In a previous communication it was pointed out that the effect of transverse magnetization on the resistance of nickel wire was inappreciable in fields below 500 C.G.S. units, thereby differing from the case of longitudinal magnetization, in which the effect was easily measurable in fields below 20. The reason of this is no doubt to be referred to the thinness of the wire in the direction of the magetizing force. To measure the effect of transverse magnetization it was necessary to form a fiat coil and insert it between the poles of a powerful electro-magnet. Considerable difficulty was experienced in winding this coil with interwound asbestos insulation, for great care had to be taken that no part of the wire cut the lines of force obliquely, otherwise there would be a resolved component of longitudinal effect, which in certain cases might altogether mask the effect looked for. The coil used in the final experiments was suitable in all respects. It was coiled between glass plates, the successive coils being separated by threads of asbestos. Round the coil another coil (of Beacon wire) was wound anti-inductively, so that any current passing through it would have no magnetic action upon the nickel wire inside. By varying the current in this external coil I was able to heat the nickel to any desired temperature up to 400° C. In any one experiment the final temperature came to a steady state, and not till this state was reached was it possible to begin the observations on the resistance change. This was measured in the manner already described in my paper on the effect of longitudinal magnetization, and it will suffice meanwhile to call attention to a remarkable result obtained when the temperature approached that at which nickel ceases to be strongly magnetic.

L'hiver passé je reçus une invitation de Sir John Murray à venir, en qualité d'assistant, au Challenger Office étudier sous sa direction une nombreuse collection de concrétions phosphatées et nodules provenant de dépôts dragués par les bateaux du “Department of Agriculture” du Cap de Bonne Espérance et envoyée par Dr J. D. F. Gilchrist, “Government Biologist of the Cape of Good Hope.”

In scientific literature the evaporation of musk has a considerable interest. Almost every writer on the divisibility of matter cites it as an instance of the extremely minute division of which matter is capable, our sense of smell enabling us to detect a more minute quantity of this form of matter than can be detected of any other kind of matter by any of the modern refined methods, such as the spectroscope, or chemical processes. It is possible we may shortly have to modify this statement, as extremely small quantities of some kinds of matter can be detected by their radio-activity; but, so far as I know, no reliable numerical values have been obtained in this direction.

We have, during the last two years, made a series of observations upon specimens of Sagartia troglodytes which are at least fifty years old, and have thought it worth while to give a somewhat detailed account of these, as, so far as we can ascertain, there is only one other recorded case of longevity in Coelenterates (see p. 302), and very few in the whole of the Invertebrata.

In a former communication it has been shown that iron demagnetised by decreasing reversals of a directional force ab, develops an induction component at right angles to the subsequent magnetising force H, when the angle θ between these two forces is other than 0° and 90°. This component after reaching a maximum tends to disappear as saturation values are reached.

The apparatus used to show that aluminium was opaque to the ions from a flame consisted (see fig. 1) of a tube A, which was

funnel-shaped at one end, the other end of which led to an enclosure B, one side of which (a b) was made of aluminium foil connected to earth, and on the other side there was an insulated metallic plate (c d), which could either be connected to earth or to a high potential battery. On the other side of the aluminium foil there was an electroscope in a closed case C. The electroscope was of the type used by C. T. R. Wilson in his experiments on the natural ionisation of air in closed vessels.

The nature of the connection of this with the theory of determinants is evident from the title. Some of the elementary portions of the memoir had in fact already appeared in Cauchy's determinant papers of the years 1812, 1840, 1841, and have been noted in our accounts of the latter. In these papers, as was natural, only such isolated properties were given as might be of immediate application to the main subject: here we have a methodically arranged and lucidly written treatise. As, however, in dealing with permutations the question of signature is not taken up, there is no explicit reference to determinants: and all that is therefore necessary is to direct attention to a storehouse of information regarding a subject closely connected with them.

§ 11. The present communication is substituted for another bearing the same title, which was read before the Royal Society of Edinburgh on January 7th, 1887, because the result of that paper was rendered imperfect and unsatisfactory by omission of the exponential factor referred to in § 10 of my paper of February 1st, 1904. I shall refer henceforth to the last-mentioned paper as §1 …. 10 above.

The following beliefs regarding vision meet with very general acceptance:—

First. Very intense light of any wave-length produces practically the sensation of whiteness.

Second. Very weak light of any wave-length produces practically the sensation of whiteness.

Third. A coloured area of normal brightness retains its colour, though with diminished purity, when gazed at steadily for a long time.

Fourth. Small, faintly luminous, objects are seen more easily by indirect vision than by direct vision.

I propose in this preliminary communication to lay before the Society some results of investigations in the theory of Seiches in a lake whose line of maximum depth is approximately straight, and whose depth, cross section, and surface breadth do not vary rapidly from point to point.

As the seiche disturbance is small compared with the length of the lake, I shall make the assumptions usual in the theory of long waves:—viz., that the squares of the displacements and of their derivatives are negligible.

In the course of a research on the boiling points of aqueous solutions, certain points came under my notice which have been introduced into this note.

After considerable experience with various forms of Beckmann's boiling point apparatus, and due consideration of the Jones type, a boiling point apparatus was designed which embraced what were considered the best points of each, in view of the research anticipated. The body of the tube was of the Jones type, and had a side tube fitted with a rubber stopper for the introduction of the salt at a short distance from the top of the tube. On the opposite side of the boiling tube, about the same height up, went off a condensing tube of the Beckmann pattern. The thermometer—one of Beckmann's—read to hundredths of a degree, and, with the aid of a Beckmann reading glass, could be estimated to thousandths of a degree. It passed through a close-fitting rubber stopper at the top of the tube.

The present paper is the continuation of a note sent to the Society in July of last year, and is for the purpose of describing the developed form of the spectrophotometer whose principle was indicated in that communication.

In this contribution an account is given of the dominant plants of aquatic and semi-aquatic habit existing in and about the lakes of the following districts of Scotland:—

1. The Loch Ness area.

2. The lakes in the Island of Lismore, Argyll.

3. Lakes situated between Nairn and the Culbin Sand Hills.

In the ordinary spectrophotometer and in Laurent's “half-shade “polarimeter, two neighbouring patches of light of the same colour but of different intensities are presented to the eye of the observer, who by an appropriate means reduces the intensity of the brighter until in his judgment it is brought down to the same intensity as the other. The accuracy of such a measurement must depend on two factors. The first factor is the accuracy with which the observer's eye can judge of the equality of the two patches of light, and the second factor is the accuracy with which the instrumental reading indicates the intensity of the comparison beam, i.e., of the beam whose brightness is reduced till it becomes equal to that of the other. Now it is found that in ordinary cases the error of the eye's judgment in such measurements amounts to about 4% or 5%, while the measurement of the instrumental regulation of the light can be made much more accurately.

1. The gradual growth of the theory of molecular magnetism from the original suggestions of Poisson and Weber is well known. The recent great development, made by Ewing, and tested experimentally by means of models, has placed the theory on a fairly firm basis, and has made essentially secure the fundamental postulate that magnetic phenomena in material bodies are due to magnetic molecules which may possibly be regarded as free from any directional control other than that supplied by their own mutual action.

(1) If the array in question be

its score of three-line determinants |a1b2c3|, |a1b2f3|,.… may be viewed as consisting of two complementary sets of ten, each of the first set containing at least two columns taken from |a1b2c3|, and each of the second set at least two columns taken from |f1g2h3|. Further, either set of ten may be viewed as consisting of one unique member and three sub-sets of three members each, the members of a sub-set being derivable from one another by performing the cyclical substitutions

(1) The fundamental propositions in regard to the sum of the signed primary minors of a determinant are—

(A) An expression for the negative sum of the signed primary minors of any determinant is got by taking a determinant of the next higher order whose first element is zero with the given determinant for complementary minor, and whose remaining elements are units all positive or all negative.

§ 65. Referring to § 63, we must, for the present, as time presses, leave detailed interpretation of the curves of fig. 17: merely remarking that, according to § 44, if δ=0, (which means that J is an integer), the disturbance, d, is infinitely great; of which the dynamical meaning is clear in (70) of § 39.

The ventricular rhythm differs from the auricular, firstly, on the occurrence of a ventricular extra-systole, and, secondly, in cases where there is allorhythmia due to depression of conductivity of the heart muscle. When conductivity is depressed, the contraction stimulus at regular or irregular intervals may be blocked at the auriculo-ventricular muscle bridge; so that whereas some stimuli induce both auricular and ventricular systole, others induce auricular systole alone, the ventricular systole being missed. That condition, incomplete heart-block, is of not infrequent occurrence in the human heart, and has been graphically recorded by Mackenzie (1), Finkelnburg (2), and other writers.

I. Axes of Compound Symmetry of the Second Order.

In recent years, since the more or less general adoption of the systematic classification of crystals under the thirty-two possible types of symmetry, it has become usual to dispense with the ‘centre of symmetry’ as one of the elements of crystal symmetry, and to adopt in its place the ‘axis of compound symmetry of the second order.’