I will make one or two of the experiments with the original gyrostats, but it will save time if I repeat the others with some of the new and improved gyrostats invented by Dr. J. G. Gray, whom I am fortunate in having to assist me on the present occasion.

[The usual experiments, illustrating precessional motion of a gyrostat with the axis horizontal, while under the influence of a couple due to the gyrostat overhanging, or to a weight hung on one end of the case surrounding the axle (Fig. 6) were performed.]

This behaviour of the gyrostat is often considered paradoxical, and must, I suppose, be regarded as difficult to explain in a popular manner. At any rate, the popular explanations are as a rule extremely unsatisfactory. Yet in this particular case of horizontality of the axis the matter is simple enough, I think. Let me illustrate by means of this pedestal top (Fig. 7). The curved arrowhead shows the direction of rotation, the projecting arrow the axis of spin, the arrow pointing down can be turned so as to show the direction of the axis of any applied couple. First observe that when I try to retard the precessional motion the axis descends, if I try to accelerate the precession the axis rises. This experiment shows that the horizontality of the axis depends

on the freedom of the gyrostat to precess at a certain definite rate. This rate, as we shall see presently, depends on the couple applied by the weight of the gyrostat acting downward in one vertical line, and the pull of the string acting upward in another line nearly vertical, and on the angular momentum of the flywheel.

Look at the thing in this way. The axis of rotation round which the flywheel has angular momentum is turning as you see towards the horizontal axis A of the couple, with angular speed, say. Now, and this is the point not recognised as a rule, this motion itself creates a rate of production of angular momentum about the axis A of the couple. For when an axis with which is associated a directed quantity, L say, is turning towards a fixed direction at right angles to it with angular speed, there is a time-rate of production of the quantity associated with the latter direction measured by the product Lo. Now the flywheel is revolving with angular speed 6, so that if its moment of inertia is m k2,

it has angular momentum m k2w about the axis R; but with angular speed 2 the axis R is

turning towards the instantaneous position of the axis A, a fixed direction to which R is at the moment perpendicular, and, in consequence of this turning, a rate of production of angular momentum m kw. exists about A.

Now for the steady motion of the gyrostat, that is, steady turning in azimuth without rising or falling of the axis, it is only necessary that this rate should be equal to the moment of the couple about A, G let us say. Thus we get m k'o Q=G, which gives Q=G/m k2w.

If I hurry the precession by giving a little impulse, and then leave the gyrostat to itself, the hurried. motion, if it continued afterwards in the horizontal plane, would result in a more rapid generation of angular momentum about A than there is moment of couple to account for, and the gyrostat would begin to turn about A, in the direction to cause the angular momentum to be produced at the proper rate, that is the axis would begin to rise. In the same way an impulse towards delaying the precession would cause the axis to begin to descend. In each case the result would be a succession of alternate rises and descents; but the subject of vibrations about steady motion will be found treated in the Appendix, § (5) [see Journal, I.E.E.].

Here it is important to remark that there are two possible precessional motions for the same spin and the same inclination of the axis of spin to the vertical, which are given in the theory as the roots of a certain quadratic equation (see Appendix). One is great, the other small. The former to the first approximation does not depend on applied forces, the other does. Lord Kelvin called the former "adynamic," the other "precessional." But in strictness both involve the forces, and they appear as the roots of a certain equation. One of these is at once approximately realised when the wheel is spun fast, the gyrostat set on the plate at rest, and left to itself. The motion is one of small oscillation about the steady motion, which is characterised by slow precession, given very nearly, but not quite exactly, by the same formula as before. The other motion of the axis in the same cone is one of much greater precessional angular speed. The popular expositions which I have seen of gyrostatic steady motion as a rule ignore this second possible motion. It can be realised by proper means.

In strictness we must regard this second precessional motion as characteristic also of the gyrostat when its axis is horizontal, but in that case the precessional angular speed is infinite, and only the slow motion is realisable.

The rule, often stated, that hurrying a gyrostat in its precession causes tilting up of the axis, and delaying the precession causes tilting downward, is true only of the slower more usual precession. For the faster precession exactly the reverse rule holds good. This fact does not seem to be generally known, as the rule is generally stated absolutely.

It is important to notice that if the centre of gravity of the gyrostat is above the point of support, supposed on the line of the axis, the two precessional motions are in the same direction; if, on the other hand, the centre of gravity be below the point of support, the precessional motions are in opposite directions. The faster motion changes sign in passing through an infinite value, when the axis is horizontal.

By the effect of hurrying or retarding the precession was sometimes explained in our lectures the rising and falling of a top spinning on a rounded peg in contact with a rough floor along which the top can move. At first the spin is fast and the slipping is such as to produce a hurrying friction couple which causes the erection of the top. After the spin has

fallen off the slipping is the other way and a couple which produces the reverse effect results, and the top falls.

[Experiments were here made with a gyrostat on gimbals, and with a gyrostat mounted on a trapeze hung by the crossed cords of à bifilar suspension. See "Gyrostats and Gyrostatic Action," NATURE, April 10, 1913, to illustrate the stabilising by spin of a gyrostat with two freedoms, both unstable without spin.]

As I have already stated, Lord Kelvin illustrated, by what he called a "liquid gyrostat," the fact that an oblate spheroidal shell filled with water behaves as regards precession as if its contents were solid. Here is the gyrostat with which the experiment was made (Fig. 8). It resembles the ordinary gyrostat, but the case is not completely enclosed, and the spheroidal globe containing water takes the place of the flywheel these are the only points of difference. I spin the globe in the ordinary way, and you see that in all respects the liquid gyrostat imitates the behaviour of the solid one.

:

instability of the motion, the energy of rotation has been entirely transformed into heat, by turbulent motion of the water, into which the rotational motion breaks down. Permanent steady rotation of the liquid globe is impossible.

Oblateness, however, is not absolutely essential for steady rotational motion of a liquid round the axis of figure in a spheroidal case turning with the liquid. It was shown by Sir George Greenhill in 1880 (three years after the meeting of the British Association at Glasgow) that steady motion is possible in a prolate

FIG. 9.-Liquid Gyrostat (Prolate).

spheroid, if it be sufficiently prolate. The axial diameter, in fact, must either be shorter than the equatorial diameter, or be more than three times as long. As Sir George Greenhill points out, a modern elongated projectile if filled with a liquid would not rotate steadily about its axis of figure, and therefore would not have a definite trajectory as a rifle bullet has; it would turn broadside on to the direction of motion.

(To be continued.)

UNIVERSITY AND EDUCATIONAL
INTELLIGENCE.

BRISTOL. The Society of Merchant Venturers, in whose Technical College the faculty of engineering is provided and maintained, has decided to offer ten scholarships, tenable in the faculty for three sessions, beginning with the session 1915-16, to the sons of officers in his Majesty's Service who have been killed in the war, and whose mothers or guardians are in needy circumstances.

CAMBRIDGE. The adjudicators of the Smith's prizes and the Rayleigh prizes are of opinion that the following essays sent in by the candidates are of distinction:-H. Glauert, of Trinity College, on the elliptical form of a rotating fluid mass as disturbed by a satellite, and H. Jeffreys, of St. John's College, on (i) certain hypotheses as to the internal structure of the earth and moon, (ii) on a possible distribution of meteors, to whom the Smith's prizes have been awarded in alphabetical order. A Rayleigh prize has been awarded to J. Proudman, of Trinity College, for his papers on tidal motions.

MR. HERBERT A. L. Fisher, vice-chancellor of the University of Sheffield, has been elected a trustee of the British Museum, in succession to the Right Hon. Sir George O. Trevelyan, Bart., O.M., who has resigned on account of ill-health.

7 Proceedings of the Cambridge Philosophical Society, 1880 Encyclopædia Iritannica," article, " Hydromechanics."

PROF. ARTHUR KEITH, Conservator of the museum of the Royal College of Surgeons of England, will deliver, during the latter part of March, a course of five lectures upon the bearing of recent discoveries on our conception of the evolution and antiquity of man. The lectures will be given under the terms of the Macbride Foundation in Western Reserve University, Cleveland.

THE London County Council has arranged for a series of five public lectures to be given at the Horniman Museum, Forest Hill, on Wednesday evenings at 7.30 o'clock. The series commenced yesterday with a lecture on the Andamanese and other pigmies. The subjects of the remaining lectures will be: the Australian Aborigines; the Eskimo; the Papuans of New Guinea; and the Maori and other Polynesians. Each lecture is complete in itself, and there is no charge for admission.

A LECTURESHIP in ophthalmology has been established in Dublin' by the bequest of Mr. R. J. Montgomery, who desired that it should be known as the Mary Louisa Prentice Montgomery lectureship, and that the appointment to it should rest each alternative five years with the Board of Trinity College, Dublin, and with the president, vice-president, and council of the Royal College of Surgeons in Ireland. Joint regulations for the lectureship have now been drawn up, and the first election will take place at the beginning of the next summer session.

THE distribution of prizes and certificates at the Sir John Cass Technical Institute and the opening of the new metallurgy laboratory for the mechanical testing of metals and alloys, presented to the institute by the Worshipful Company of Goldsmiths, by Sir Robert G. C. Mowbray, Bart., Prime Warden of the Worshipful Company of Goldsmiths, will be held on Wednesday, March 3, at 8 D.m. The chair will be taken by Sir Thomas H. Elliott, K.C.B., chairman of the governing body. There will be an exhibition of work by students of the department of arts and crafts and by members of the Arts and Crafts Society, as well as an exhibition of students' work and apparatus in the laboratories and workshops.

A NOTE in the Daily Chronicle of February 24 refers to the effect of the war upon the attendance of students in the twenty-two German universities. It appears that entered on their books are 52,504 students, against 59,600 this time last year. But of these 29,882 have been "permitted" to join the military forces of the Empire, including 300 women students in the army medical department. The actual attendance at lectures is given as 18,922 men and 3700 women. If the students of technical high schools with university status are added the grand total of 38,400 is reached, or about 75 per cent. of the entire number. The universities most depleted of students are those nearest the frontiers-Bonn and Heidelberg in the west, and Königsberg and Breslau in the east. It is stated in Science of February 12 that there are matriculated in the University of Berlin 7037 men and 898 women, as compared with 8200 men and 859 women last winter. These numbers show a marked contrast with those of our own universities; for at Oxford and Cambridge alone the number of undergraduates now in residence is about 2300, whereas at the like period last year it was 6700.

THE Council of the London (Royal Free Hospital) School of Medicine for Women is now arranging for a considerable extension of laboratory and teaching accommodation. This extension is necessitated both by the increasing number of women desirous of entering the medical profession and by the recogni

tion of the fact that research work must be regarded as an integral part of education, and that no medical school can be considered as satisfactorily equipped without full facilities for the carrying out of scientific investigations. A site adjoining the present buildings of the school has been secured, and the extension will include additional accommodation for teaching and much improved facilities for research work. For this very necessary extension the sum of 25,000l. is necessary for building and equipment, and a further similar sum for endowment. By the kindness of the Duchess of Marlborough a meeting was held at Sunderland House on February 18 to promote the extension. The speakers were the Duchess of Marlborough (in the chair), Surgeon-General Sir Alfred Keogh, Dr. Mary Scharlieb, Dr. Florence Willey, Dr. Winifred Cullis, and Mr. Acland, M.P. The Duchess of Marlborough in her speech brought out the extreme urgency of the careful use of medical service during this present crisis and the great necessity for an increased service in the future, and particularly of medical women, who were needed as medical inspectors of school children and as workers in maternity and infant welfare centres, whilst there was also a very great need amongst women for practitioners of their own sex. Sir Alfred Keogh, Director-General of the Army Medical Service, paid an eloquent tribute to the work of the school, with which he had familiarised himself when, a few years ago, he had for the Board of Education to inspect practically every medical school in the country, saying that he yielded He further to none in his admiration of the school. made the gratifying announcement that as a result of the excellent work done by medical women in the war he had offered to two medical women who had

organised a hospital unit in Paris, and later one at Boulogne, a hospital of 500 beds, or, if they could staff it, of 1000 beds here in England. The other speakers emphasised the necessity there would be for medical women after the war, when prophylactic measures would be of greater importance than before, and such work as ante-natal treatment and infant care would be of even greater significance when every child would be of added value.

SOCIETIES AND ACADEMIES.
LONDON.

Royal Society, February 18.-Sir William Crookes, president, in the chair.-Prof. W. A. Bone and others: Gaseous combustion at high pressures. Mixtures of methane with less than its own volume of oxygen were exploded in steel bombs at initial pressures of between 8 and 32 atmospheres. The results were in harmony with the "hydroxylation" theory of hydrocarbon_combustion put forward some years ago by Prof. Bone. Results of experiments upon an equimolecular mixture of ethane and oxygen have again confirmed the hydroxylation theory. Another section of the paper deals with an experimental determination of the relative affinities of methane, hydrogen and carbon monoxide for oxygen in flames. It is shown (1) that the affinity of methane is at least twenty times as great as that of hydrogen; (2) that when mixtures corresponding to CH,+O2+xH, are fired under high initial pressures, in which the partial pressures of methane and oxygen are kept constant and x only varied, the distribution of oxygen between the methane and hydrogen varies with x2-which means that hydrogen is burnt directly to steam in flames as the result of the tri-molecular change 2H2+0=2H2O, and not (as some have supposed) indirectly through hydrogen peroxide. The affinity of carbon monoxide

to

is shown to be comparable with that of hydrogen for oxygen in flames. The final section describes experiments in which the whole pressure curves, up to and far beyond the attainment of maximum pressure, were recorded when mixtures corresponding (1) 2H2+O2+4N2, (2) 2CO+O2+4N2, and (3) CH+O2+4N, are exploded under initial pressure of about 50 atmospheres. The rates of attainment of maximum pressure in each case have no direct relation to the order of affinities of the various gases for oxygen.-Prof. W. M. Hicks: The orbits of a charged particle round an electric and magnetic nucleus. Two problems are discussed-the orbits of a-particles and the orbits of electrons round nuclei containing mass, a definite number, n, of positive electronic charges and a definite number, N, of co-axial magnetonsthe motion being in their equatorial planes. It is found that combined systems (atoms) with a-particles may exist in which the a-particle revolves in permanent connection with the nucleus, provided the internal energy of the atom is greater than a certain critical value, and that states of "radio-active" instability occur in which, after a combination of long duration, the a-particle is shot off to infinity. The exact velocity of emission in any case depends on the values of the n, N, but it is of the order of magnitude of the velocity of emission of a-rays from radium. In the case of electronic orbits, in addition to the combined systems with internal energy less than from infinity, there can exist also permanent systems in which the internal energy is greater than that from infinity, although less than a certain critical amount, and in which again states of radio-active" instability occur of the proper order of magnitude.S. Chapman: The lunar diurnal magnetic variation and its change with lunar distance. Balfour, Stewart, and Schuster have developed a theory of the solar diurnal magnetic variations which attributes them to electric currents in the upper atmosphere, impelled by electromotive forces produced by the motion of the air across the earth's permanent magnetic field. The atmospheric conductivity is supposed to be wholly or partly due to solar influence and varies with the sun's hour angle. This theory apparently applies also to the lunar diurnal magnetic variations which possess a semi-diurnal component of constant phase, together with other components the epochs of which depend on the angular distance between the moon and sun; hence, when averaged over a lunation, all components save the former disappear. The suggested solar influence on the atmospheric conductivity is thus supported, and a semi-diurnal atmospheric oscillation-such as a lunar atmospheric tide—is suggested as the source of the magnetic variations. Before this theory was developed, Brown (Trevandrum Observations, 1863) had found that the amplitude of the 12-hour magnetic component at perigee was to that at apogee in the ratio of (lunar distance)-3 at the two epochs-" as in the tidal theory," he briefly remarked; but Figee (Batavian Observations, 1903) disputed this conclusion. The present paper discusses the evidence, of this direct kind, for or against a tidal origin of these magnetic variations. Brown's and Figee's data are used, together with much newly computed material from other observatories. The total hypothesis is confirmed, although on account of the accidental errors affecting the minute quantities under discussion, the exact law of (distance)-", with n=3, is not beyond question, but if n is assumed necessarily integral, its value is certainly 3 and not 2 or 4.-Lt.-Col. J. W. Gifford Some temperature refraction coefficients of optical glass. This is a supplement to a paper read in 1912 in which the refractive indices for 13 wave-lengths of 27 different glass meltings were given by the author. To this

table are now added similar indices for six more Jena glass meltings, including those for the recent fluor crown. This is followed by a table of the temperature refraction coefficients for all the glass meltings dealt with, and attention is directed to the abnormal coefficients for fluor crown which is a minus quantity. An attempt is then made to determine, if only approximately, the influence of barometric changes on the refractive powers of optical glass which would seem to be, similarly, a minus quantity, amounting to something like six units in the sixth decimal place only.

Royal Meteorological Society, February 17.-Capt. H. G. Lyons, president, in the chair.-A. E. M. Geddes : Observations of the upper atmosphere at Aberdeen by means of pilot balloons. These observations were made at the Observatory, King's College, Aberdeen, during the years 1912 and 1913; and in every case two theodolites were used, thus securing an accurate determination of the flights to a level of 3000 metres. In clear weather the upward velocity of the balloon is shown to be fairly uniform, but to depend on more than the free lift. When clouds are present they influence considerably this velocity, the effect differing according to the nature of the cloud. The gradient wind velocities and directions have been calculated and compared with those actually found by observation.-V. G. Anderson: Influence of weather conditions upon the amounts of nitric acid and of nitrous acid in the rainfall at Melbourne, Australia. The author described the methods adopted and stated that the results of the daily determinations from November 1, 1912, to February 28, 1914, when correlated with the meteorological data for Melbourne and the isobaric charts for Australia, reveal the existence of a relation between weather conditions and the amounts of the

nitrogen acids in the rainfall. The concentration of

nitric acid reached a maximum in summer, a minimum in winter, and an intermediate position in autumn and spring. The concentration of nitrous acid reached a maximum in winter and a minimum in summer. Nine well-defined recurring types of rainstorms have been investigated, the amounts (pounds per 1000 acres) of oxidised nitrogen per day varying from 15 in the case of certain antarctic storms to 35'0 in the case of intense tropical storms.

Institution of Mining and Metallurgy, February 18.Dr. F. H. Hatch, president, in the chair.-J. Morrow Campbell Notes on some gold occurrences in Ashanti. Some 30 miles to the west of Kumasi are to be found igneous rocks intruding through the schist, some of which are granite, and non-auriferous. The nongranite dykes, on the other hand, are mostly auriferous, and the author has devoted special attention to three of these in his paper. All three are comparatively old, and show abundant internal evidence of the continuance of the crustal movements to which they owe their existence. These movements have produced fracturing, and have resulted in the formation of quartz veins traversing the igneous rock in all directions, and varying in width from more than a foot to mere partings. After describing in detail the composition and characteristics of these dykes, the author draws certain deductions. He points out that in Ashanti pyrites is abundant in quartz veins, and elsewhere, quite unassociated with gold, but that where arsenopyrite occurs gold so frequently accompanies it as to lead to the conclusion that their association cannot be fortuitous. He thinks it fair to conclude that the arsenopyrite caused the precipitation of the gold, and that the solution transporting the gold contained the latter in combination

with silica either as a silicate or as alkaline aurosilicate. The phenomena, he thinks, demand a single solution from which gold and silica may be precipitated simultaneously.-W. G. Holford: Some features in the mining problems of the eastern Witwatersrand area. This paper is a general review of the more intricate geological problems associated with mining in the particular area referred to, where conditions are somewhat different from those met with in the central Rand. For example, while it is found on the central Rand that the close proximity of the zones in which economic gold values are contained are in such close proximity as almost to constitute defined shoots, on the eastern rand the zones are less frequent and are of greater economic value in the synclinal portions of the areas. The author goes on to describe in detail the various features of mining practice in the district under consideration, dealing respectively with mining areas, shaft sinking, initial development, the mechanical equipment, and the labour problems encountered. Incidentally he makes a strong argument in favour of circular as against rectangular shafts.W. B. Middleton: Prospecting tin land in Malaya. This is a practical paper concerning itself with the alluvial deposits which are the principal source of the tin production of the Malay Peninsula. The author gives full particulars of the various methods employed in treating, prospecting, and sampling the ground, including an elaborate description of the tools required, and as an appendix he furnishes a set of tables for calculations and conversions in connection with the work, which should prove of great utility. CAMBRIDGE.

Philosophical Society, February 8.-Dr. Barnes, vicepresident, in the chair.-Sir J. J. Thomson: Theory of the mobility of negative ions.-Dr. G. F. C. Searle : (1) The determination of the focal length of a thick mirror. (2) Experiment on the focal lines formed by refraction at a plane surface. (3) Calculation of the electrical resistance of a certain network of conductors. -C. T. R. Wilson: A method of measuring the thickness of thin plates. The method is a modification of that of Macé de Lépinay and Buisson in which μe, the product of refractive index and thickness, is obtained by measurements of the thin-plate fringes and (μ- 1)e by observing the retardation produced by the plate when inserted in the path of a beam of light.-G. W. White Investigation of the wolf-note in bowed stringed instruments. With all stringed instruments of the violin type a pitch can be found at which it is difficult and often impossible to obtain a pure steady tone. In the preliminary experiments to investigate this imperfect note photographs were obtained of the belly vibration of a 'cello by reflecting a beam of light from an optical lever to a moving photographic plate. A series of notes through the "wolf-note " played with a constant bow pressure was studied. At the wolfnote" the vibration curve had an extremely big amplitude and showed that the unsteady nature of the tone was due to a "beating" of the instrument belly. The experiments proved conclusively that the "wolfwas caused by the impressed string pitch coinciding with the pitch of best resonance of the instru

note

ment.

MANCHESTER.

64

Literary and Philosophical Society, January 26.—Mr. F. Nicholson, president, in the chair. W. C. Jenkins : Manchester fogs of the last ten years. A comparison of the fogs in Manchester during 1904-1913 inclusive showed that the number of days affected by this phenomenon has increased during the latter years by at least 30 per cent. as compared with the earlier years of this period. By a rearrangement of the figures

into seasonal effects the most striking feature is the increase of days classified as "gloomy" during the summer months, the number during the winter months of October to March remaining fairly constant. The number of days affected by "gloom" increased 100 per cent. during the period of the last four years as compared with the number so classified in the first four years of the period under consideration. These fog glooms are situated close to the earth's surface, as is shown by a comparison of sunshine records taken from the roof of the School of Technology and on the ground, the hours of sunshine measured on the ground being approximately 10 per cent. less than the amount recorded from the roof (100 feet higher).-Prof. W. W. Haldane Gee: Note on the monthly variation of sunshine. As a result of his examination of the Campbell-Stokes records, the author found that the average percentage of the possible sunshine usually reaches a maximum in May. A number of examples of this law were quoted. It was true for Glasgow, Douglas (I. of M.), Llandudno and Stonyhurst, 1880-1885; for St. Aubins (Jersey), 1880-1885; Blackpool, 1882-1885; Buxton, 1881-1885; Durham, 1880-1884; and for the Godlee Observatory (Manchester School of Technology), 1906-1910. The records for Stonyhurst for the thirty-three years from 1880-1912 also show the maximum in May. For 1910, Manchester (Oldham Road), Manchester (Whitworth Park), Buxton, Blackpool, and Llandudno also show the maximum in May. The author thought that the sunlight in May must have an important influence on vegetable growth.-W. C. Jenkins: Weather repetitions, with suggestions for long-distance forecast. Attention was directed to the repetitions in the weather for periods of twelve hours, twenty-four hours, seven days, and the lunar month, and also annual repetitions, making certain allowances-using particularly the records of rainfall. With the view of establishing these repetitions to a definite origin, the author showed the connection between numerous cyclonic paths and extra terrestrial phenomena, and assuming similar forces acting in temperate latitudes, he proceeded to demonstrate that cyclonic movements in the regions of this kingdom followed very much the variations expected under these conditions.

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