May 15, 1902] 
NATURE 
Fu 
continuation of the author’s researches on nitrogen halides in 
which propionyl is a substituent. A number of these derivatives 
are described. 
Mathematical Society, May 8.—Dr. E. W. Hobson, 
president, in the chair,—Dr. Ganesh Prasad read a paper on the 
use of Fourier’s series in the theory of conduction of heat. It 
is pointed out that the received theory may break down through 
discontinuity in the initial conditions ; and a method is described 
for forming an equation which shall, at the discontinuities, take 
the place of the usual partial differential equation of conduction. 
The modified theory thus deduced is equivalent to the ordinary 
theory at all places and times at which there is no discontinuity 
in initial or boundary conditions.—Mr. A. E. Western pointed 
out an exception to a theorem of Fermat’s on binary powers. 
—Dr. F. S. Macaulay read a paper on some formulze of elimina- 
tion. The resultant of any number of equations, which are 
homogeneous in an equal number of variables, is proved to be 
expressible as the quotient of a certain determinant by a certain 
minor of the same; certain formule are also given connecting 
the determinants with the roots of the equations which, for 
this purpose, are made non-homogeneous by equating one 
variable to unity.—The following papers were communicated 
from the chair.—Prof. Burnside, on groups in which every two 
conjugate operations are permutable. The general character of 
the operations of a group which satisfy this condition of permut- 
ability is determined, and it is shown that the sufficient and 
necessary conditions that the group may be of finite order are 
that the generating operations are of finite order. In general 
for such a group, the commutator of any two operations is a 
self-conjugate operation. The case in which the order is a 
power of three is exceptional.—Mr. H. S. Carslaw, the applica- 
tion of contour integration to the solution of general problems 
in the conduction of heat and to the expansion of an arbitrary 
function in series. The solutions of certain special problems are 
transformed so that they are expressed in terms of integrals 
taken along certain paths in the plane of an auxiliary complex 
variable. The solutions of more general problems, built up by 
synthesis, are then transformed so that they are expressed by 
means of infinite series. The methods are applied to problems 
of conduction of heat in a finite rod and in a cylinder, and it is 
pointed out that they admit of extension to other branches of 
mathematical physics. 
Geological Society, April 16.—Prof. Charles Lapworth, 
F.R.S., president, in the chair.—The Carlisle Earthquakes of 
July 9 and 11, 1901, by Dr. C. Davison. The shocks were 
at least four in number, and there are single records of four 
other shocks. The isoseismal 5 of the first and principal shock 
is very nearly a circle 29 miles in diameter, with its centre 7 
miles south-south-west of Carlisle, and is excentric with regard 
to the isoseismal 4.. The continuity of the shock over a band 
extending from Carlisle to Coniston implies a corresponding 
continuity in the focus. The investigation of the earthquakes 
has led to the recognition of a deep-seated fault, the average 
direction of which is N. 5° E. and S. 5° W. andthe hade 
throughout is to the east. In the surface-rocks there is no sign 
whatever of such a structure. The movements along the fault 
were somewhat peculiar. In the first shock the focus was of 
considerable length, and consisted of two principal portions, the 
centres of which were about 23 miles apart, connected by a 
region wherein the slipping was continuous throughout, and 
much less in amount. The northern part of the focus was 
smallerthan the other, but was marked bya much_ stronger 
impulse. The third slip was complementary to the first, for it 
appears to have occupied the whole of the region between the 
two principal portions of the first focus, and to have been greatest 
near the centre of that region and to have gradually diminished 
towards both ends.—The Inverness Earthquake of September 
18, 1901, and its accessory shocks, by Dr. C. Davison. Since 
the Comrie earthquake of 1839, which was followed by 330 
tremors and earth-sounds within little more than two years, no 
British earthquake has been attended by so many accessory 
shocks as this one. The unusual intensity of the earthquake, its 
apparent connection with the great northern boundary-fault of 
the Highlands, and the possibility of tracing oscillations in 
Successive centres of disturbance along the fault-surface, com- 
bined in rendering a detailed investigation desirable. With a 
few exceptions, the earthquakes originated beneath the district 
lying between Inverness and the north-eastern end of Loch Ness. 
The mean direction of the fault, which follows the line of the 
NO. 1698, VOL. 66] 
Great Glen, is N. 35° E. and S. 35 W. and its hade is to the 
south-east. The isoseismal 8 contains 67 square miles, and its 
centre is about one-and-a-half miles east-north-east of Doch- 
garroch and three-quarters of a mile south-east of the fault-line. 
The correspondence between the position of the great boundary- 
fault and of the fault inferred from the seismic evidence is so 
close that there can be little doubt that the earthquake was due 
toaslip along this fault. The nature of the shock, the sound ‘phe- 
nomena, time-relations and after-shocks are described in detail, 
and some account is added of the earthquakes of 1890 and of sym- 
pathetic earthquakes in the valley of the Findhorn. There were two 
distinct slips in rapid succession, with continuous slight motion be- 
tween them, the second being greater in amount and extending over 
an area which probably overlapped, even if it did not entirely in- 
clude,that within which the first took place. The great slip reached 
nearly from Loch Ness to Inverness, and was greatest at a point 
about half-way between. The three chief after-slips resulted 
in an extension of this area in both directions along the fault- 
surface, the extension to the north-east being small, while that 
to the south-west amounted to 6 miles or more. In addition to 
this migration of the focus, there was also a continuous decrease 
in the depth of the focus. The earthquakes provide no evidence 
with regard to the direction of displacement along the boundary- 
fault. There can be little doubt, however, that Loch Ness is 
still growing ; but it can hardly be determined whether the lake 
is now contracting in area, or whether it is gradually pushing its 
way outward to the sea.—The Wood’s Point Dyke, Victoria 
(Australia), by Mr. F. P. Mennell. 
Zoological Society, May 6.—Prof. G. B. Howes, 
F.R.S., vice-president, in the chair.—A note was read by Mr. 
Roland Trimen, F.R.S., upon.a moth of the genus Cossus, 
which had been reared in the Society’s insect-house from a 
chrysalis sent home from South Africa. The specimen was 
apparently referable to the common goat-moth of Europe 
(Cossus ligniperda), which had probably been introduced in 
logs of wood into South Africa.—Mr. Oldfield Thomas, F.R.S., 
read a paper on the mammals obtained during the Whitaker 
Expedition to Tripoli. At Mr. J. I. S, Whitaker's expense, 
Mr. E. Dodson had made a successful collecting expedition 
into Tripoli, and the specimens of mammals obtained had been 
‘presented to the National Museum. Twenty-one species were 
referred to, and, among others, a hare (Lepus whztakere), allied 
to L. aethzopicus, but of a bright pinkish buffy colour, and a 
gundi (Crenodactylus valz) like C. gundi, but with much larger 
bullae, were described as new.—A communication from Mr. 
G. A. Boulenger, F.R.S., contained lists of four species of 
fishes, eight species of batrachians and thirty-five species of 
reptiles, of which specimens had been collected by Mr. J. ffolliott 
Darling in Mashonaland. Amongst these were described as new 
two species of fishes (Zaseo darlinez and Barbus rhodesianus), 
one of batrachians (Xana darlingi) and two of reptiles 
(Homopus darlingt and Ichnotropis longipes).—A communi- 
cation was read from Hans Graf von Berlepsch and M. Jean 
Stolzmann containing a second part of their memoir on the 
ornithological researches of M. Jean Kalinowski in Central 
Peru. It gave an account of 188 species and subspecies, of 
which twelve were described as new.—A paper contributed by 
Sir Charles Eliot contained notes on the nudibranchs of the 
eastern and western coasts of Zanzibar. Zatterta brown?z, 
Dunga nodulosa and Crosslandia viridis were described as 
new genera and species, and remarks were made upon the little- 
known species Meltbe fimbriata and Marrella ferruginosa.— 
Prof. G. B. Howes, F.R.S., communicated a paper by Prof. 
G, Elliot Smith on a case of abnormal dentition in a lemur. 
The author recorded the occurrence in an individual of Lemur 
Julous of a fourth lower molar, present on both sides, in’ its 
characters a diminutive counterpart of the normal third molar 
as regards its postero-external cusp. MJeverting to the fact that 
certain fossil lemurs, marsupial-like, possess four molar teeth, 
and to the presence in Otocyon of four molars, and in the in- 
sectivore Centetes of a fourth upper molar, the author asserted a 
belief in a four-molared ancestry for the Primates. 
Paris, 
Academy of Sciences, May 3.—M. Bouquet de la Grye 
in the chair.—The permanent secretary announced to the 
Academy the death of M. L. Fuchs, correspondant for the 
Section of Geometry.—Studies of batteries founded on the use 
of saline solutions with the reciprocal action of oxidising and 
reducing liquids, by M. Berthelot.—On the functions of the 
