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to be imperfect, there has arisen internationally a necessity for its adoption unti it shall be met or superseded by some other device; and the object of the author, by this paper, is to bring before the notice of the British Association for the Advancement of Science the question, which has been otherwise publicly agitated by him, whether the principle of "invulnerability," as based on "armour-plating." may not be superseded by the principle of "unsinkability," as based on the principle of constructing ships with such a mass of uninflammable materials of a specific gravity less than that of water as shall support the hull and its entire load and float, however perforated by shot laterally through the sides of the ship er vertically through the deck and bottom of the vessel by the still more formidabe effect of an improved mortar-practice pitching shells of great weight with an fallible precision at short range, or even still float in parts when severed by the concussion of a hostile ram.

Though the vessel may thus be "unsinkable," it is not professed or anticipated by the author that war would be prosecuted without the sacrifice of blood; for though the proposed construction of shipping would be well adapted for protecting the crews of ships from small arms, still the cannon or the mortar would take efect The chief point on which the principle of "unsinkable ships" is put forward by the author as claiming consideration is that, by the adoption of this principle, the whole crew of a ship would not be simultaneously drowned through the effective application of a single shot, shell, or ram-stroke, as might be the case with armoured ships, seeing that the direct fire of artillery is still paramount, and the mortar prac tice above referred to has not yet been tried.

A further advantage consequent on adopting the principle of "unsinkability" would be that it does not necessitate the construction of ships of such large size as is required for carrying out the principle of "invulnerability" by armour-plating. Also by avoiding top-weight, by which armour-plated ships are so much encum bered, many difficulties in the prosecution of naval architecture are obviated. It is therefore conceived that this principle of "unsinkability" would be well adapted for gun-boats and mortar-vessels destined to act in cooperation with each other in assailing larger vessels at close quarters, or doing service in shoal waters, such vessels receiving their stores from high-speed steamers of ordinary build acting as store and hospital and barrack ships, to be kept out of harm's way. Also the principle of unsinkability would be well adapted for troop ships and the safe conveyance of valuable cargoes and treasure.

The details of construction of the "unsinkable ship," as respects the disposal of its unsinkable materials, will be dependent on the purpose for which the ship may be especially intended. For example, the whole mass of material on which the ship depends for its unsinkability may be in a solid mass, with the whole of its hold accommodation above the deep-draught water-level; or the vessel may have a hold below the level of the load water-line, provided that the required mass of buoyant material be otherwise disposed of, constituting the sides or ends and bottom and decks of the vessel. Of course such a vessel with a hold below the load-line level may become water-logged, and, if a steamer, disabled; but still such a vessel would sail, and the crew would be alive to do good service from her deck; at all events, her whole crew could not be simultaneously sent to the bottom, which is the great catastrophe intended to be obviated by the principle of unsinkable ships—a catastrophe to which armour-plated ships, though bulkheaded, will be liable if artillery or mortar practice become paramount.

The required brevity of this abstract does not admit of the details of calculation and of construction for the production of "unsinkable ships" of given capabilities being here entered upon; such an exposition, to be complete, would be elaborate, and may engage the future attention of the author.

On Coryton's Vertical-Wave-Line Ships, Self-Reefing Sails, and Guide-Propeller. By JoHN CORYTON, of Lincoln's Inn, Barrister-at-Law. The object of the inventor has been to produce a form of vessel which shall combine the weatherly qualities of a clipper ship, with the advantages of increased speed when going free, and greater safety when scudding before a gale, riding at an

anchor, or becoming suddenly unmanageable through loss of masts, damage to her machinery, &c.

This object is attained by a revolution in the tactics of sailing, as well as in a change of form. When close-hauled, or steaming head to wind, the vessel goesto use the parlance applicable to the present form of ships-head foremost; when sailing or steaming off the wind, she goes, so to speak, stern foremost. In still water the vessel proceeds always on the latter plan. The terms stem, bow, and stern being obviously unsuited to vessels of the proposed form, the inventor substitutes for them the "weather end" and "lee end "respectively.

Novel as the general idea pervading this invention may appear, the deviation in point of form of a Vertical-Wave-Line vessel from the type of ships at present existing is very slight. Taking as a standard a fast clipper schooner of the latest build with a "tumble home" bow, fine entry lines, beam carried right aft to the taffrail, and a flat counter, something very like the proposed form will be obtained by cutting away the entire after-keel almost from the fore-foot; the "weather end" thus becoming (approximately) a vertical wedge, and the "lee end" (approximately alse) a horizontal wedge. Provided these forms are preserved, the intermediate work is of little consequence, and may be constructed simply with regard to the ordinary rules of carpentering a point of economy which those practically acquainted with ship-building will not fail to appreciate. "It seems," is the observation of M. Vial de Clairbois in his 'Architecture Navale' (p. 22), “that naval architects have hitherto affected to avoid straight lines, although geometrically they have the advantage of simplicity over all others." By a coincidence which may appear almost accidental, it will be found that at two points of the vessel constructed on the new principle (and in these, in the larger class of vessels, it is proposed to bulk-head them), sections made by planes slightly out of the perpendicular approach very nearly the catenary-a self-supporting curve. The inventor proposes to construct his vessels of laminated iron up to the water-line, and to make the works above, for the convenience of rough repairs, of wood. By making the iron planks taper towards the ends, and decrease in number as they are placed higher on the ship's side, the greatest strength of the vessel may be placed with almost mathematical accuracy at the point exposed to the greatest strain.

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The advantages of this system, besides economy and strength, may be shortly stated thus:-Safety. If disabled, instead of rolling in the trough of the sea like the Great Eastern" on a recent occasion, a Vertical-Wave-Line ship flies head to wind at once, and remains so as long as she can hold together. In boats of this construction "broaching-to" (the fertile source of disaster in passing through surfs or being beached) is entirely avoided, the boat being always kept by the action of the water in the only position compatible with safety. The same peculiarity of form, offering a maximum deflection to an impinging body, renders Vertical-Wave-Line ships admirably adapted for the purposes of naval warfare. A model of a Shield Ship on this principle was exhibited at the International Exhibition during the present year.

Stability.-Vertical-Wave-Line ships will never accumulate rolling motion. From the form of the immersed body, if lateral disturbance take place, the axis of rotation changes with such rapidity as to render it all but impossible that any subsequent impact of wind or sea can have the effect of increasing, and almost certain that each such impact will actually neutralize, the existing momentum. It is this peculiarity, coupled with its safety in exposed situations, that has induced the inventor to suggest this form as suitable for the establishment of a system of Fairway Lighting in the English and Irish Channels, plans and models of which were recently exhibited at the International Exhibition of 1862.

In respect of Speed, a very remarkable phenomenon presents itself, in the case of Vertical-Wave-Line ships sailing off the wind or steaming free, working consequently "lee end" foremost. For every increase of speed there is a decrease of draught. That there is a limit to the truth of this is of course evident; but as a totally new problem, the inventor anticipates from its investigation very extraordinary results. From the absence of keel at the lee end, the vessel steers of course with great handiness, and with the Guide-Propeller can be made to turn in her own length.

The revolution in tactics alluded to above, rendered of course the orde system of rigging useless, and the inventor has consequently devised the sy Self-reefing traversing sails (also lately exhibited at the International Exhibiti The masts, which are T-shaped, are supported by revolving shears, and the are fixed on spars rigidly attached to the masts. The mast is thus inclined wind, or "rakes," to use the ordinary term, whether the vessel be by the wiz going free-an arrangement which, for the same vertical height of masts, is greater and far more efficient spread of canvas than can be produced by any of th systems now in use. On a smart breeze springing up, the sails reef themselve the compass requisite for the vessel's progress; and, as the gale freshens, reí úz reef is taken in, until, when it is at its height, her sails will be found close-re without the employment of a single hand. If the ship be clear of the land. sails can be furled, her helm left, and the ship will ride the gale out head to wai Ships and boats on this principle can, of course, equally with any others, be pelled by steam or other power. In his Atmospheric Guide-Propeller (exhibited also in 1851 (Class VIII. 82) and 1862 (Class XII. 2746)), the inventor has end voured to introduce a great simplification into ship propulsion, by combining i processes of steering and propelling. The plan consists in pumping a current of through tubes which are led outside the vessel into the water, this current ba capable of the nicest regulation and change of direction by means of valve Water may be used instead of air, and is recommended for boats, in which, it may be observed, oars are entirely dispensed with, and propulsion is effected by haulag on an endless rope.

The last point is Ventilation, and for the appreciation of the advantages of the new system in this respect it is almost necessary to refer to models. In the Exhibition of 1862 a model was shown, made to a scale, and intended to test the relative merits of a ship on this system and the Great Eastern.' The dimensions of the vessel on the Vertical-Wave-Line system of equal tonnage were, length 432 feet (as against 700 in the case of the 'Great Eastern'), breadth 108 feet, depth

76 feet.

Models and drawings illustrative of the construction and propulsion of VerticalWave-Line ships may be seen at the Naval Museum of the Royal United Service Institution, Middle Scotland Yard, and at the Museum of the Commissioners of Patents, South Kensington.

A New Marine Boiler for generating Steam of High Pressure.
By Dr. F. GRIMALDI.

The boiler was a cylindrical tubular boiler, with certain arrangements of radial tubes for taking up and conveying the steam, and made to rotate slowly in the furnace on its axis. The advantages claimed were freedom from priming, smallness of space occupied, superheating the steam, and economy of fuel."

On the Prevention of Railway Accidents. By J. SEWELL.

The author considered that the main cause of accidents was the want of punctuality in the trains; and that this arose mainly from the overloading of them, which rendered it impossible that they could keep time. Engines were made to perform certain work, and draw certain loads, and if these were exceeded it was impossible that time could be kept. This was a matter that the public could not ascertain for themselves, and he therefore advocated the importance of having engines licensed, like boats, omnibuses, &c., by Government, to draw certain loads; and a statement giving that information should be placed conspicuously on the engine. This would prevent the overloading, as it would be in the power of every passenger to see whether the power of the engine was duly apportioned to the carriages it had to draw.

On the Failure of the Sluice in Fens, and on the Means of securing such Sluices against a similar Contingency. By W. THOROLD, M.I.Č.E.

The author described the circumstances attending the failure of the sluice, and

pointed out by a diagram that, in his opinion, the mode of preventing such an accident in future was the employment of double sluices, one behind the other, the water between the two being always kept locked in, at a mean height between the water in the drain and that on the sea-side, during the time the sea doors are closed by the tide; by this mode, the pressure of the highest tide, on each set of doors, will be only one-fourth of that on the single set of doors, on the fallen sluice, at the time of the disaster. Hence its undoubted safety.

On the Merits of Wooden and Iron Ships, with regard to cost of repairs and security for life. By L. WILLIAMSON.

The author called attention, in particular, to an iron ship, the 'Santiago,' which met with a collision, the consequences of which would have been absolute destruction of the vessel had she been of wood; whereas, being of iron and having watertight compartments, the vessel was able to pursue her voyage, and was repaired at the cost of a few hundred pounds, instead of several thousands which would have been necessary had she been made of wood and could have been preserved from foundering.

Oblate Projectiles with Cycloidal Rotation, contrasted with Cylindro-ogival Projectiles having Helical or Rifle Rotation. By R. W. WOOLLCOMBE. The object of this paper was further to discuss the views of the author given in a paper read before the Royal Society in March last (1862), entitled, "An Account of some Experiments with Excentric Oblate Bodies and Discs as Projectiles," and to show the result of further experiments. Rifled cannon, it appears, cannot project heavy elongated shot with high initial velocity; and, except with the Whitworth flat-headed shot, the penetration of iron plates can only be effected by means of a high velocity. The author considers that however well the helical or rifle method with cylindrical elongated shot may answer for small arms, yet that, when we wish to project great weights with great and sustained velocities, we shall succeed better if our mechanical arrangements are less antagonistic than the rifle principle to the great laws of nature, as exhibited in the form, method of rotation, and translation of the great natural projectiles, the planets. None of these are prolate bodies projected with helical rotation about their longest diameters and in the direction of such axis. The author states that he has found it practicable to project a body that, instead of being prolate, is more or less oblate,-that, instead of having helical rotation at the expense of translation, has cycloidal rotation in aid of translation. A projectile, having a circular periphery in the line of motion in the gun, leaves the bore as a common round shot, and has the additional security for high initial velocity of windage less than for round shot of similar weight. The terminal velocity is also provided for by the oblateness, and by the axis of rotation being always transverse to, and not in the plane of, the trajectory. The gun has a similar transverse section to that of the projectile, the bore being straight and smooth. The projectile is a disk, and it should be slightly excentric to make it rotate-so slight as to be little more than the inevitable excentricity of every spherical projectile. The author then gave the results of some actual experiments with a gun and projectiles made on this principle. The gun was 20 inches long; the calibre, long diameter 13 inch, and short diameter inch. The shot weighed nearly 8 ounces, with a charge of 24 ounces, or three-fifths the weight of the shot; the penetration at 25 yards from an oak target was a mean of 11 inches, reckoning to the near side of the disk, and to the far side nearly 18 inches.

The initial velocity, measured by Havez's electro-ballistic apparatus, was 1487 feet per second. A comparison was made with a small brass gun, length of bore 34.625 inches, or nearly double the length of the author's gun in calibres. The mean calibre of the brass gun was 16 inch, the mean diameter of the round shot was 1:43 inch; and this gun, fired with a proportionate charge of powder, showed that the disk gun gave more than double the penetration of the brass gun, and an initial velocity of 1487 to 1091 of the latter. He thought that these remarkable experiments showed that the subject was worthy of further consideration.

APPENDIX.

On the Solution of the Linear Equation of Finite Differences in its most General Form. By Prof. SYLVESTER, F.R.S.

The author exhibited (and illustrated with examples) a simple and readily ap plied method of obtaining the general term (and consequently the complete solution) of an equation of finite differences with any number of independent variables, a question which, although touched upon by Libri and laboriously investigated by Binet, had hitherto, to the best of his knowledge, remained unsolved even in the case of an equation with but one independent variable with non-constant coefficients: when the coefficients are supposed constant, the well-known solution flows as an immediate corollary from the author's general form. Essentially the method depends upon the adoption of a natural principle of notation for the given coefcients, according to which each coefficient is to be denoted by a ticofold group of indices, the number of the double indices in a group being equal to the num ber of independent variables in the given equation. Thus, supposing us, m. p... lê be expressible by means of the given general equation, as a sum of u's with infe rior indices, the coefficient of u U u, v, π in that sum must be denoted by the double index group m, n, P...]. The process for obtaining the general term in

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... is then shown to be reducible virtually to the problem of effecting the simulta neous decomposition of the integer variables x, y, z... into parts in every possible manner and order of relative arrangement, the magnitudes of such parts being limited by the degree or degrees of the given equation in respect of these variables. The collective value of the terms thus obtained constituting the complete solution may be termed, in the author's nomenclature, a hyper-cumulant, whose properties and their applications remain to be studied out as those of the elementary kinds of common_cumulants have been to a considerable extent in the ordinary theory of continued fractions. The first stage in the process of constructing the terms of a general cumulant or general hyper-cumulant is almost identical with that of finding the coefficients in the expansion of a power of a polynomial function of one or several variables, differing from it indeed only in the circumstance that permutations which lead to repetitions in the latter case, represent distinct values in the former.

On Aërolites. By Professor N. S. MASKELYNE.

Professor Maskelyne prefaced a series of notices of meteorites lately added to the collection in the British Museum by some observations on the phenomena that accompany the fall of such bodies to the earth. Loud reports and the development of brilliant light in the sky are among the most generally observed of these phenomena. The fallen mass or its fragments, besides the marked characters they constantly present, as well in composition as in the mode of aggregation of their component minerals, exhibit also invariably a superficial enamelling or incrustation. The meteorite which fell at Butsura, in India, on May 12, 1861, accompanied by successive reports and a luminosity in the sky visible in the daytime, presented some new and very interesting facts bearing on the cause of this incrustation. The whole of the fragments found, though they fell in four places, at distances of three or four miles apart, formed the parts of a large piece of an aerolite, fitting to one another with great exactness, with the exception of two of them, between which an intermediate fragment had been lost. Some of the fragments were found to be entirely coated with crust, yet capable of being adjusted to each other with unmistakeable accuracy; others again exhibited no such incrustation at the parts where they fitted to each other, and were yet, like the former, found several miles asunder. It was obvious from this that some of these fragments had become coated with crust after they had been severed, while others had been so severed without becoming subsequently incrusted.

That the incrustation was the result of superficial fusion seems the best explanation of its presence on the meteorite, as well as of the partiality with which it was distributed. Such a superficial fusion, however, could only result from the development of heat of enormous temperature very instantaneously; and the best if not

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