The wonderful fact that uranium held in the neighbourhood of an electrified body diselectrifies it was first discovered by H. Becquerel. Through the kindness of Prof. Moissan we have had a disc of this metal, about 5 cm. diameter and ½ cm. thickness, placed at our disposal.

We made a few preliminary observations on its diselectrifying property. We observed first the rate of discharge when a body was charged to different potentials. We found that the quantity lost per half-minute was very far from increasing in simple proportion to the voltage, from 5 volts up to 2100 volts; the electrified body being at a distance of about 2 cm. from the uranium disc. [Added March 9, 1897.—We have to-day seen Prof. Becquerel's paper in Comptes Rendus for March 1. It gives us great pleasure to find that the results we have obtained on discharge by uranium at different voltages have been obtained in another way by the discoverer of the effect. A very interesting account will be found in Prof. Becquerel's paper, which was read to the French Academy of Sciences on the same evening, curiously enough, as ours was read before the Royal Society of Edinburgh.]

These first experiments were made with no screen placed between the uranium and the charged body. We afterwards found that there was also a discharging effect, though much slower, when the uranium was wrapped in tinfoil. The effect was still observable when an aluminium screen was placed between the uranium, wrapped in tinfoil, and the charged body.

1. If all the negative terms of the determinant ∣ a1b2c3 … ∣ be changed in sign, we obtain a symmetric function, dealt with by Borchardt and Cayley, known as a Permanent and denoted by

The more important elementary properties of such functions are given in a paper published in the Proc. Roy. Soc. Edin., xi. pp. 409–418. As might be expected, relations are found to exist between them and determinants, an important instance being the theorem of § 7 of the said paper. Another theorem, not hitherto noted, deserves now to be put on record.

2. For the case of the 2nd order it is

the truth of it being self-evident.

For the case of the 3rd order it is

which is easily verified by observing that the coefficients of a1, a2, a3 in the expression on the left-hand side are respectively

and that by the previous case each of these vanishes.

In the course of his valuable researches on the heats of combination and decomposition of bodies, the late Professor Thomas Andrews, of Belfast, arrived at the conclusion that “If three metals, A, B, C, be so related that A is capable of displacing B and C from their combinations, and also B capable of displacing C; then the heat developed in the substitution of A for C will be equal to that developed in the substitution of A for B, added to that developed in the substitution of B for C; and a similar rule may be applied to any number of metals similarly related.” A tabular statement of experimental results is given, and from them illustrations of the above conclusion may be obtained. For example, let A represent zinc, B lead, and C copper; then, for equivalent quantities of the metals, it was found that the number of (grammewater) heat units centigrade developed when zinc displaces copper is approximately equal to the number developed when zinc displaces lead, added to that obtained when lead displaces copper. But, in contact electricity, the electromotive force between zinc and copper is equal to that between zinc and lead added to that between lead and copper. These facts led Andrews to make the following important remark:—“Electromotive forces which are really due to contact of dissimilar bodies are also the very forces which cause heat when chemical combination ensues, potential energy being converted into kinetic energy by the rushing together of the particles under attracting forces.”

1. Denoting by A, B, C, F, G, H the co-factors of a, b, e, f, g, h, in the determinant

the problem in question is to eliminate x, y, z from the three equations

and it lias been discussed by Sylvester, Cayley, Muir, Tait, and Lord M'Laren.

Sylvester deduces from (1) this new system

and hence finds the dialytic eliminant

the expansion of which (an obvious error being corrected) he states to be

where

so that “rejecting the special (N.B., not irrelevant) factor abc, we obtain”

The problem in question is to determine the equation of the curve traced out by any point of an elliptic or hyperbolic disc which touches two fixed rectangular axes. Mechanically constructed figures of different forms of the curve have been given by Tait, who also showed that the same glissette can be traced either by means of an ellipse or a hyperbola. If p, q are the coordinates of the tracing point referred to the axes of the disc as axes of coordinates, the glissette is clearly the θ eliminant of

and Cayley stated that it would be found to be of order 8 in x, y. The actual elimination was first performed by Muir, who obtained in the first instance an equation of order 10. On dividing by an extraneous quadratic factor a lengthy equation of order 8 was obtained; and subsequently Lord M'Laren verified the accuracy of the terms of highest order in this equation.

The cosine of the angle through which a unit vector ρ is turned by the homogeneous strain ϕ is

This is to be a maximum, with the sole condition

Differentiating, &c, as usual we have

Operate by S.ρ and we have

Hence the required vector, its positions after the strain, and after a subsequent application of the conjugate strain, lie in one plane; and the tangent of the angle between ρ and its first distorted position is half of the tangent of the angle between it and its doubly distorted position.

When the strain is pure, the required values of ρ are easily found. Let the chief unit vectors of ϕ be α, β, γ, and its scalars g1, g2, g3.

In the third Book of The Wars of the Jews, Chap. VIII. § 7, we are told that Josephus managed to save himself and a companion out of a total of 41 men, the majority of whom had resolved on self-extermination (to avoid falling into the hands of Vespasian) provided their leader died with them. The passage is very obscure, and in a sense self-contradictory, but it obviously suggests deliberate fraud of some kind on Josephus' part.

“And now,” said he, “since it is resolved among you that you will die, come on, let us commit our mutual deaths to determination by lot. He whom the lot falls to first, let him be killed by him that hath the second lot, and thus fortune shall make its progress through us all; nor shall any of us perish by his own right hand, for it would be unfair if, when the rest are gone, some-body should repent and save himself.” Whiston, Works of Flavius Josephus, IV. 39.

Bachet, in No. XXIII. of his Problèmes plaisants et délectables, makes a definite hypothesis as to the possible nature of the lot here spoken of; so that the problem, as we have it, is really his.

“Supposons qu'il ordonna que comptant de 3 en 3 on tuerait toujours le troisième, …. il faut que Josèphe se mît le trenteunième après celui par lequel on commençait a compter, au cas qu'il visât à demeurer en vie lui tout seul.

Ever since the remarkable discovery by Graham in 1866 that palladium possesses the power of occluding hydrogen gas in large quantity, various views have from time to time been put forward to explain the true nature of the phenomenon. Whilst some observers regard hydrogenised palladium as an alloy or solid solution, others again consider it to be, or at least to contain, a definite chemical compound or hydride. Those who hold the latter opinion, however, are not agreed as to which compound or hydride is formed, as is proved by the fact that different formulae have been ascribed to it. Graham himself recognised the possibility that a definite chemical compound might be formed, for he says (Researches, 287) that in fully-charged palladium there exists one equivalent of palladium to 0·772 equivalent of hydrogen, or an approximation to single equivalents which would be represented by the formula PdH. His opinion was, nevertheless, opposed to the idea of such a definite chemical combination, one of his chief objections being that no visible change is occasioned to metallic palladium by its association with hydrogen. He regarded the product simply as an alloy of the volatile metal hydrogenium, in which the volatility of the one element is restrained by its union with the other, and which owes its metallic aspect equally to both constituents.

Considerations of a purely chemical character have up to the present time proved insufficient to decide which of these views is correct.

1. Apparatus.—The following are needed:—Electric or lime light; standard hæmatinometer (i.e., of 1 cm. between the parallel sides) entirely of glass (for many pigments white glass flat-sided stoppered bottles do perfectly well); large direct-vision spectroscope (Messrs Hilger), or a Tollen's carbon-disulphide glass prism (base 5 inches, refracting angle 45°); a well-stretched dead-white screen to receive the spectrum 4 feet long at least, about 12 feet from the lantern.

Following Preyer (1), one can with such apparatus first of all demonstrate the different spectroscopic appearance according as blood is or is not diluted. Placing blood newly received from the slaughter-house (defibrinated blood) in the hæmatinometer, we show that it is opaque in a thick layer, no light passes to the prism at all, there is no spectrum, we can say that the percentage of HbO2 is, at least, greater than 7·3. Dilute with pure cold water until a faint gleam of red light appears at the extreme left, the concentration of HbO2 is now not less than 1 per cent.; continue the dilution until the first glimmer of extra-linear green appears, the percentage is now about ·9 per cent.; dilute until the first glimmer of intra-linear green appears, when the percentage is now ·7; add to this its own volume of water, making the percentage fall to ·35. From this point further dilution caused progressive faintness of the two bands, until the vanishing point of the fainter β band is just reached when the hæmoglobin is ·01 per cent.; continue the attenuation until the α band is alone visible, at which point the percentage can be stated to be certainly less than ·01 per cent.

The following research was made with the object of determining whether the digestion of starch is affected favourably or unfavourably by its admixture with other articles of food.

As regards the quantity of saliva secreted per twenty-four hours, this is stated to vary from 200 to 1500 grammes. Investigating this in my own case I found that the average amount was 400 grammes.

Method of Investigation.—Ten grammes of each of the various foods as prepared for the table were accurately weighed out, placed in a large tube, and heated to 38° C. Two cubic centimetres of mixed human saliva were then added. A series of these tubes were prepared, and the whole was placed on a water-bath kept at a uniform temperature of 38° C. At intervals a tube was removed, and the condition of its contents noted.

This paper is in continuation of two others, on the same subject, previously communicated to the Society. It consists of two parts, the first experimental, the second theoretical.

The wire which was experimented upon was the one which was used in the previous experiments, and the apparatus was that described in the latter of the communications above referred to.

The most important part of the paper has to do with the behaviour of certain iron and nickel tubes, considerably shorter and narrower than those discussed in Part I. Two iron bars, A and B (A being twice the length of B), and a nickel bar, B, were bored out by successive stages, so as to give three series of tubes of increasing bore. Each tube was subjected to four distinct experiments. These were—

1. Measurements in various magnetic fields of the corresponding changes of volume of bore.

2. Measurements in the same fields of changes of length.

3. Measurements in the same fields of changes of volume of the material of the tube.

4. Measurements in the same fields of apparent external changes of volume, the tube being plugged and treated as a bar.

The prime object of the following paper is to assist in deciphering the irregular traces which represent the consonants in a phonographic record, by investigating a priori, from the causes which create the consonant, the elements which probably lie entangled in the tracing to be interpreted. Accurately speaking, the difference between vowel and consonant is not one of nature, but of function. To define either vowel or consonant, it is necessary first to define a syllable. All human speech proceeds in rapid alternations of louder and softer, more sonorous and less sonorous. These alternations vary considerably in energy; any one of them may be twice as long, or twice as loud, or twice as sudden in its rise or in its fall as its next neighbour. They seem, in fact, to tend both in duration and in form and in energy rather to a successive change than to any regularity; but each of them is a syllable. A syllable, then, is a wave of sonority, one climax of sound, with its accompanying rise and fall. Accurately speaking, this climax is a subjective one.

During the winter session I had occasion to prepare several supersaturated solutions for lecture demonstration. Among them, was a solution made by fusing crystals of sodium thiosulphate. Next day this solution had deposited a considerable quantity of crystals, but had not solidified. The crystals were separated from, the liquid, washed, dried, and analysed. Their composition agreed approximately with the formula Na2S2O3, 2H2O. Other crystals having this composition were then obtained by driving off part of the water from fused crystals of the pentahydrate, and allowing the solution to cool.

They were analysed by conversion into sodium sulphate.

I.—1·2186 gm. substance gave 0·9027 gm. Na2SO4= 24·02 percent. Na.

II.—1·3977 gm. substance gave 1·0320 gm. Na2SO4 = 23·95 percent. Na.

In order to find out the temperature condition for the formation of this hydrate, a solubility curve was constructed from the data given by Mulder and by Kremers. There appeared to be a change in the curve between 50° C. and 60° C., but the data were insufficient to fix the temperature with accuracy.

I therefore made a series of solubility determinations, extending, from 0°C. to 100°C. The form of apparatus used was that described by van't Hoff. The stirrer was driven at about 3000 revolutions a minute by means of an electric motor; and the temperatures were constant to 0·1°C. Below 50°C. the solutions were in contact with Na2S2O3, 5H2O; above 50°C. in contact with Na2S2O3, 2H2O; and at 50°C. solutions were prepared in contact with each of them, and found to have the same concentration.

As is well known, the molecular depression of the freezing-point of aqueous solutions of electrolytes is greater than 1·87, van't Hoff's constant, with which the molecular depressions of nonelectrolytes have been found to agree extremely well. This is in accordance with the dissociation theory; and for binary electrolytes the molecular depression may approximate to 1·87 × 2, for ternary electrolytes to 1·87 × 3, etc., but cannot exceed these values.

Substances such, as potassium ferrocyanide, which, according to the dissociation theory, might be expected to give values approximating to 1·87 × 4 or 1·87 × 5, have not been found to give molecular depressions greater than 1·87 × 3. This has been held to be an objection to the dissociation theory.

The method of electrolytic synthesis of dibasic acids described by Crum Brown and Walker has hitherto been found to be applicable to dibasic acids of the formula CnH2n (COOH)2 whether normal or with side chains, and to camphoric acid, which is no doubt a saturated cyclic compound. In all other cases which have been tried the anion is oxidised and broken up.

One of us long ago found that this was the case with tartaric acid, and in 1894 v. Miller and Hofer showed that when the salts of monobasic hydroxy-acids are electrolysed the anion is oxidised and broken up. They showed that this is the case also with methoxyacetic acid, so that it would appear that the replacement of H by ORʹ, where Rʹ is an alkyl, leads to the same destruction of the anion as does the replacement of H by OH. We examined ethoxysuccinic acid, and found that here also no ethereal layer is formed on the electrolysis of the ethyl potassium salt.

Indiarubber has come to be so nearly synonymous in popular language with waterproof that it seems almost as much of an impertinence to inquire whether it really is so, as it would be to ask whether lead is heavy or iron strong. The question, however, came before me in a practical shape; and I have made out some facts, in attempting to answer it, which may be of interest.

A water-bed is simply a hollow indiarubber mattress, capable of being filled with water and secured by metal screws. Such beds are largely used in the treatment of paralysed and feeble patients; and it is well known to nurses and others who have much to do with them that they need every now and then to be filled up in order to keep them comfortable. I first became acquainted with this fact in the course of medical work at the Longmore Hospital, where there are always many of them in use. Every three months or so a considerable quantity of water needs to be added to each of them, because it becomes so slack that the patient sinks through the cushion of fluid and rests on the solid mattress below, at the points where pressure is greatest. It seemed to me that this circumstance was worth inquiring into. Is it simply due to stretching of the material, or is there an actual transudation through the indiarubber? As I could get no answer to the question from people or from books, I determined to interrogate Nature for myself.

In geodetical and astronomical computations it frequently happens that we have to use the logarithmic sines or tangents of small arcs, or to find the small angles corresponding to their artificial sines or tangents; and in all trigonometrical tables directions are given to guide the learner in these operations. It might seem, then, superfluous to refer to such a matter. A variety of methods in the solution of a simple problem has, however, sometimes advantages, and the method I have been in the habit of using, though obvious enough, is not usually given.

In Vega's great Thesaurus Logarithmorum Completus (1794), based on A. Vlack's Tables, the rules for the functions of small arcs make use of second differences; and the 7th and later editions of Hutton's Tables (1830, 10th ed., 1846) follow the same method.

In a recent paper embodying the results of my work upon Actinotrocha, I was led to suggest a theory of the segmentation of cœlomate animals, the essential features of which were as follows:—

1. There can be demonstrated, in the morphology of the Cœlomata, two distinct types of segmentation—(a) a primitive or archimeric type, having in its constitution certain evidences of a radial origin, and (b) a secondary or metameric segmentation, superposed upon the former and bearing evidence of a bilateral origin.

2. A certain number of the Cœlomata retain, under varied disguise, the archimeric segmentation throughout life, together with a number of other primitive characters in common. These groups, being genetically allied, may be conveniently classified in one division, for which the name Archi-cœlomata is proposed.

3. In the truly segmented animals, such as the Annelida, Arthropoda, and Eu-chorda, the bilateral or metameric segmentation ⟨of the posterior archimeric segment⟩ tends to completely replace the archimeric. In at least two of these groups there has been an independent evolution of metameric segmentation.

In attempting to bring forward facts in support of this theory, one may approach the subject from three stand-points.

(A.) Firstly, an attempt may be made, by general reasoning, to construct a hypothetical ancestor of the Cœlomata as a group. In this way may be obtained a schematic outline of an organism possessing each system of organs in its most archaic condition.

The view that a peculiar likeness exists between the northern and southern extra-tropical faunas, and particularly between those of the Arctic and Antarctic regions, was suggested by Théel in discussing the remarkable deep-sea group of the Elasipoda, whose discovery we owe to the Challenger Expedition. A somewhat similar view is hinted at or referred to more than once in other Reports of the same Expedition. It was afterwards stated in an ampler way by Pfeffer (Versuch über die Erdgeschichtliche Entwickelung der jetzigen Verbreitungsverhältnisse unserer Thierwelt, 1891), and has of late been dealt with in great detail, and in relation to the antecedent causes that might have led to such a phenomenon, by Sir John Murray. On the other hand, Dr Ortmann, considering the hypothesis from the point of view of our knowledge of the distribution of Crustacea, has rejected it entirely (“Uber Bipolarität in der Verbreitung mariner Thiere,” Zool. Jahrb., 1896; cf. also “Marine Organismen und ihre Existenzbedingungen,” ib., 1897), and Dr Chun, dealing with the pelagic fauna (“Die Beziehungen zwischen dem arktischen und antarktischen Plankton,” Stuttgart, 1897), while showing how in truth a certain small number of forms are common to far northern and far southern seas, holds that the facts are sufficiently accounted for by the continuous distribution or gradual intermixture of forms in the depths of the intervening oceans under present conditions, without our needing to have recourse to an explanation of the phenomenon in the different conditions of a former age.