Bidder has himself been working at Naples for the last five years. His appreciatory remarks on Dendy's researches prove how much of interesting and new matter lies in manuscript in the laboratory at Naples, and leads us to express the hope that Mr. Bidder will soon follow the example of his senior, and give us a monograph of the Calcarea Homocoela of the Gulf of Naples; with more details on the glandular ectoderm.

Travaux de la Société des Naturalistes de St. Pétersbourg, Section de Zoologie et de Physiologie, tome xxi., livr. I (Russian). On the influence of temperature, and the distance from the section of a nerve, on its electrical irritability, by B. F. Verigo.-Observations on the Araneina, by V. Wagner.-The minutes of proceedings contain several interesting notes: namely, a list of the Bryozoa of the Murman coast of Russia, by M. Khvorostansky, containing eighty-one species; on the blood of some invertebrates, by V. Wagner, from which it appears that it always contains two different kinds of cells- the granulous and coloured ones, and the amoeboid ones or leucocytes, besides some other cells which, however, must be considered as derived from the above two kinds.-M. Shimkevitch's remarks on the artificial incubation of ostriches in the ostrich park at Heliopolis are also worth mentioning.

Bulletin de la Société des Naturalistes de Moscou, 1891, No. 1. On the group of the sillimanite and the part played by aluminium in the silicates, by W. Wernadsky (in Russian, summed up in French). The paper contains, besides the description of the experiments already published in the Comptes rendus, a discussion of the facts, which brings the author to the following conclusions: the compounds of silicon with aluminium have an acid reaction; they may be embodied in one group, that of the sillimanite. Some of them are hydrates, and some others are salts of these, or of other possible anhydrides. Polymorphic varieties arise in this group with the change of physical conditions, without any perceptible change in the chemical composition. -On the morphology and classification of the Chlamydomonads, by Prof. Goroshankin (in German, with three coloured plates); being a full monograph on the family, in which the following new species are described: Chlamydomonas De-Baryana, C. Perty, C. Steinii, C. Kuteinikowi, C. reticulata, and C. Ehrenbergii.-On some peculiarities in the development and the structure of the skull of Felobates fuscus, by A. N. Sewertzow.-Note on the Hipparion crassum, by Marie Pavloff (French).-On the fossil plant-bearing deposits of East Russia and Siberia, by C. Kosmovsky (in French). The close similarity between the supposed Jurassic fresh-water deposits of East Russia and Siberia and the "Artinsk" series is briefly indicated.

SOCIETIES AND ACADEMIES.

LONDON.

Royal Society, November 19.- "On the Loci of Singular Points and Lines which occur in connection with the Theory of the Locus of Ultimate Intersections of a System of Surfaces.' By M. J. M. Hill, M.A., Sc. D., Professor of Mathematics at University College, London. Communicated by Prof. Henrici,

F.R.S.

Introduction.

In a paper "On the cand p-Discriminants of Ordinary Integrable Differential Equations of the First Order," published in vol. xix. of the Proceedings of the London Mathematical Society, the factors which occur in the c-discriminant of an equation of the form f(x, y, c) = 0, where f(x, y, c) is a rational integral function of x, y, c, are determined analytically.

It is shown that if E o be the equation of the envelope locus of the curves ƒ (x, y, c) = 0; if N- o be the equation of their node locus; if C o be the equation of their cusp locus, then the factors of the discriminant are E, N2, C3.

The object of this paper is to extend these results to surfaces. PART I.- The Equation of the System of Surfaces is a Rational Integral Function of the Co-ordinates and one Arbitrary

Parameter.

When there is only one arbitrary parameter, each surface of the system intersects the consecutive surface in a curve, whose equations are the equation of the surface and the equation obained by differentiating it with regard to the parameter. (These The theorem was originally given by Prof. Cayley, in the Messenger of Mathematics, vol. ii., 1872, pp. 6-12.

equations will be called the fundamental equations in this part.) Hence each surface touches the envelope along a curve. It is known that the equation of the envelope may be obtained by eliminating the parameter from the fundamental equations and equating a factor of the result to zero. But it frequently happens that there are other factors of the result (or discriminant) which, when equated to zero, do not give the equation of the envelope. These factors are connected with loci of singular points. If each surface have one singular point, the locus of all the Its singular points of the surfaces of the system is a curve. equations, therefore, cannot be found by equating a factor of the discriminant to zero. But if each surface of the system have upon it a nodal line, then the locus of the nodal lines of all the surfaces is a surface, and its equation may be found by equating to zero a factor of the discriminant.

The singular points in space, the form of which depends only on the terms of the second order, when the origin of co-ordinates is taken at the singular point, are :

(i.) The conic node.

(ii.) The biplanar node or binode.
(iii.) The uniplanar node or unode.

It is shown that a surface cannot have upon it a curve at every point of which there is a conic node. Hence there are two varieties of nodal lines to be considered; the first, being such that every point is a binode, may be called a binodal line; and the second, being such that every point on it is a unode, may be called a unodal line. It is shown that if E o be the equation of the envelope locus, Bo the equation of the locus of binodal lines, U = 0 the equation of the locus of unodal lines, then the factors of the discriminant are, in general, E, B2, U3, respectively.

This is the general theorem, but it is assumed in the course of the investigation, when the discriminant is being formed, that the fundamental equations are satisfied by only one value of the parameter at each point on the envelope locus or on a locus of binodal or unodal lines.

The investigation is accordingly carried a step further, and it is shown that if the fundamental equations are satisfied by two equal values of the parameter at points on an envelope locus, or on a locus of binodal or unodal lines, the factors of the discriminant are E2, B3, U4, respectively.

The geometrical meaning of the condition that the fundamental equations are satisfied by two equal values of the parameter in the case of the envelope is that the line of contact of the envelope with each surface of the system counts three times over as a curve of intersection, instead of twice as in the ordinary case. The meaning of the condition in the case of the loci of singular lines is that each of these loci is also an envelope.

PART II.-The Equation of the System of Surfaces is a Rational Integral Function of the Co-ordinates and two Arbitrary

Parameters.

When there are two arbitrary parameters in the equation of the system of surfaces, the equation of the locus of ultimate intersections is found by eliminating the parameters between this equation and the two equations obtained by differentiating it with regard to the parameters. (These equations will in this part of the investigation be called the fundamental equations.)

In general the locus of ultimate intersections is a surface. The exceptional cases in which it is not a surface are enumerated at the end of the paper. These include the case where the equation of the system of surfaces is of the first degree in the parameters. Hence it will be supposed that the degree of the equation of the system of surfaces in the parameters is above

the first.

In general, the locus of ultimate intersections possesses the envelope property, and the equation of the envelope is determined by equating the discriminant, or a factor of it, to zero.

If factors of the discriminant exist which, when equated to zero, give surfaces not possessing the envelope property, then these surfaces are connected with loci of singular points.

Now the locus of singular points of a system of surfaces whose

equation contains two arbitrary parameters is in general a curve. Hence its equations cannot be determined by equating to zero a factor of the discriminant.

But if every surface of the system have a singular point, then in general its co-ordinates may be expressed as functions of the two parameters of the surface to which it belongs. Hence the It will be proved that locus of the singular points is a surface.

it is a part of the locus of ultimate intersections. Hence its

equations can be obtained by equating to zero a factor of the discriminant.

Let Eo be the equation of the envelope locus,

Co be the equation of the conic node locus, Bo be the equation of the biplanar node locus, Uo be the equation of the uniplanar node locus. Now at any point on the locus of ultimate intersections(I.) There may be one system of values of the parameters satisfying the fundamental equations.

In this case there may be envelope, conic node, or biplanar node loci; and the corresponding factors of the discriminant are E, C2, B3 respectively.

(II.) There may be more than one system of distinct values of the parameters satisfying the fundamental equations.

In this case the effect of the distinct values is additive. Thus if there be systems of values at a point on the envelope locus, the factor E would occur to the pth power.

(III.) Two or more systems of values of the parameters satisfying the fundamental equations may coincide.

The results must be stated differently in the cases (a) where the degree in the parameters of the equation of the system of surfaces is greater than two; (B) where the degree in the parameters of the equation of the system of surfaces is two.

In the case (a) it will be shown that there may be envelope loci in which the envelope has stationary contact with each surface of the system; conic node loci, which are also envelopes; biplanar node loci, in which the edge of the biplanar node always touches the biplanar node locus; and uniplanar node loci: and the corresponding factors of the discriminant are E2, C3, B4, U respectively.

The case (8) always falls under the next case(IV.) The values of the parameters satisfying the fundamental equations may become indeterminate.

If the equation of the system of surfaces be of the second degree in the parameters, and the analytical condition hold which expresses that the fundamental equations are satisfied by two coinciding systems of values, then this condition requires to be specially interpreted. For now the second and third fundamental equations are of the first degree in the parameters, so that if they are satisfied by two coinciding systems of values, they must be indeterminate.

It is, however, possible to determine a single system of values of the parameters satisfying them. In this case the three surfaces represented by the fundamental equations intersect in a common curve (which is fixed for fixed values of the parameters) lying on the locus of ultimate intersections; whereas in the previous cases they intersect in a finite number of points lying on the locus of ultimate intersections.

The surface of the system, corresponding to the fixed values of the parameters, touches the locus of ultimate intersections along the above-mentioned curve.

In general, there are two conic nodes of the system at every point of the locus of ultimate intersections. The parameters of the surfaces having the conic nodes are determined by two quadratic equations, called the parametric quadratics; and in general the roots of each parametric quadratic are unequal. In this case the corresponding factor of the discriminant is C2. If the roots of both parametric quadratics are equal, the two surfaces having conic nodes are replaced by one surface having a biplanar or uniplanar node. In this case the corresponding factors of the discriminant are B3, U4, respectively.

If the parameters of one of the surfaces having a conic node become infinite, this surface may be considered to disappear, and there is but one conic node at each point of the locus of ultimate intersections. In this case the corresponding factor of

the discriminant is C2.

If the parameters of both surfaces having conic nodes become infinite, both these surfaces may be considered to disappear, and the locus of ultimate intersections is an envelope locus (touching each surface of the system along a curve). In this case the corresponding factor of the discriminant is E3.

If the parameters of both surfaces having conic nodes become indeterminate, then there are at each point an infinite number of biplanar nodes, and each surface of the system has a binodal line lying on the locus of ultimate intersections. In this case he corresponding factor of the discriminant is B4.

Physical Society, November 20.-Prof. W. E. Ayrton, F.R.S., President, in the chair.-Dr. Philippe A. Guye gave a short account and discussion of the various forms which have

been given to the general equation expressing the behaviour of liquids and gases under different conditions of volume, temperature, and pressure, by Van der Waals, Clausius, Sarran, Violi, Heilborn, and Tait. He first considered the equation of Van der Waals, which, although only an approximation to the true one, may be made to lead to numerous important deductions. He then showed that, of the various more exact formula proposed, that of Sarran is the simplest, and may be used with less expenditure of time and trouble than any of the others. In conclusion, he insisted on the necessity of experi mental researches as the only means of arriving at a definite conclusion as to which of the various formula is the true one; such researches should involve determinations, as exact as

possible, of the critical constants, and of isotherms at high temperatures and great pressures. Prof. Ramsay inquired whether the constants in the formula of Clausius had any physical meaning, or were they merely numbers? M. Guye, in reply. said that, although some of the constants in the improved formulæ nad physical interpretations, Van der Waals's equation was the only one in which all the constants had precise physical signi. fications. Prof. Rücker said it was only necessary to look at the formulæ to see how important a factor Van der Waals's expres sion had been in later developments of the subject. Although it did not agree with experiment under all conditions, particularly at small volumes, yet it was a close approximation over a considerable range, and was the only formula in which all the constants had definite physical meanings. Prof. Tait had pointed out that the number of constants were too few to fully represent the facts, for, by following Andrews's reasoning, he had shown that about the critical point a straight line cuts the isotherm in five points. Nevertheless, during the last twenty years all the so-called improved formula were modifications of Van der Waals's expression, and this, he thought, showed how valuable the original formula was. Prof. Fitzgerald said he once tried how far lausius's formula agreed with the experimental results published by Messrs. Ramsay and Young, and after several months' work, relinquished it on account of the tremendous labour involved. He thought that such complicated formule retarded rather than advanced science; simple ones (even if less accurate) were likely to lead to greater advanceProf. Carey Foster remarked that the expression pv = RT, which is nearly true for gases, was the starting-point of all subsequent advances. Van der Waals had arrived at a still closer approximation by taking into account the volume The occupied by the particles and their mutual pressure. President said Van der Waals's memoir had been adversely criticized because of its supposed insufficient recognition of Andrews's investigations on the subject. Better acquaintance with the work had, however, shown this criticism to be un deserved. Dr. C. V. Burton read a paper on a new theory It is assumed that it concerning the constitution of matter.

ment.

is possible to have in the ether a distribution of strain which is itself in equilibrium. Such a distribution is called a "strainfigure." An atom is looked upon as an aggregation of strainfigures, the possible varieties of strain-figures (and hence of atoms) being limited by the conditions of equilibrium, and the sizes of possible strain figures dependent on the coarse grained ness of the turbulent motion or other structure of the ether. The motion of matter is considered to be merely the trans. ference of a strain distribution from one portion of the ether to another. This the author illustrated by causing a loop to travel along a rope, the loop being regarded as a strain distribution which is propagated along the rope, whilst the rope itself is not transferred. Such transference may occur without encountering any resistance, and the strain-figure will retain the same form, provided the velocity is small compared with that at which gravitation is propagated. The equations of motion of a strainfigure are deduced, and are shown to be identical with those of ordinary matter, provided certain conditions of symmetry are realized. It is also shown under what conditions an atom consist. ing of strain-figures would have a finite number of degrees of freedom, and some attempt is made to examine how gravitation and other attractions might follow from a distribution of stress in the strained ether.

cussed.

An inquiry is also made into the reason why elements have fixed properties, and their transmutation is dis Prof. Fitzgerald, referring to the elastic-solid theory of the ether, said Sir W. Thomson's more recent papers had thrown considerable doubt upon it. The propagation of strainfigures was, he thought, a case of wave motion. In his lectures he had likened the passage of matter through space to that of a drop of water through ice, the ice in front melting, and the rear

of the drop freezing as the liquid state progressed. Many points raised in the paper were, he said, very interesting, and the suggestion that the discrete nature of atoms is the result of the coarse-grainedness of matter, very good. On the other hand, he considered the static treatment of strain-figures improper, for the ultimate conditions must be kinetic. Dr. O. Lodge agreed with Prof. Fitzgerald in regarding the motion of the loop along the rope as a wave motion whose velocity of propagation is equal to that of the loop. A similar case occurs when a ring of rope is spinning, and has a pulse impressed on it at one point, for the pulse travels at the same speed as the rope. -A paper on a permanent magnetic field, by Mr. W. Hibbert, was postponed until next meeting.

Royal Microscopical Society, November 18.-Dr. R. Braithwaite, President, in the chair.-A special meeting was first held, at which certain alterations in the by-laws were proposed by the Council, and accepted by the Fellows. The ordinary meeting was then constituted.-Mr. C. L. Curties exhibited and described a small heliostat made on the lines laid down by Mr. Comber. It was simple and effective, and was adapted for use in any latitude between 15 and 70°.-Mr. J. W. Gifford read a paper on the resolution of Amphipleura pellucida. Mr. Gifford said he had examined a frustule of A. pellucida with sodium light illumination, that being the most convenient form of monochromatic light at the time. Under this light A. pellucida unmistakably showed dots, which became more marked as the frustule was shifted to the side of the field of vision. The question then arose as to the possibility of photographing the object by the light of the sodium flame, and plates treated with an erythrosine bath were used. It occurred to him that a trough containing a solution of iron perchloride used as a screen would cut off all the blue end of the spectrum, and also some of the green, leaving only the green yellow, yellow and red; but on the other hand, he found the erythrosine plates were only sensitive as far down as the yellow, more especially to the green-yellow. In this way the part of the spectrum used for photographing could be reduced to a narrow band about midway between the D and E lines in the solar spectrum. By this means he succeeded in obtaining the photographs exhibited, and which he had avoided touching up. Whether these markings were true or spurious was a question he did not touch, but they appeared to have as good a claim as those on Surirella gemma. He thought it more probable that in both cases they were simply multiplied rings of the midrib and sides produced by the higher order of diffraction spectra according to the Abbe theory. The mounts of A. pellucida used were of realgar, or rather a higher sulphide of arsenic, prepared by mixing sulphur with realgar. He found it extremely difficult to make mounts with such a large proportion of realgar. The mounts being of a deep orange colour inclining to red, enabled the coloured screen to be dispensed with. But this highly refracting medium very soon cracks off the coverglass. The advantage of working with this form of illumination and a suitable colour-correct plate is that ordinary achromatic object-glasses perform almost as well as apochromatic. He could not see the beaded markings with any glass of less aperture than 14; the best results being obtained with Powell and Lealand's apochromatic of 15, also with their achromatics of 15 and of 143. He also used in photographing a Zeiss projection ocular. Mr. E. M. Nelson, speaking of the value of drawings made with Beale's neutral tint reflector, said he had tested the matter by making a drawing of lines on a micrometer scale of 185 mm. under an apochromatic objective giving a magnifying power x 850; he found on measuring that they showed only a very slight displacement.-Mr. Curties exhibited a new form of microscope made on the Nelson model. -Mr. Nelson described some improvements in his apparatus for producing pure monochromatic light for use with the microscope.-Mr. A. W. Bennett gave a résumé of his paper on the fresh-water Algae of Southwest Surrey, in which he describes several new species.

CAMBRIDGE.

Philosophical Society, November 9.-Dr. Gaskell in the chair. The following communications were made:-On a Peripatus from Natal, by Mr. A. Sedgwick.-On variations in the colour of cocoons (Saturnia carpini and Eriogaster lanestris), with reference to recent theories of protective coloration, by Mr. W. Bateson. The cocoons of several moths, e.g. the emperor and small egger, vary in colour from dark brown to white. It is believed by some that these colours have a protective value as a means of concealment, and fit has been

stated by Poulton and others that when spun on leaves which will turn brown, or in dark surroundings, the cocoons are dark, while they are white if spun on white paper. To account for this phenomenon "the existence of a complex nervous circle" has been assumed. The present experiments showed that it is true that larvæ left to spin on their food-leaves produce dark cocoons, and also that if they are taken out and put in white paper the cocoons are white. But it was found that larvæ similarly taken out and made to spin in dark substances also spun white cocoons, and indeed that starvation, parasites, or interference at the time of spinning, lead to the production of a white cocoon. On the contrary, if white paper is put amongst the food, so that the larvæ can, of their own choice, walk into it and spin, the cocoons are generally dark. It was noticed in several cases that larvæ which had been shut up evacuated a quantity of dark juice having the natural tint of the cocoon, and the suggestion was hazarded that absence of colour in the cocoon perhaps results from the loss or retention of this juice, which may be of the nature of meconium.-Exhibition of Phylloxera vastatrix, by Mr. A. E. Shipley.-On digestion in Ammocætes, by Miss R. Alcock (communicated by Dr. Gaskell).-On the reaction of certain living cells to methylene-blue, by W. B. Hardy. The chair was taken by Prof. Hughes during the reading of the last two papers.

from each other.

PARIS.

Academy of Sciences, November 30.-M. Duchartre in the chair. The reclaiming and cultivation of land in the Camargue, by M. Chambrelent. A description of the irrigation, cultivation, procuring of potable waters, and means of transpor, introduced in the Camargue. This district is contained between two branches of the Rhone, 50 and 58 kilometres long re. spectively, which reach the sea at points about 40 kilometres The bifurcation occurs at Arles, about 50 kilɔmetres from the coast. At the beginning of this century the land was absolutely unfertile, and the inhabitants were unprovided with potable water. The author states the success that has attended the efforts that have been made to remedy this state of things, and bring the land under cultivation. -Observations of the asteroid discovered by M. Borrelly, at Marseilles Observatory, on November 27, 1891, by M. Borrelly. The positions are given for November 27 and 28.-Résumé of solar observations made at the Royal Observatory of the Roman College, during the third quarter of 1891, by M. P. Tacchini. (See Our Astronomical Column.)-On the tides of the Bay of St. Malo, The author has made tidal observations at by M. Heurtault. St. Malo for the last eighteen years, and states some of the results. The mean monthly level of the sea appears to have a The minimum value in April and a maximum in October. mean annual level increased gradually from 1874 to 1883, and has since been diminishing. The establishment of the port also indicates similar variations. Thus it passed from 6h. 55m.

in 1874 to 6h. 10'24m. in 1884, and has since exhibited a tendency to diminish. Its months of maxima are April and September, and of minima July and December, the general mean being 6h. 89m. Contrary to Laplace's statement-" Plus la mer s'élève lorsqu'elle est pleine, plus elle descende en basse mer suivante"-it has been found from observations of 45 tides, that in only 25 did the lowest sea follow the highest tide; 3 times it immediately preceded, and 17 times it occurred two tides before.

(1) The

Phosphides of boron, by M. A. Besson. The preparation and properties of boron phosphide, PB, are described; the possible existence of a more stable compound is also indicated.-On the bromine derivatives of methyl chloride, by M. A. Besson. The compounds CH,BrCl and CHBrCl have been prepared. The author has not yet succeeded in isolating CBr Cl. compound CH,BrCl is a colourless liquid distilling without decomposition at + 68°, solidifying at 55; its specific gravity is 1'90. (2) CHBrCl boils between 117 and 119, and solidifies at - 32°.-On a modification of the calorimetric bomb of M. Berthelot, and upon the industrial determination of the calorific power of combustibles, by M. Pierre Mahler.-On the fixation of free nitrogen by plants, by MM. Th. Schloesing, Jun., and Em. Laurent. The conclusions drawn from the data obtained are

the following:-(1) There are some inferior green plants capable of fixing gaseous nitrogen. (2) Under the conditions of experiment peas take up much atmospheric nitrogen, whereas fallow soils, oats, mustard, cress, and spurrey are not capable of fixing a measurable quantity. The paper has remarks by M. Berthelot appended. The ammonia in the atmosphere and in the rain of

a tropical region, by MM. V. Marcano and A. Muntz. The observations were made at Caracas, in the Gulf of Venezuela, lat. 103 N., altitude 922 metres. An examination of twenty samples of rain gave a mean proportion of ammonia of 1.58 milligram per litre, with a minimum of 0.37 and a maximum of 401. The proportion of gaseous ammonia present has been determined by exposing a known surface of acidulated water to the air and observing the ammonia absorbed in a certain time. Eleven determinations, extending over 174 days, have been been made, and they show that, on the average, an acid surface of 1 mq. absorbed, in twenty-four hours, 12:52 mgr. of ammonia, with a minimum of 5 30 mgr. and a maximum of 27 mgr. It appears, therefore, that the air of the tropical station is not so rich in gaseous ammonia as that of temperate regions.-Influence of the sun's rays on the bacilli of fermentation found on the surface of grapes, by M. V. Martinand.-On some effects of the parasitism of plants, by M. A. Magnin.

DIARY OF SOCIETIES. LONDON.

THURSDAY, DECEMBER 10.

ROVAL SOCIETY, at 4.30.-n a Compensated Air-Thermometer: H. L. Callendar.-Note on the Necessity of using Well-annealed and Homogeneous Glass for the Mirrors of Telescopes: A. A. Common, F.R S.On some of the Properties of Water and of Steam: Prof. Ramsay, F.R.S., and Dr. Young.-On the Surya Siddhanta (Hindoo Astronomy): W. Brennand.-Repulsion and Rotation produced by Alternating Electric Currents: G. T. Walker.

MATHEMATICAL SOCIETY, at 8.-The Equations of Propagation of Disturbances in Gyrostatically-loaded Media: Dr. J. Larmor.-Theory of Elastic Wires: A. B. Basset, F.R.S.-Researches in the Calculus of Variations; II. Discrimination of Maxima and Minima Solutions when the Variables are connected by Algebraical Equations, the Limits being supposed Fixed: E. P. Culverwell.

INSTITUTION OF ELECTRICAL ENGINEERS, at 8.-Annual General Meeting. -Election of Council and Officers.-On the Specification of Insulated Conductors for Electric Lighting and other Purposes: W. H. Preece, F.R.S. LONDON INSTITUTION, at 7.- An Hour with my Mozart Manuscripts (Illustrated): Prof. Bridge.

CAMERA CLUB, at 8.-A Short Description and Demonstration of New Telescopic Lens for Photography: T. R. Dallmeyer.-The Use of the Lantern for Scientific Illustration: Dr. A. H. Fison.

SUNDAY LECTURE SOCIETY, at 4-The Origin and History of the Thames (with Oxybydrogen Lantern Illustrations): Prof. J. F. Blake. MONDAY, DECEMBER 14.

SOCIETY OF ARTS, at 8.-The Pigments and Vehicles of the Old Masters: A. P. Laurie.

ARISTOTELIAN SOCIETY, at 8.-The True Sense of the Term a priori: J. H. Muirhead.

LONDON INSTITUTION, at 5.-Tropical Plants and Flowers (Illustrated): D. Morris.

CAMERA CLUB, at 8.30.-Development: Lyonel Clark.

TUESDAY, DECEMBER 15.

ROYAL STATISTICAL SOCIETY, at 7.45.-Enumeration and Classification
of Paupers and State Pensions for the Aged: Charles Booth.
UNIVERSITY COLLEGE BIOLOGICAL SOCIETY, at 5.15.-The Sources of
Nitrogenous Food of Leguminous Plants: H. Thompson.
INSTITUTION OF CIVIL ENGINEERS, at 8.-The Sale of Water by Meter in
Berlin Henry Gill. (Discussion.)

WEDNESDAY, DECEMBER 16.

SOCIETY OF ARTS, at 8.-Typological Museums, as Exemplified by the Pitt Rivers Museum at Oxford: General Pitt Rivers.

ROYAL METEOROLOGICAL SOCIETY, at 7.-Report on the Thunderstorms of 1888 and 1889: William Marriott.-On the Prevalence of Fog in London during the Twenty Years 1871-90: Frederick J. Brodie.

ROYAL MICROSCOPICAL SOCIETY, at 8.-On the Resolution of Podura: Hon. J. G. P. Vereker.

INSTITUTION OF CIVIL ENGINEERS, at 2.-Students' Visit to the Stations of the Westminster Electric Supply Corporation, 11 Millbank Street, and Eccleston Place, S.W.

CAMERA CLUB, at 8.-Retouching Class.

THURSDAY, DECEMBER 17.

ROYAL SOCIETY, at 4.30.
LINNEAN SOCIETY, at 8.-Development of the Head of the Imago of
Chironomous: Prof. L. C. Miall and A. R. Hammond.-On Two Species
of Cumacea in New Zealand: G. M. Thomson.
CHEMICAL SOCIETY, at 8.-The Composition of Cooked Vegetables: Miss
K. Williams-On some Metallic Hydrosulphides: S. E. Linder and H.
P.cton. On the Physical Constitution of some Solutions of Insoluble
Sulphides: Harold Picton.-Solution and Pseudo-solution: H. Picton
and S. E. Lindor.-The Change proceeding in Acidified Solutions of
Sodium Thiosulphate when the Products are retained within the System;
and The Action of Sulphurous Acid on Flowers of Sulphur: Dr. A.
Colefax.-The a and 8 modifications of Chlorobenzene Hexachloride :

Dr. Matthews.-Camphrone, a Product of the Action of Dehydrating
Agents on Camphor: Drs. Armstrong and Kipping.-Studies on the
Dibromonaphthalenes: Dr. Armstrong and Mr. Rossiter.

LONDON INSTITUTION, at 6.-Winchester Cathedral (illustrated): Very
Rev. the Dean of Winchester.
CAMERA CLUB, at 8. 30.-Simplified Collographic Process (Description and
Demonstration): Leon Warnerke.

FRIDAY, DECEMBER 18.

PHYSICAL SOCIETY, at 5.-On Interference with Alternating Currents: H. Kilgour.

CAMERA CLUB, at 8.-Retouching Class.

BOOKS, PAMPHLETS, AND SERIALS
RECEIVED.

BOOKS.-The Universal Atlas, Part IX. (Cassell).-The Powers which Propel and Guide the Planets: S. Laidlaw (Kegan Paul),-Progressive Mathematical Exercises, First Series: A. T. Richardson (Macmillan) The Principles of Chemistry, 2 vols.: D. Mendeléeff; translated by G. Kamensky; edited by A. J. Greenaway (Longmans).-Lehrbuch der Vergleichenden Entwicklungsgeschichte der Wirbellosen Thiere, Specieller Theil, Zweites Heft: Dr. E. Korschelt and Dr. K. Heider (Jena, Fischer). -Proceedings of the American Association, August 1890 (Salem).-Oriental Cicadida, Part 4: W. L. Distant (London) -Annalen der k.k. Univer sitäts-Sternwarte in Wien, Band vii. (Williams and Norgate)-Travels in Africa during the Years 1879-1883: Dr. W. Junker; translated by A. H. Keane (Chapman and Hall).-An Essay on Reasoning: E. T. Dixon (Cambridge, Deighton).-Proceedings of the U.S. National Museum, vol xiii., 1896 (Washington).-An Introduction to Chemical Theory: Dr. A. Scott (Black).-Himalayan Journals: Sir J. D. Hooker (Ward, Lock) Falling in Love, &c. Grant Allen; new edit (Smith, Elder).-Nature and Man in America: N. S. Shaler (Smith, Elder).-Annuaire 1891, par le Bureau des Longitudes, Paris (Gauthier-Villars).-Connaissance des Temps ou des Mouvements Célestes, 1893 (Gauthier Villars).-Ephémérides des Etoiles de Culmination Lunaire et de Longitude pour 1891: M. M. Lowy (Gauthier-Villars).-The Harveian Oration on Harvey in Ancient and Modern Medicine: Dr. W. H. Dickinson (Longmans).-The Cause of an Ice Age: Sir R. S. Ball (Kegan Paul). Scientific Results of the Second Yarkand Mission-Introductory Note and Map, 1878-91.-Scientific Results of the Second Yarkand Mission-Aves: Dr. R. B. Sharpe (Taylor and Francis).-Animal Sketches: C. Lloyd Morgan (Arnold)-A Manual of Physics: Dr. W. Peddie (Bailliere).Memory, its Logical Relations and Cultivation: Dr. F. W. Edridge Green; 2nd edition (Baillière).

PAMPHLETS.-Connaissance des Temps, Extrait pour l'an 1892 (Paris, Gauthier-Villars).-Australian Museum, Sydney; Hand-List of Australian Mammals: J. D. Ogilby (Sydney).-Compass-Deviation; Syllabus of Examination in the Laws of Deviation (Imray).

SERIALS.-Records of the Australian Museum, vol. i., No. 9 (Sydney). North American Fauna, No. 5 (Washington).-Proceedings of the Academy of Natural Sciences of Philadelphia, 1891, Part 2 (Philadelphia) - Brain, Parts 54 and 55 (Macmillan).

THE MOON. By Sir ROBERT S. BALL, LL.D., F.R.S., Royal Astronomer of Ireland. Illustrated. Post 8vo, Cloth Boards, 2s. 6d.

THE STORY OF A TINDER-BOX. By

CHARLES MEYMOTT TIDY, M.B.M.S., F.C.S. With numerous
Illustrations. Post 8vo, Cloth Boards, 25.

THE BIRTH AND GROWTH OF
WORLDS. A Lecture by Prof. GREEN, M.A., F.R.S. Post 8vo,
Cloth Boards, 1S.
SOAP BUBBLES, AND THE FORCES
WHICH MOULD THEM. Being a Course of Three Lectures de-
livered at the London Institution, in December 1889 and January 1890,
before a Juvenile Audience. By C. V. BOYS, A.R.S. M., F.R.S.
With numerous Diagrams. Post 8vo, Cloth Boards, 2s. 6d.
SPINNING TOPS. The Operatives' Lec-
ture of the British Association Meeting at Leeds, September 1890.
Prof. J. PERRY, M.E., D.Sc., F.R.S. With numerous Diagrams.
Post 8vo, Cloth Boards, 2s. 6d.

By

THE DAWN OF EUROPEAN LITERATURE.

[A Set of Works designed to present the Chief Races of Europe as they emerge out of prehistoric darkness into the light furnished by their earliest recorded words. The Literature dealt with covers a period stretching from its beginning until the Middle Ages.] FRENCH LITERATURE.

By the late

GUSTAVE MASSON, B. A., Assistant Master and Librarian of Harrow School. Fcap. 8vo, Cloth Boards, 2s. 6d.

ANGLO-SAXON LITERATURE. By the Rev. Prof. EARLE. Fcap. 8vo, Cloth Boards, 2s. 6d.

SLAVONIC LITERATURE.

By W. R. MORFILL, M. A. Fcap. 8vo, Cloth Boards, 28. 6d. "His book will supply an admirable introduction to a systematic study of Slavonic literature."- Scotsman.

Others in preparation.

NEW SERIES OF PHOTO-RELIEVO MAPS

(Patented).

Presenting each Region as if in actual relief, and thus affording an accurate Picture of the Configuration of the Earth's Surface.

ENGLAND AND WALES. Size 56 in. by

46 in. Mounted on Canvas, Roller, and Varnished, Coloured, 135. SOUTH LONDON. Size 19 in. by 14 in. Stretching from London Bridge to Caterham, and from Greenwich to Hampton Court.

The importance of teaching Geography by beginning in a small centre has been strongly insisted upon by experts. This Map will be useful, therefore, to all the schools in the district embraced, as well as to others.

No. 2. PHYSICAL CONFIGURATION, Railways, Roads, and Chief Places. 6d.

SCOTLAND. Size 19 in. by 14 in. No. 1,

OF

EUROPE. Chiefly International. From the beginning of the Roman Empire to the Present Day. By ARTHUR REED ROPES, M.A. Post 8vo, Cloth Boards, 25 6d.

THE OUSE. By the Rev. A. J. Foster, M.A. With Map and several Illustrations. Crown 8vo, Cloth Boards, 3s. 6d. CAPITAL, LABOUR, and TRADE, and the OUTLOOK. Plain Papers by MARGARET BENSON. Small Post 8vo, Cloth Boards, 2s. 6d.

EARLY CHRONICLERS OF EUROPE.

[The object of this Series is to bring readers face to face with the Sources of Early European History, and thus enable them to obtain a more intelligent grasp of the subject than can be had from second-hand compilations ]

Crown 8vo, Cloth Boards, each 45.

ITALY. By Ugo Balzani.

"Its literary merits are very considerable."-Scotsman.

ENGLAND. By James Gairdner, Author

of "The Life and Reign of Richard III."

The book is well and thoroughly done, and makes a very valuable addition to the stock of historic manuals."-Athenæum.

AND WALES,

AND ASIA, same size and price.

EUROPE

BOTANICAL WALL DIAGRAMS. PRINTED IN COLOURS. Size 31 in. by 24 in. Edges Lined with Canvas, with Binders for Hanging up, price One Shilling each; Canvas, Varnished, One and Sixpence each; or Roller, Two Shillings each. These Prints are particularly suited for Class Teaching. An accurate life-size representation of one single plant is given, as a rule, in each, accompanied by greatly enlarged reproductions of the various characteristic parts. of each subject-viz. Leaf, Blossom, Parts of the Blossom, Husk, and Seed. The Plants selected are for the most part indigenous, a few exceptions being made in the case of specimens important on account of typical characteristics or of their value in commerce.

Cheapness, accuracy, and artistic excellence are the chief merits claimed

MARSH MARIGOLD.

YELLOW WATER LILY)
WHITE
ОАК.
POTATO.
SCARLET RUNNER.

on one sheet.

HOPS.

MARTAGON LILY AND SNOWDROP. MEZEREON.

Over Thirty others are in course of preparation.