on the South African gold-fields, which include much information on the present condition of the whole of South Africa as far north as the Zambesi. The observer points out that, while the Delagoa Bay and other lines of communication are much discussed, the fine artery of the perfectly navigable Limpopo is entirely neglected, notwithstanding Captain Chaddock's navigation of it a few years ago. The writer remarks that "this river flows mainly through regions under the influence or protectorate of England; the Transvaal people on the one side, and those of Matabeleland on the other, would certainly be glad to avail themselves of this outlet for their produce. As it traverses only a small tract of Portuguese territory about its estuary, I hope and believe that Portugal will not be allowed to treat the Limpopo as she is now attempting to treat the Zambesi. The subject is of such importance that it cannot fail soon to be brought before the British Parliament." Referring to the negotiations at present going on in connection with the Swaziland question, he observes, in the same spirit :-"The Swazi people must, sooner or later, yield either to the Transvaal or to England, and if to the former, it must be to the entire detriment of British interests. England, as the suzerain power in South Africa, should be the first in the field, both in her own interest and in that of her other colonies and subjects. If she does not assume the protectorate of Swaziland, besides losing the control of a vast and rich mineral district, she will deprive the colony of Natal of all further hope of expansion. If she ignores her responsibility in this matter, and allows the Transvaal Republic to absorb Swaziland, she will add another to the long list of blunders that threaten to destroy all prospect of consolidating a dominion as large as Canada, and may end disastrously for British interests in South Africa.'

A FRENCH traveller has just achieved a feat of great interest. Captain Trivier, equipped by the newspaper La Gironde, started some eighteen months ago for the Congo State. He went up the river to Stanley Falls, and thence proceeded to Central Africa and the Lake region, accompanying caravans. just arrived at Mozambique.

He has

Globus reports that during the past summer M. Thoroddsen, the well known student of Iceland, has carried out a journey in the waste region known as Fiskivötn, lying between Hecla and the Vatna Jökul, which has hitherto been unvisited for the most part by any inquirer. To the east and north of Hecla he discovered a new obsidian region. Crossing the Tunguaa, he went to the Fiskivötn group of lakes, all true crater lakes. The district between this and the Vatna Jökul has absolutely no plant-life whatever; it consists of lava-fields, and plains of volcanic sand. In it he found a lake, Thorisvatn, the second largest in the island. Thence, after a day's journey through an utterly desolate district, he reached the hitherto unknown source of the Tunguaa. To the south of this he discovered, between three ranges of hills, previously unknown, a new and very long lake.

MR. DAUVERGNE has, says the Times of India, completed an adventurous journey in the regions of North-West Cashmere. His course was from Leh northwards to the Kilian Pass, in Kashgaria, and then northwards across the Pamir to the Upper Oxus. He reached Sarhad in safety, and after six days' halt there, crossed the Hindu Kush by the Baroghil Pass, as he did not wish to visit Chitral. He then turned eastwards, and after a trying journey through the snow, crossed the Ishkaman Pass, north of Yasin. Thence he travelled southwards by the Karambar Valley, and eventually reached Gilgit, a short time after Captain Durand had started for Chitral. Mr. Dauvergne reports that the Russian explorer, Captain Grombc hevsky, whose attempt to reach Kafiristan was noticed some time ago, was stopped at Kila Panjah on the Oxus, by the Afghan

authorities.

THE ST. PETERSBURG PROBLEM.

TH HIS celebrated problem, which is first mentioned before 1708 in a letter from the younger Nicholas Bernoulli to Montmort, has been frequently discussed by Daniel Bernoulli (1730) and other eminent mathematicians. It may be briefly stated as follows:

A tosses a coin, and undertakes to pay B a florin if head comes up at the first throw, two florins if it comes up at the second, four florins if it be deferred until the third throw, and so What is the value of B's expectation?

on.

Hence the total value of B's expectation is an infinite series, each term of which is a shilling, or it is infinite.

This result of the theory of probability is apparently directly opposed to the dictates of common-sense, since it is supposed that no one would give even a large finite sum, such as £50, for the prospect above defined.

Almost all mathematical writers on probability have allowed the force of the objection, which they have endeavoured to evade by various ingenious artifices all more or less unsatisfactory.

The real difficulty of the problem seems to lie in the exact meaning of infinite and value of the expectation.

Since the infinite value of the result is only true if an infinite number of trials are paid for and made, all such considerations as want of time and the bankruptcy of A or B are precluded by the terms of the question.

The value of B's expectation is frequently confused with how much he can or ought to pay for it; thus Mr. Whitworth ("Choice and Chance," p. 234) finds that if B have 1024 florins, he may give very little more than 6 florins for the venture. This ingenious, solution seems to have no reference to the original problem, which has been modified by Mr. Whitworth's introduction of the word "advantageously" (p. 232).

B can pay for his expectation in three ways: (i.) a sum before each toss; (ii.) a sum before each series of tosses ending with head; (iii.) a sum for the total result of A's operations.

Mr. Whitworth apparently assumes the first method of pay ment, and shows that the larger B's funds are the more he may safely pay for each toss, since he can continue to play longer. Many mathematicians take the second method of payment. "However large a fee I pay for each of these sets, I shall be sure to make it up in time ("Logic of Chance," p. 155).

It is easy to show in this case also that what may be safely paid before each series increases with the number of series.

Suppose a very large number of tosses made, about half would come up heads and half tails; each head would end a series, when a fresh payment must be made by B. Suppose the tosses limited to one series, if B pays one florin he cannot possibly lose, if he pay anything more he may lose by head coming up the first time, and the more he pays the greater will his chance of loss be, since the series of tails must be longer to cover it. But, however large a finite sum he pays, he is not certain to lose, e.g. head may not come up till the hundred and first toss, when he would receive

2100

1,267 650,600 228,229 401,496 703,205 376 florins. If the sets are limited to one hundred, about 50 heads would probably come up the Ist toss.

£50 per set, we must expect a number of sets represented by 301 figures.

Lastly, what is the value of B's expectations if A's operations are continued indefinitely. With great deference to contrary opinions, I believe this to be the correct meaning of the problem in its original form. The theoretical result is in this case easily realized by the aid of the following illustration. Suppose the person A replaced by an automatic machine similar to that used for weighing sovereigns, which tosses continuously ten times per minute. On the average of a large number of tosses, B cannot receive less than one shilling a toss, I every two minutes, or £720 a day for ever. If the current rate of interest be 3 per cent., he may safely pay for this perpetual annuity £8,760,coo. Suppose, instead of this comparatively slow rate, the machine increased the rapidity of its operations indefinitely, the sum to be paid for the result would also increase indefinitely, or the expectation would become infinite.

SYDNEY LUPTON.

UNIVERSITY AND EDUCATIONAL
INTELLIGENCE.

CAMBRIDGE.-The Newall Telescope Syndicate has drawn up a scheme for building a dome for the telescope on a site adjoining the present Observatory, with an observer's house; and they recommend that an observer be appointed, at a stipend of £250 per annum, with a house, to devote himself to research in stellar physics, under the general direction of the Director of the Observatory.

The results of this year's commercial examination, held by the School's Examinations Board, are satisfactory. Geography was still very imperfect. Elementary mechanics has now been added to the list of compulsory subjects.

An influential syndicate has been appointed to consider the question of the mechanical workshops, their management and utility.

SOCIETIES AND ACADEMIES.
LONDON.

Royal Society, December 12.-" An Experimental Investigation into the Arrangement of the Excitable Fibres of the Internal Capsule of the Bonnet Monkey (Macacus sinicus).” By Charles E. Beevor, M.D., F.R.C.P., and Victor Horsley, B.S., F.R.S. (from the Laboratory of the Brown Institution).

After an historical introduction, the authors proceed to describe the method of investigation, which was conducted as follows. The animal being narcotized with ether, the internal capsule was exposed by a horizontal section through the hemisphere. By means of compasses the outline of the basal ganglia and capsule were accurately transferred to paper ruled with squares of one millimetre side, so that a projection of the capsule was thus obtained, divided into bundles of one millimetre square area. Each of these squares of fibres was then excited by a minimal stimulus, the same being an induced or secondary interrupted current. The movements were recorded and the capsule photographed.

In all forty-five experiments were performed, and they are arranged in eight groups, representing eight successive levels (i.e. from the centrum ovale to the crus) at which the capsule was investigated.

Before the results are described in detail a full account is given of previous investigations, experimental, clinical, and anatomical, on the arrangement of the internal capsule.

The anatomy of the part and the relation of the fibres to the basal ganglia are then discussed, and a full description given of each of the groups examined.

The general results are next given at length, of which the following is a résumé.

Firstly, the rare occurrence of bilateral movement is discussed, and the meaning of the phenomenon defined. Secondly, the lateral arrangement and juxtaposition of the fibres are considered. Thirdly, the antero-posterior order in which the fibres for the movements of the different segments are placed is described, and

upper limb (shoulder preceding thumb). trunk.

lower limb (hip preceding toes).

The character or nature of these movements is set out in a table giving the average localization of each segment. Speaking generally, it may be said that the movements are arranged in the same way as has already been shown by the authors to exist in the cortex (vide previous papers in Phil. Trans., 1887, 1888), viz. that the representation of extension is situated in front of flexion for the segments of the upper limb, while for the toes flexion is obtained, as in the cortex, in front of extension.

Numerous tables and diagrams are appended, showing the extent of appropriation of fibres for each movement.

Physical Society, November 15.-Prof. Reinold, F. R.S., President, in the chair.-Mr. Enright resumed the reading of his paper on the electrification due to contact of gases with liquids. Repeating his experiments with zinc and hydrochloric acid, the author, by passing the gas into an insulated metallic vessel connected with the electrometer, proved that it was always charged with electricity of the opposite kind to that of the solution. The electrical phenomena of many other reactions have been investigated, with the result that the gas, whether H, CO, SO3, SH, or Cl, is always electrified positively when escaping from acids, and negatively when leaving a solution of the salt. In some cases distinct reversal is not obtainable, but all these seem explicable by considering the solubility and power of diffusion of the resulting salts. Various other results given in the paper tend to confirm this hypothesis. Seeking for an explanation of the observed phenomena, the author could arrive at no satisfactory one excepting "contact" between gases and liquids, and if this be the true explanation he hoped to prove it directly by passing hydrogen through acid. In this, however, he was unsuccessful, owing, he believes, to the impossibility of bringing the gas into actual contact with the liquid. True contact only seems possible when the gas is in the nascent state. Some difficulty was experienced in obtaining non-electrified gas, for the charge is retained several hours after its production, even if the gas be kept in metallic vessels connected to earth. Such vessels, when recently filled, form condensers in which the electricity pervades an inclosed space, and whose charge is available on allowing the gas to escape. Soap bubbles blown with newly generated hydrogen were also found to act as condensers, the liquid of which, when broken, exhibited a negative charge. This fact, the author suggested, may explain the so-called "fireballs," sometimes seen during thunderstorms; for if, by any abnormal distribution of heat, a quantity of electrified air becomes inclosed by a film of moisture, its movements and behaviour would closely resemble those of fire-balls. A similar explanation was proposed for the phenomenon mentioned in a recent number of NATURE, where part of a thundercloud was seen to separate from the mass, descend to the earth, and rise again. The latter part of the paper describes methods of measuring the contact potential differences between gases and liquids, the most satisfactory of which is a "water dropper," and by its means the P.D. between hydrogen and hydrochloric acid was estimated to be about 42 volts. Prof. Rücker asked if the experiment with zinc and hydrochloric acid could be started in the second stage by having the acid partly saturated with salt. Dr. C. V. Burton thought it probable that contact could be made between a gas and a liquid by shaking them up together in a bottle. In reply, Mr. Enright said the experiment could be started at any stage, and reversal effected as often as desired by adding either acid or a solution of salt to the generating vessel.-Mr. Herbert Tomlinson, F.R.S., read a paper on the effect of repeated heating and cooling on the electrical resistance and temperature coefficient of annealed iron. In a paper recently presented to the Royal Society, the author has brought forward an instance of an iron wire, which when subjected to magnetic cycles of minute ange alternately at 17° and 100° C., had its molecular friction and magnetic permeability reduced respectively to about one-quarter and one-half their original values. The present experiments were undertaken to see whether by

such heatings and coolings the temperature coefficient of iron could be brought down to something approaching the number given by Matthiessen for "most pure metals." The wire experimented on was first annealed by heating to 1000° C. for several hours and allowing to cool slowly in a furnace placed at right angles to the magnetic meridian; the process was repeated three times. Afterwards the wire was covered with paper and wound doubly into a coil. This coil was inclosed in a water-jacketed air-chamber, and connected with a sensitive Wheatstone bridge. Thermo-electric and Peltier effects were eliminated by always keeping the galvanometer circuit closed. By repeated heating to 100° C. and cooling to 17° C. for long intervals, the specific resistance at 17° C. was reduced from 11,162 to 10,688 C.G.S. units, after which the operations produced no further change. At the same time the temperature coefficient increased in the proportion of I: 1'024. From careful determinations of the resistance at different temperatures, the formula R = R(+0.005131 +0000008152) was deduced, whilst that obtained from Matthiessen's results for pure iron annealed in hydrogen is R= R(1+00054251+0000008312). Taking his own determination of specific resistance of impure iron as correct, coupled with Matthiessen's law connecting the resistances and temperature coefficients of metals and their alloys, the author finds that the specific resistance of pure iron deduced from Matthiessen's results is from 4 to 5 per cent. too high. In conclusion, Mr. Tomlinson expresses a hope that the B.A. Electrical Standards Committee may be induced to determine the absolute resistance and temperature coefficient of the pure metals which are in ordinary use. Prof. Ayrton thought Matthiessen's results were expressed in B. A. units, and hence might appear I or 2 per cent. too great. Mr. Tomlinson, however, believed the number he took were expressed in legal ohms. Dr. Walmsley asked for what value of the magnetizing force the permeability of the iron mentioned in the beginning of the paper was determined; to which Mr. Tomlinson replied that they were much smaller than the earth's horizontal component.-Dr. Thompson's paper on geometrical optics was postponed.

EDINBURGH.

Royal Society, December 2.-Sir Douglas Maclagan, VicePresident, in the chair.-Prof. Tait communicated a paper by Dr. G. Plarr, on the transformation of Laplace's coefficients. Mr. A. C. Mitchell read a preliminary note on the thermal conductivity of aluminium. A comparatively rough first experiment shows that this metal slightly exceeds good copper in conducductivity. Dr. John Murray discussed the question of the origin and nature of coral reefs and other carbonate of lime formations in recent seas. He first referred to experiments which have recently been made regarding secretion and solution of carbonate of lime. Carbonate of lime remains are found in great abundance at the sea bottom in shallow waters, but the amount steadily diminishes as the depth increases, until at 4000 fathoms almost every trace has disappeared. This is due to solution, as the organisms slowly fall to the bottom. Everywhere within 500 fathoms of the surface the ocean teems with life. Greely Expedition was starving within ten feet of abundant food which might have been obtained by breaking a hole through the ice and using a shirt as a drag-net. Dr. Murray then proceeded to discuss his theory of the formation of coral reefs, bringing forward in reply to objections by Dana and others, some recently obtained facts regarding the existence of shallow regions in what is, on the whole, deep water. He showed that carbonate of lime is continually produced in great quantity in warm tropical water by the action of sulphate of lime in solution on effete products. This explains the great growth of coral in tropical regions. The absence of coral on certain shores in tropical districts is explained by the uprise of cold water due to winds blowing off shore. His paper was illustrated by an elaborate series of lime-light diagrams.

PARIS.

The

Academy of Sciences, December 9.-M. Hermite in the chair. On the nitrification of ammonia, by M. Th. Schloesing. In a recent communication (September 9) the author described three experiments on the nitrification of ammonia in vegetable humus, tending to prove that this phenomenon is accomplished without any appreciable loss of nitrogen liberated in the gaseous state. He now reports the results of two other experiments, showing that this is no longer the case when a larger proportion of ammonium carbonate is introduced into the soil.-Correction

in the tables of Jupiter's movement worked out by Le Verrier, by M. A. Gaillot. Comparing the secular terms of the eccentricity and perihelion of Jupiter's and Saturn's orbits as determined by Le Verrier, Hill (Astronomical Journal, No. 204) came to the conclusion that there must be an error of sign in the terms of the second order relating to Jupiter's orbit. M. Gaillot has now gone over the calculations again, and finds that Le Verrier's manuscript is correct, but that, as conjectured by Hill, a misprint of a sign occurs in the published work. In vol. x. p. 242, the sign + appears instead of - before the term oo15,5548' cos(w '). On the characteristic temperatures, pressures, and volumes of bodies, by M. Ladislas Netanson. These researches tend to show that for every gas there exists an infinite number of characteristic values, t, p, v, which, being adopted as units of the general variables t, p, v, have the remarkable property of eliminating all difference in the characteristic equations of the different gases. The systems usually employed in measuring temperatures, pressures, and volumes, having nothing in common with the intimate nature of the bodies themselves, give rise to differences in the equation F(t, p, v) = 0, which disappear when for each body the physicist employs a special system in accordance with its properties.-On the localization of the interference fringes in thin isotropic plates, by M. J. Macé de Lépinay. In studying the exact conditions of the fringes in thin prismatic plates, the author finds a complete verification of the general theory expounded by him in a previous communication (Comptes rendus, July 22, 1889). The consequences of the theory may be considered as entirely verified by these experiments.-On the want of accuracy in thermometers, by M. E. Renou. On a recent occasion (July 1) M. Cornu remarked that hitherto these instruments have been liable to an error of from 0° 2 to 0° 3. It is now shown that observations hitherto recorded may give rise to the greatest inconvenience, more perhaps in future than at present. These remarks were supplemented by M. Cornu, who pointed out that errors in the mercury thermometer as great as o°2 or o° 3 occur only in observations taken at considerable intervals of temperature and with instruments not sufficiently tested. —Variations in the mean temperature of the air at Paris, by M. Renou. Twenty years ago the author attempted to show that severe winters return in groups of five or six every forty-one years. This somewhat elastic period is perhaps reproduced better in groups of years than in single years. It also appears that the Observatory of Paris gives a mean temperature higher by o°7 than that of the surrounding rural districts-10°7 as compared with 100 of the Parc Saint-Maur Observatory.-On the observations of temperature on the top of the Eiffel Tower, by M. Alfred Angot. These observations, begun on July 1, are being still continued with a Richard registering thermometer, placed 336 metres above the sea, and about 301 above the ground. Compared with those of the Parc Saint-Maur (50 metres) they show that the normal decrease of about 1° for every 180 metres is greatly exceeded in summer and during the day (means of the maxima), and correspondingly diminished in winter and at night (means of the minima); or there is generally even an inversion in the temperatures, the air being then warmer at 300 metres than near the ground.-Papers were submitted by M. Raoul Varet, on the ammoniacal cyanides of mercury; by M. L. Prunier, on the simultaneous quantitative analysis of sulphur and carbon in substances containing sulphur; by M. E. Guinochet, on an acid isomerous with tricarballylic acid; by M. C. Tanret, on two new sugars extracted from quebracho (Aspidosperma quebracho); by M. Arnaud, on carotine, its probable physiological action on the leaf; and by MM. André Thil and Thouroude, on a micrographic study of the woody tissues of native trees and shrubs, prepared for the special exhibition of the Forest Department. The sealed paper, by M. A. Joannis, on compounds of potassium and sodium with ammonia gas, was opened by the Secretary.

BERLIN.

Physical Society, November 22..-Prof. du Bois Reymond, President, in the chair.-Dr. Lehmann spoke on the nature and distribution of the Babylonian metrical system. He expressed his desire to lay before the competent judgment of the Physical Society, the results of his most recent archæological researches, so far as they are of direct physical interest, and then proceeded to describe the numerical system employed by the ancient Baylonians, explaining that it consisted of a sexagesimal system with decimal subdivisions. The unit of time, the double

=

minute, was the time occupied by the sun's rising, measured at the Equinox, and could thus be recovered at any time. It was measured by the mass of water which flowed out of a certain vessel from the instant at which the upper edge of the sun appeared above the horizon to the moment at which his lower edge was exactly touching the horizon. The day consisted of 720 of these units. The unit of length was the ell, which was used in two forms, either as a single- or double-ell; subdivisions used were the foot double-ell, the hand-width, and the finger-length. The unit of weight was the mine, also occurring as single-mine or double-mine. The derivation of units of weight from units of length, as in the modern case of grams and centimetres, was also known, but of course the water used was not distilled and was not weighed at 4° C. The speaker had, however, succeeded in discovering a measuring-scale on an ancient monument dating from the year 2500 B. C., which had enabled him to compare the Babylonian measures with those of our own time. It appeared from this that a hand-breadth 994-99 6 mm. ; a double-ell 994-996 mm. ; and the foot € 331-332 mm. He had further discovered several stamped weights, and thus found that the double-mine = 9824-985'8 grams. The single-mine weighed half as much as the double-mine, but the gold-mine and silver-mine were equal to five-sixths of a single-mine. The royalmine was I per cent. heavier than the gold-mine, and was employed for the payment of tribute. The coinage was based upon the mine and its sexagesimal division. Dr. Lehmann remarked how surprising it is to find that the length of a seconds-pendulum at Babylon is 992'5 mm., and was inclined to advance the hypothesis that the Babylonian unit of length was derived from a seconds-pendulum, the foot being one-third the lengh of the pendulum. He next proceeded to give an account of the spread of the Babylonian mine, and of the Phoenician which was derived from it, as a unit of weight among the civilized nations of Europe. The discovery of an old Roman balance had enabled him to determine that the old Etrurian pound was equal in weight to the Babylonian mine. The Babylonian unit of weight is found not only in Italy and the Mediterranean generally, but also the old Dutch and French pounds and the Russian pood are equal in weight to the mine. The speaker considered it to be quite impossible that in all the above cases we are dealing with a chance correspondence between the several weights. In the discussion which ensued, objections were raised on several sides against the hypothesis that the ancient Babylonians had knowledge of the secondspendulum, which had subsequently been lost. On the other hand, it was pointed out by others that the ancients were not improbably acquainted with the plummet, and used it for squaring stones, &c.; and since, further, they employed the double-minute as unit of time, it is not impossible that they were acquainted with the seconds pendulum. The cause of their not having employed this instrument to supply a time-unit may perhaps be found in their ignorance of any means by which the pendulum could be kept in continuous and uniform motion. In conclusion, the speaker laid stress on the high state of culture which the Babylonians had attained three thousand years B.C., and expressed his regret that a complete blank exists with regard to everything of an earlier date than the cuneiform inscriptions.

STOCKHOLM.

Royal Academy of Sciences, November 13-On the vegetation of the southmost part of the Isle of Gotland, by Prof. Wittrock.-Myxochate, a new genus of fresh-water Alga, by Herr K. Bohlin. - On determinations of the longitude and observations on the pendulum executed in Sweden during the year 1889, by Prof. Rosén.-On a reform in the analysis of gaseous bodies, by Prof. O. Pettersson. -On the invariants of linear, homogeneous differential equations, by Prof. MittagLeffler. The form of the observations on linear differential equations, by Herr A. M. Johanson.-On the case of Poincaré as to the three bodies problem and some analogous dynamical propositions, by Herr E. Phragmen.—On the observations made at the Observatory of Upsala for the determination of the equinoctium in the spring of 1889, by Dr. K. Bohlin and Herr C. A. Schultz-Steinheil.-Definitive orbit elements of the comet 1840 iv., by Herr Schultz-Steinheil.-Study of the infra-red spectra of carbonic acid and of carbonic oxide, by Dr. K. Angström. On the action of nitric acid on naphthalin-a-sulphon acid, by Prof. P. J. Cleve.-On naphthalin-1-5, calogenesulphon-acids, by Herr R. Manselius.

DIARY OF SOCIETIES.

LONDON.

THURSDAY, DECEMBER 19.

ROYAL SOCIETY, at 4.30.-(1) Comparison of the Spectra of Nebula and
Stars of Groups I. and II., with those of Comets and Aurora; (2) the
Presence of Bright Carbon Flutings in the Spectra of Celestial Bodies:
Prof. J. N. Lockyer, F.R.S.-Some Observations on the Amount of
Luminous and Non-luminous Radiation emitted by a Gas-flame: Sir J.
Conroy, Bart.-On the Effects of Pressure on the Magnetization of
Cobalt C. Chree. -On the Steam Calorimeter : J. Joly.-On the Exten-
sion and Flexure of Cylindrical and Spherical Thin Elastic Shells: A. B.
Basset, F.R.S.
LINNEAN SOCIETY, at 8.-Intensive Segregation and Divergent Evolution
in Land Mollusca of Oahu: Rev. John T. Gulick.-Dictopteris; with
Remarks on the Systematic Position of the Dictyotaceæ: T. Johnson.
CHEMICAL SOCIETY, at 8.-On Frangulin: Prof. Thorpe, F.R.S., and H.
H. Robinson.-Arabinon, the Saccharon of Arabinose: C. O'Sullivan,
F.R.S.-Note on the Identity of Cerebrose and Galactose: H. T. Brown,
F.R.S., and Dr. G. H. Morris.

SUNDAY, DECEMBER 22.
SINDAY LECTURE SOCIETY, at 4.-Algeria and Morocco: some Artistic
Experiences (with Oxyhydrogen Lantern Illustrations): Henry Black-
bu rn.
SATURDAY, DECEMBER 28.
ROYAL INSTITUTION, at 3-Electricity (adapted to a Juvenile Auditory):
Prof. A. W. Rücker, F.R.S.

BOOKS, PAMPHLETS, and SERIALS RECEIVE D. East Africa and its Big Game: Sir J. C. Willoughby (Longmans).Measurement of Small Mammals, &c. : Dr. C. H. Merriam (Washington).North American Fauna, Nos. 1 and 2: Dr. C. H. Merriam (Washington) Report of the Ornithologist and Mammalogist for 1888; Dr. C. H. Merriam (Washington).-Physical Memoirs, vol. i., Part 2 (Taylor and Francis).Journal of the Royal Agricultural Society, October (Murray).—Mitteilungen des Vereins für Erdkunde zu Halle A/s, 1889 (Halle).-Proceedings of the Academy of Natural Sciences of Philadelphia, Part 2, 1889 (Philadelphia).-Notes from the Leyden Museum, vol. xi., No. 3 (Leyden, Brill).—