 
due. 
Mineralogical Society, February 2.—Dr. Hugo Miller, 
president, in the chair.—Mr. Harold Hilton contributed a 
paper on the gnomonic net. This net consists of lines 
giving equal longitudes and latitudes for every ten degrees 
on a plane touching a point on the equator, the former being 
hyperbola and the latter straight lines. The author pointed 
out how the net could be used for the graphical determin- 
ation of angles between poles on the sphere.—Mr. G. T. 
Prior described a new sulphostannite of lead from Bolivia, 
to which he gave the name Teallite, in honour of the 
Director of the Geological Survey. The mineral in its 
graphite-like appearance resembles franckeite and cylindrite, 
but differs from them in not containing antimony. It has 
the simple formula PbSnS,, and is orthorhombic with 
angles c(oo1) \ o(111) = 62°, (oor) Ap(221) = 75°, and 
m(110) Am/’(1i0)=86°. It has a perfect cleavage parallel 
to c(oor) and a specific gravity of 6-36. In connection with 
the investigation of this mineral new analyses were made 
of franckeite and cylindrite—Mr. W. F. Ferrier gave an 
account of his discovery of the deposits of corundum in 
Canada, and Prof. H. A. Miers described a visit to the 
Rashleigh collection of minerals now deposited in the 
Museum of the Royal Institution of Cornwall at Truro. 
Chemical Society, February 4.—Dr. W. A. Tilden, 
F.R.S., president, in the chair.—It was announced that the 
council proposed to send a congratulatory address to Prof. 
Mendeléeff on the occasion of his seventieth birthday, 
Tuesday, February 9, which was also the date of his official 
retirement.—The following papers were read :—The consti- 
tution of epinephrine: H. A. D. Jowett. The hamostatic 
constituent of suprarenal gland secretion was first isolated 
by Abel and Crawfurd, and was subsequently obtained by 
Takamine, who named it adrenalin, and by von Furth, who 
called it suprarenine. The author finds that this substance 
has the composition C,H,,O,N, and that when fully 
methylated and oxidised it furnishes trimethylamine and 
veratric acid, whence he suggests that it should be repre- 
sented by the formula 
C,H,(OH),.CH(CH,OH).NHMe(: : 
n 
: 4) 
or 
is) 
C,H,(OH),.CH(OH).CH,.NHMe(r : 2 : 4), 
the latter being the more probable.—Studies on the electro- 
lytic oxidation of phenols, part i.: A. G. and F. M. Perkin. 
By the oxidation of pyrogallol, purpurogallin was obtained, 
whilst gallic acid furnished purpurogallincarboxylic acid.— 
Action of nitrogen peroxide on 1-nitrocamphene: M. O. 
Forster and I. M. G. Micklethwait. In this reaction a 
number of complex compounds were obtained the con- 
stitutions of which have not yet been determined.—The 
tautomeric character of the acyl thiocyanates: R. E. Doran. 
A study of the conditions under which acetyl thiocyanate 
reacts as such or as the tautomeric thiocarbimide.—Resolu- 
tion of a-B-dihydroxybutyric acid into its optically active 
constituents: R. S. Morrell and E. K. Hanson. The 
physical characters of the two optically active acids which 
were obtained by fractional crystallisation of the quinidine 
salt of the racemic acid are described.—Aromatic compounds 
obtained from the hydroaromatic series, part i., the action 
of bromine on 3: 5-dichloro-1 : 1-dimethyl-A?:4-dihydro- 
benzene: A. W. Crosstey. <A description of the derivatives 
obtained.—The action of nitrogen sulphide on organic sub- 
stances: F. E. Francis and O. C. M. Davis. An enumer- 
ation of the cyanidins obtained by the action of nitrogen 
sulphide on aromatic aldehydes.—Dibenzoylchloroimide : 
F. D. Chattaway. The author claims priority, over 
Stieglitz and Earle, in the description of this compound and 
some of its derivatives. 
Mathematical Society, February 11.—Prof. H. Lamb, 
president, and temporarily Prof. E. B. Elliott, vice-presi- 
dent, in the chair.—The following papers were communi- 
cated :—On the roots of the equation =const. : 
$ [ (w+1) 
When the constant on the right hand side 
NO. 1790, VOL. 69] 
G. H. Hardy. 
is zero, the rate of increase of the nth root approximates to 
that of n when n is large, and this result constitutes an 
exception to a general law which regulates the relation of 
the rate of increase of the roots to that of the function. It 
is shown that when the constant is not zero the rate of 
increase of the nth root is that of n/log n, and the excep- 
tion is removed. The significance of the result in relation 
to the theory of integral functions is discussed.—Some 
extensions of Abel’s theorem on power series on the circle 
of convergence: G. H. Hardy. The extension is to double 
series. When a double power series converges on the locus 
that corresponds to the circle of convergence of a simple 
series, either (a) when summed first by rows, or (b) when 
summed first by columns, or (c) when the two suffixes are 
simultaneously increased, its sum is equal to the limit of 
the function at the corresponding point of the locus, pro- 
vided the limiting operations are performed in ways that 
correspond to the three specified methods of summation.— 
On group-velocity : Prof. H. Lamb. The paper contains a 
new proof of the relation between wave-velocity and group- 
velocity, and the possibility of a negative group-velocity is 
discussed. If the group-velocity were negative, the waves 
and the groups would travel in opposite directions. Such 
a possibility has been suggested in connection with very 
intense absorption. Examples are given of mechanical 
systems free from dissipation which possess the required 
property. In such systems the disturbance that travels 
away from any source, when analysed into harmonic waves, 
is found to consist of waves travelling towards the source, 
but the groups by which the energy is propagated travel 
away from the source. The reflection and refraction of 
waves at the boundary of a medium in which the relation 
between wave-velocity and wave-length is compatible with 
a negative group-velocity are discussed, and the ratio of 
amplitudes of incident and reflected waves is found.—On a 
certain double integral: Prof. A. C. Dixen.—On an 
appropriate form of conductor for a moving point singu- 
larity: Prof. A. W. Conway.—On the irreducibility of 
perpetuant types: P. W. Weoed.—On the representation of 
wn 
ii cn xt e~¢ dt and other like integrals by means of con- 
{ 
tinued fractions: Prof. L. J. Rogers. The paper deals with 
a generalisation of the so-called ‘* addition theorem ’’ for 
Bessel functions of zero order. A series of functions 
fis fe, . - +. can be determined from a given function f so 
that f(x+y)=Af@)f(y) + Bf (A+ ChO)FLO)+ .. - . The 
determinants that arise in the process of obtaining these 
functions are closely related to the process of converting a 
series into a continued fraction. It is generally difficult to 
complete the latter process, but the relation between the two 
processes leads to a simplification. 
CAMBRIDGE. 
Philosophical Society, January 18.—Dr. Baker, presi- 
dent, in the chair.—On differences between the spectra at 
anode and kathode in certain gases, and on_ probable 
reasons for those differences: Prof. Liveing, F.R.S. The 
author found that in hydrogen at 7 mm. pressure the light 
at the anode gives only the second spectrum of hydrogen, 
at lower pressure the kathode glow shows only the first 
spectrum, and by further reduction of pressure the second 
spectrum is driven quite up to the anode and is then seen 
only in a bright spot upon the anode. The behaviour of 
the two banded spectra of nitrogen is exactly similar. In 
pure oxygen the anode is dark, but the kathode glow emits 
all the three spectra described by Schuster. The anode 
spectrum of the halogens is a continuous one, while the 
kathode glow gives a spectrum of lines, and the gas along 
the whole line of the discharge emits rays which, like 
kathode rays, make the tube fluoresce. The vapours of 
such metals as could be readily observed in glass tubes give 
each but one spectrum, the same in all parts of the tube. 
The spectra of the two oxides of carbon are indistinguish- 
able from each other, and are the same at both electrodes. 
Cyanogen gives in the kathode glow the well-known blue 
and violet shaded bands, and at the same time the bands 
at the red end shaded the reverse way, but no trace of 
either the carbonic oxide or of the candle-flame spectrum 
in any part of the tube. The appearance of the positive 
column in all cases agrees well with Prof. Thomson’s theory 
