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(4) Every straight line from the "cæcus focus" of the parabola to a point on the curve being said to be parallel to the axis, the idea of the concurrence of parallel lines at a point at infinity has at length been formed and announced. It is to be noticed that the new doctrine of parallels is here presented in relation to one plane, and not as springing out of the consideration of figures in perspective in space.

Taking into account also Kepler's Nova Stereometria we conclude that by his contributions to the doctrine of the infinite and the infinitesimal and his firm grasp of the principle of continuity, he is entitled to the foremost rank amongst the founders of the modern geometry.

November 8, 1880.

PROFESSOR NEWTON, PRESIDENT, IN THE CHAIR.

The following communications were made to the Society:

(1) On a new arrangement for sensitive flames. By Lord RAYLEIGH, M.A., F.R.S., Professor of Experimental Physics.

A jet of coal gas from a pin-hole burner rises vertically in the interior of a cavity from which the air is excluded. It then passes into a brass tube a few inches long, and on reaching the top, burns in the open. The front wall of the cavity is formed of a flexible membrane of tissue paper, through which external sounds can reach the burner.

The principle is the same as that of Barry's flame described by Tyndall. In both cases the unignited part of the jet is the sensitive agent, and the flame is only an indicator. Barry's flame may be made very sensitive to sound, but it is open to the objection of liability to disturbance by the slightest draught. A few years since Mr Ridout proposed to enclose the jet in a tube airtight at the bottom, and to ignite it only on arrival at the top of this tube. In this case however external vibrations have very imperfect access to the sensitive part of the jet, and when they reach it they are of the wrong quality, having but little motion transverse to the direction of the jet. The arrangement now exhibited combines very satisfactorily sensitiveness to sound, and insensitiveness to wind, and it requires no higher pressure than that of ordinary gas-pipes. If the extreme of sensitiveness be aimed at, the gas pressure must be adjusted until the jet is on the point of flaring without sound.

VOL. IV. PT. I.

2

The apparatus exhibited was made in Prof. Stuart's workshop. An adjustment for directing the jet exactly up the middle of the brass tube is found necessary, and some advantage is gained by contracting the tube somewhat at the place of ignition.

(2) On an effect of vibrations upon a suspended disc. By Lord RAYLEIGH, M.A., F.R.S.

In the British Association experiment for determining the unit of electrical resistance, a magnet and mirror are enclosed in a wooden box, attached to the lower end of a tube through which the silk suspension fibre passes. Under these circumstances it is found that the slightest tap with the finger-nail upon the box deflects the mirror to an extraordinary degree. The disturbance appears to be due to aerial vibrations within the box, acting upon the mirror. We know that a flat body, like a mirror, tends to set itself across the direction of any steady current of the fluid in which it is immersed, and we may fairly suppose that an effect of the same character will follow from an alternating current. At the moment of the tap upon the box the air inside is made to move past the mirror, and probably executes several vibrations. While these vibrations last, the mirror is subject to a twisting force tending to set it at right angles to the direction of the vibration. The whole action being over in a time very small compared with that of the free vibrations of the magnet and mirror, the observed effect is as if an impulse had been given to the suspended parts.

The experiment shewn is intended to illustrate this effect. A small disc of paper, about the size of a sixpence, is hung by a fine silk fibre across the mouth of a resonator of pitch 128. When a sound of this pitch is excited, there is a powerful rush of air in and out of the resonator, and the disc sets itself promptly across the passage. A fork of pitch 128 may be held near the resonator, but it is better to use a second resonator at a little distance in order to avoid any possible disturbance due to the neighbourhood of the vibrating prongs.

(3) On an apparatus illustrating the movement of sound-waves and water-waves. By SEDLEY TAYLOR, M.A., late Fellow of Trinity College.

This was an apparatus illustrating wave-motion. The arrangement consists of sixteen toothed wheels of brass, centred along a straight line upon a flat board, and connected by intermediate pinions in such a manner that, when one of the end-wheels is set in motion by means of a winch attached to it, all the others rotate with the same velocity and in the same direction. Sixteen slender stems

of equal lengths, each supporting a small wooden ball, are inserted in the wheels perpendicular to their plane near their circumferences, at such points that the phase-difference between any two adjacent balls is one-eighth of a revolution. The balls thus disposed represent two complete equal waves, and, when the winch is turned, the effect of wave-motion is produced. Different positions of an observer's eye with reference to the apparatus lead to the presentation of waves due to different types of particle-movement, both orbital and vibrational. Let the board be first placed with its plane vertical, and with the straight line joining the centres of the wheels horizontal. Let the observer's eye be situated in front of, and at some distance from, the apparatus, in a horizontal plane through the line of centres. Waves due to circular particle-movements in the plane of wave-propagation, like those on the surface of deep water, are now seen. The observer's eye remaining stationary, let the board be next gradually turned about the line of centres. The circles are thus projected into ellipses with major axes horizontal, such as give rise to water-waves below the surface. These degenerate, when the plane of the board becomes horizontal, into straight vibrational paths in the direction of propagation, harmonically described, and giving rise to waves like those of a sound of one degree of pitch, or 'simple tone.' By suitably altering the position of the observer's eye in the plane on which it is situated, these paths can be made to look as if executed obliquely to the direction of wave-propagation. Lastly, replacing the board in its original position, let it be gradually turned about a vertical axis on its own plane. The circles then pass into ellipses with vertical major axes, degenerating ultimately into straight lines transverse to the direction of wave-propagation, and thus presenting the case of plane-polarized light. All the types of wave-motion ordinarily requiring illustration, with the exception of circularly and elliptically polarized light, are, therefore, capable of being represented by this apparatus.

November 22, 1880.

PROFESSOR NEWTON, PRESIDENT, IN THE CHAIR.

C. Creighton, M.A., Demonstrator of Anatomy, was balloted for and duly elected a Fellow of the Society.

The following communications were made to the Society: (1) On the experiments made by Biot and others on horizontal refraction. By J. B. PEARSON, D.D., Fellow of Emmanuel College. I was led to investigate this question by some remarks made

upon a memoir I presented to the Society last spring (Proceedings, Vol. III. pp. 352-8), describing some observations of the Sun on the northern horizon, made by me last summer at the North Cape. At the commencement of this century, the question seems to have excited some interest: there being papers on the subject by Mr Huddart, Prof. Vince, and Mr Wollaston in the Philosophical Transactions for 1797, 1799, and 1803. As these memoirs however do not seem to me to contain any precise results, although they record several interesting natural phenomena, I shall not trouble my readers with an abstract of them. The investigations however, of M. Biot, M. Le Gentil, and in a less degree those of M. Bouguer in Peru, seem to me so relevant to the question of my own observations, that I have thought that an abstract of them may be of interest to science.

It must be premised that the altitude of the Sun or a star when close to the sea-horizon involves two things: the apparent depression of the horizon itself, or the dip, technically so called, and the atmospheric refraction. M. Biot's experiments are confined to the former; those of the two other savans mainly to the latter: while my own observations, taken on the sea-horizon from the deck of a ship at a height of about 18 feet, will evidently be affected by both.

Having premised this, I subjoin first an abstract of M. Biot's observations, which were taken by him with the aid of M. Mathieu at Dunkirk during the winter of 1809-10, and were published by him at Paris in a separate volume in the following year. They were taken with a graduated quarter-circle with telescope attached and adjusted by a spirit level, and from stations at different altitudes above the level of the sea: viż. (1) actually on the sand: (2) a timber staging: (3) different stories of a house on the beach and lastly, from the top of the tower of the church. The annexed Table shews the place of observation, and its elevation in feet, the date, the temperatures of the sea and air on Fahrenheit's scale, and the amount by which the observed result varied from that which would be expected on theoretical grounds, a negative sign (-) being affixed where the depression of the horizon was greater than the normal, and a positive one (+) when it is less. By the normal or theoretical result is meant that given by the theory explained at length by M. Biot in the same volume. I am unable to say how far his theory at that time coincides with the views on the subject laid by him before the French Academy in several papers in the years 1854 and 1855. He then allowed that the system generally adopted was that of Bessel, and spoke with approval of the abstract of it issued by the Greenwich Observatory in 1853 but he was evidently dissatisfied with Bessel's method, as

well as with Ivory's, at any rate for low altitudes; preferring to employ a formula of Laplace's, corrected by experiments made under all different circumstances. Myself, merely for convenience, I employ Ivory's Tables, which at Z. D. 89°. 30", Th. 50 F. Bar. 29.6, differ from Bessel's by 33" only: but I subjoin an extract from M. Biot's concluding paper, as probably of value on a subject of which I have little or no theoretical knowledge myself.

M. Biot in summing up the results of the series of papers published by him in 1854, 5, seems to say that he looks with great suspicion on any but the simplest theory of refraction, at any rate for low altitudes.

He says that he has taken as a basis of his arguments the formula of Laplace, which he seems entirely to accept: but then he continues by saying, that when he constructs atmospheres such as the theories of Ivory and Bessel assume......"en comparant ces résultats à ce que nous connaissons de l'atmosphère reelle, on aperçoit avec évidence, qu'aucune de ces atmosphères hypothétiques ne lui est, même approximativement, assimilable; et qu'ainsi elles ne peuvent pas donner les vraies réfractions; surtout celles qui s'opérant près de l'horizon, se montrent perpétuellement troublées par des accidents lointains, dont les hypothèses ne tiennent aucun compte. A cela on pourra répondre que ces dernières réfractions échappent inévitablement à toute théorie; et que, dans l'impossibilité où l'on est de prévoir leurs caprices, on ne doit démander aux hypotheses que de reproduire leur valeurs moyennes. C'est en effet un des genres d'utilité qu'Ivory et Bessel ont prétendu obtenir de celles qu'ils ont employées. Mais alors il faudrait, comme l'a fait Laplace, borner l'empirisme à cette portion irrégulière du phénomène, et ne pas l'étendre à des déterminations qui peuvent en être rendues indépendantes. Même pour ce but particulier, les hypothèses sont encore inutiles. Car en s'aidant de la formule de Laplace judicieusement appliquée, on peut, comme je le montre, obtenir par observation seule, de Tables de ces valeurs moyennes qui seront propres à chaque localité; qui les donneront telles qu'elles se produisent réellement,...et qui offriront encore cet avantage, que si, un peu au delà des distances zénithales auxquelles la formule de Laplace s'applique, il existe entre les réfractions et les indications météorologiques quelque relation assez constante pour qu'on puisse s'en prévaloir, on aura toute chance de la découvrir. Des Tables ainsi construites d'après l'observation pure, pour les distances zénithales que la formule approximative ne peut atteindre, fourniraient sur la constitution des, couches inférieures de l'atmosphère, des documents certains, qui se rattacheraient efficacement à ceux que les physiciens croient recueillir dans ces couches mêmes, ce qui aurait le double avantage d'assurer le présent, et de préparer l'avenir." C. R. XL. 603, 4. (1855).

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