XCII. Reviews, and Notices respecting New Books.

The Principles of Hydrostatics. By Thomas Webster, M.A., of Trinity College, Cambridge. 1835.

The Theory of the Equilibrium and Motion of Fluids. By the same Author. Cambridge, 1836.

IN

N the Preface to the first of these works Mr. Webster states that he has "endeavoured to develop the principles of the science of Hydrostatics with the use of none but the most elementary mathematics; so that the student, who now either partially or wholly neglects this beautiful branch of natural philosophy from the uninviting character which analysis presents to those who are not familiar with it, may at once proceed to its study if he is only acquainted with the first principles of algebra and mechanics. It is not from thinking other methods preferable or even comparable with the analytical that I have adopted this plan, but with the view of bringing the subject within the reach of those who have not been initiated in analysis." By pursuing this plan the author has produced a work of more general utility than if he had introduced more analytics, since many that might not have ability or inclination to follow a train of reasoning conducted by mathematical symbols, would take interest in and receive benefit from an exposition of the principles on which such reasoning may be founded, and by a statement of facts and results. Besides which, the nature of the work admits of the introduction of subjects which in the present state of science do not admit of exact mathematical treatment, and which are nevertheless fully as useful in a practical point of view, or instructive as branches of natural philosophy, as many of those that do. These subjects are, Steam and its applications; the mechanical application of the Motion of Fluids; Dalton's law of the diffusion of Gases coexisting in the same space; Winds; Trade Winds; Evaporation; Theory of Rain, &c., which will be found to be clearly and concisely treated in this work. It adds, however, to the confidence we place in works of this description to know that they are written by mathematicians. Mr. Webster establishes a claim to being considered such by the able manner in which the second of the above-named treatises is composed, which is purely mathematical, being intended to carry the student to the highest analytical deductions from the first principles of hydrostatics and hydrodynamics that could be prudently introduced into an elementary work. Accordingly, besides the usual propositions, treated for the most part in the usual manner, there is additional matter on subjects that have scarcely yet acquired a standing in elementary treatises, viz. Laplace's Theory of Capillary Attraction, Specific Heat, and the Law of Cooling, in the statical part; aerial vibrations and their propagation, considerd as the immediate causes of sound, together with musical vibrations in cylindrical tubes, in the dynamical part. In these portions of the work Mr. Webster has drawn largely from recent memoirs both of foreigners and our own countrymen, and has endeavoured to make their productions more accessible to the mathematical student by breaking up the simpler parts into distinct propositions.

As these subjects are inferior to few in the interest that attaches to them, and would be more generally attended to if the mathematical calculation by which the reasoning in most of them is necessarily conducted could be simplified, any attempt, like that in the work before us, to do this, is deserving of our approbation.

1836. Feb. 25.

XCIII. Proceedings of Learned Societies.

ROYAL SOCIETY.

412

PAPER was read, "On an artificial Substance resembling Shell; by Leonard Horner, Esq., F.R.S. L. and Ed.: with an account of the examination of the same; by Sir David Brewster, K.H., LL.D., F.R.S., &c."

The author, having noticed a singular incrustation on both the internal and external surfaces of a wooden dash-wheel, used in bleaching, at the Cotton Factory of Messrs. J. Finlay and Co., at Catrine, in Ayrshire, instituted a minute examination of the properties and composition of this new substance. He describes it as being compact in its texture, of a brown colour, and highly polished surface, with a metallic lustre, and presenting in some parts a beautiful iridescent appearance: when broken, it exhibits a foliated structure. Its obvious resemblance, in all these respects, to many kinds of shell, led the author to inquire into its intimate mechanical structure, and into the circumstances of its formation. He found, by chemical analysis, that it was composed of precisely the same ingredients as shell; namely, carbonate of lime and animal matter. The presence of the former was easily accounted for ; as the cotton cloths which are placed in the compartments of the wheel, in order that they may be thoroughly cleansed by being dashed against its sides, during its rapid revolutions, have been previously steeped and boiled in lime water. But it was more difficult to ascertain the source of the animal matter; this, however, was at length traced to the small portion of glue, which, in the factory where the cloth had been manufactured, was employed as an ingredient in forming the paste, or dressing, used to smooth and stiffen the warp before it is put into the loom. These two materials, namely lime and gelatine, being present in the water in a state of extreme division, are deposited very slowly by evaporation; and thus compose a substance which has a remarkable analogy to shell, not only in external appearance, and even pearly lustre, but also in its internal foliated structure, and which likewise exhibits the same optical properties with respect to double refraction and polarizing

powers.

A letter from Sir David Brewster, to whom the author had submitted for examination various specimens of this new substance, is subjoined; giving an account of the results of his investigations of its mechanical and optical properties. He found that it is composed of laminæ, which are sometimes separated by vacant spaces, and at others, only slightly coherent; though generally adhering to each Third Series. Vol. 8. No. 50, Supplement. June 1836. 3 I

other with a force greater than that of the laminæ of sulphate of lime, or of mica; but less than those of calcareous spar. When the adhering plates are separated, the internal surfaces are sometimes colourless, especially when these surfaces are corrugated or uneven; but they are almost always covered with an iridescent film of the most brilliant and generally uniform tint, which exhibits all the variety of colours displayed by thin plates or polarizing laminæ. This substance, like most crystallized bodies, possesses the property of refracting light doubly; and, as in agate and mother-of-pearl, one of the two images is perfectly distinct, while the other contains a considerable portion of nebulous light, varying with the thickness of the plate, and the inclination of the refracted ray. Like calcareous spar, it has one axis of double refraction, which is negative; and it gives, by polarized light, a beautiful system of coloured rings. It belongs to the rhombohedral system, and, as in the Chaux carbonatée basée of Haüy, the axis of the rhombohedron, or that of double refraction, is perpendicular to the surface of the thin plates. As mother-of-pearl has, like arragonite, two axes of double refraction; this new substance may be regarded as having the same optical relation to calcareous spar that mother-of-pearl has to arragonite.

The flame of a candle, viewed through a plate of this substance, presents two kinds of images; the one bright and distinct, the others faint and nebulous, and having curvatures, which vary as the inclination of the plate is changed: the two kinds being constituted by oppositely polarized pencils of light. On investigating the cause of these phenomena, Sir David Brewster discovered it to be the imperfect crystallization of the substance; whence the doubly refracting force separates the incident light into two oppositely polarized pencils, which are not perfectly equal and similar. In this respect, indeed, it resembles agate, mother-of-pearl, and some other substances; but it differs from all other bodies in possessing the extraordinary system of composite crystallization, in which an infinite number of crystals are disseminated equally in every possible azimuth, through a large crystalline plate; having their axes all inclined at the same angle to that of the larger plate, and producing similar phenomena in every direction, and through every portion of the plate: or this remarkable structure may be otherwise described, by saying that the minute elementary crystals form the surfaces of an infinite number of cones, whose axes pass perpendicularly through every part of the larger plate.

An examination of the phenomena of iridescence afforded by this new substance, leads him to the conclusion that the iridescent films are formed at those times when the dash-wheel is at rest, during the night, and that they differ in their nature from the rest of the substance. These phenomena illustrate in a striking manner some analogous appearances of incommunicable colours presented by motherof-pearl, which had hitherto baffled all previous attempts to explain them; but which now appear to be produced by occasional intermissions in the processs by which the material of the shell is secreted and deposited in the progress of its formation.

March 3.-A paper was read, entitled, "Researches on the Tides. Fifth Series: On the Solar Inequality and on the Diurnal Inequality of the Tides at Liverpool." By the Rev. William Whewell, F.R.S., Fellow of Trinity College, Cambridge.

The inequality both in the height and time of high water in the morning and evening tides of the same day, which varies according to a law depending on the time of the year, is termed by the author the diurnal inequality, because its cycle is one day. The existence of such an inequality has often been noticed by seamen and other observers; but its reality has only recently been confirmed by regular and measured observations; and its laws have never as yet been correctly laid down. The author gives an account of the observations now in progress at different ports, from which he expects they will be ascertained with great precision. He traces the correspondence of the observations of the diurnal inequality already made with the equilibrium theory; and remarks that the semi-diurnal tides, alternately greater and less, which are transmitted from the Southern Ocean to Liverpool, may be compared to the oscillations of a fluid mass: and that they are augmented by the action of the forces occurring at intervals equal to those of the oscillations. Hence the oscillations go on increasing for a considerable period after the forces have gone on diminishing, and reach their maximum a week after the forces have passed theirs.

The remaining sections of this paper are devoted to the investigation of the Solar inequalities at Liverpool. By carefully eliminating the Lunar effects, which the author is enabled to do by the aid of the preceding researches, he has determined the approximate circumstances of the Solar correction for the height. He has also obtained evidence of the existence, and some knowledge of the laws of the Solar inequalities of the times; and these inequalities, as thus discovered, are found to exhibit the same general agreement with the equilibrium theory which has been disclosed in all the inequalities hitherto detected. The results of the extensive observations now obtained are sufficiently precise to indicate the defects of our mathematical theories of hydrodynamics; and some of these are pointed out by the author, who remarks that although a short time ago the theory was in advance of observation, at present observation is in advance of theory; which mathematicians are therefore called upon to remodel and perfect.

The author proceeds to consider the effect of the Moon's declination on the Tides at Liverpool; which, as before observed, it is necessary to eliminate, in order to obtain the Solar inequality; and gives an explanation of various formulæ and tables constructed for that object. He then investigates the laws of the solar inequalities, first, as to the heights; and secondly, as to the times of high water at Liverpool, by applying to them these methods of calculation.

March 10. Report of Magnetic Experiments tried on board an Iron Steam-Vessel, by order of the Right Hon. the Lords Commissioners of the Admiralty." By Edward J. Johnson, Esq., Commander, R.N., accompanied by plans of the vessel, and tables showing the ho

rizontal deflection of the Magnetic Needle at different positions on board, together with the dip and magnetic intensity observed at those positions, and compared with that obtained on shore with the same instruments. Communicated by Captain Beaufort, R.N., F.R.S., Hydrographer to the Admiralty; by command of the Right Hon. the Lords Commissioners of the Admiralty.

This report commences with a description of the iron steam-vessel, the "Garryowen," belonging to the City of Dublin Steam Packet Company, and built by the Messrs. Laird, of Liverpool. She is constructed of malleable iron, is 281 tons burthen, and draws only 5+ feet water, although the weight of iron in the hull, machinery, &c. is 180 tons.

This vessel was placed under the directions of the author, in Tarbert Bay, on the Shannon, on the 19th of October, 1835, for the purpose of investigating its local attractions on the compass. The methods which were adopted with that view are given; together with tables of the results of the several experiments, and plans of the various parts of the Garryowen. The horizontal deflections of the magnetic needle at different situations in the vessel were observed, for the purpose of ascertaining the most advantageous place for a steering compass, and also for the application of Professor Barlow's correcting plate: and the dip and intensity in these situations were, at the same time, noted.

An experiment is detailed, showing that where several magnetic needles, freely suspended, were placed upon the quay, in Tarbert Bay, and the vessel warped from the anchorage towards them, first with her head in that direction and then with her stern, opposite deflections were produced: in the first case all the needles showing a deviation to the eastward, and in the latter to the westward, of the true magnetic meridian.

Considering the height of the general mass of iron in the vessel and also that of the head and stern, together with the distance (169 feet) at which some of the needles indicated a deviation, the author concludes that the respective deflections were caused by the magnetic influence of the iron in the vessel; the combined effect of that about the bows representing the north pole of a magnet, and that about the stern a south pole. He then offers several suggestions for future observation on this subject, and connected with the little oxidation that is reported to have taken place in the vessel.

The experiments having been interrupted by a continuance of wet and stormy weather, the author proceeds to draw the following general practical conclusions, deduced from the series of observations already made, and points out the further experiments which he considers necessary to be tried.

1st. The ordinary place for a steering-compass on board ship is not a proper position for it in an iron steam-vessel.

2nd. The binnacle-compass in its usual place on board the Garryowen is too much in error to be depended upon.

3rd. In selecting a proper position for a steering-compass on board iron steam-vessels, attention should be paid to its being placed, as