well known, we dare say, to many of our readers by the name of the "Pekin parasol." It is one of a class of articles which exemplify very strikingly the beneficial operation of the recent Act for the protection of new designs. The amount of inventive ingenuity displayed in it is not great, consisting simply in bending down by heat the ends A A of the whalebone ribs, whereby a greater degree of shade is obtained, and the article rendered much more elegant in its general form and configuration. And though, it is perhaps the handsomest thing of the sort which has yet appeared, it is very certainly destined to be supplanted ere long (in the same way as it is about supplanting its Chinese precursor) by some newer novelty-so essential is novelty, above all things, to the goddess of fashion-so insatiable her demands-so absolute her decrees. But novelty is a real want of society as it is, which must be supplied in some way or other; the supplying of it, no matter how slight may be the differences or variations on which it turns, gives employment and bread to thousands; and if we cannot manufacture novelty enough of our own to meet the home demand, we must go abroad to make up the deficiency. Now the best stimulant to native ingenuity is, undoubtedly, protection, and that protection it has never, until the recent acts we speak of, enjoyed in more than a very limited degree. Five years ago such an article as this Windsor parasol could not have been protected at all, except at the prohibitory price of letters patent, (for who would patent for fourteen years, a thing which could last but for a season or two?) and were the state of things now as it was then, it is almost certain that we should have had no such home invention as this to notice in our pages. We should, in all probability, have left the trouble of invention, as of old, to our French neighbours, and contented ourselves with such profits as we could gleanfrom the retailing of their inventions. But as it is, the invention and the manufacture are alike of home production; and trivial though the design may be which has called forth these remarks, it is one which, besides amply rewarding the proprietor of it, will set hundreds of people to work, who would otherwise have been idle, and, but too probably, a prey to want and misery. HOT WATER CIRCULATOR-SUITABLE FOR HORTICULTURAL, DOMESTIC, AND OTHER PURPOSES-BENJAMIN FOWLER, OF DORSET-STREET, SALISBURY-SQUARE, IRON FOUNDER, PROPRIETOR. [Registered under the Act for the Protection of Articles of Utility.] 66 to a thorough practical acquaintance with his subject far more philosophy than falls commonly to the lot of the class of practical men." In this pamphlet Mr. Fowler condemns-very justly, in our opinion-all the hot air and steam modes of heating, as applied to domestic and gardening purposes, and gives the following cogent reasons for preferring the hot water system : "If we follow, in the system of artificial heat, the plan which nature universally adopts, we shall endeavour to obtain an equality of heat by radiation from a large surface at a low temperature; for we have already seen, that heat radiated at a high temperature is positively injurious to animal life, by altering the chemical properties of the air. The plan which appears to obviate all objections most completely, is that of diffusing heat by means of hot water, circulating through large iron pipes; a plan so simple and efficient, that whatever improvements may be made upon it in the course of time, will not, in all probability, in any way affect its principles, but only apply to its universality of adaptation. To describe here the position of the pipes and boiler of this kind of apparatus would be impossible, as their arrangement is nearly as various as the situations to which they are applied; suffice it to say, the pipes and boilers communicate so as to afford a continued stream of hot water from the boiler to the pipes, which give off, by radiation, the heat they thus receive; the water then returns to the boiler by another pipe, to receive a fresh supply of heat, again to part with it as before. The circulation of the water in these pipes is much more rapid than would be it will travel through a length of imagined; two or three hundred feet, in five or six minutes; the cause of this action and rapid flow being nothing more than the different specific gravities of hot and cold water. "The distinguishing feature of this description of apparatus is, that it has, at some point or other, a free communication with the atmosphere; and as the temperature of the water cannot rise above 212° while this communication continues, the apparatus must always be perfectly free from any accumulation of steam; and there is, therefore no pressure upon it, except the actual height of the water, equal to lb. per square inch for every foot of perpendicular height. "The principal advantages of this invention-leaving out of the question its economy in fuel, though even in this particular its claims to recommendation are not inconsiderable-are, first, the amount of moisture in the air is neither increased nor diminished by its use; secondly, there is no deleterious gas of any kind generated; thirdly, the vital quality of the air is not the least deteriorated, or its chemical properties at all changed, the radiating surface being of too low a temperature to produce such effects; and, lastly, its perfect safety. "These are not unimportant advantages when the apparatus is employed to warm dwelling-houses; and where it is used for conservatories, and other horticultural purposes, it possesses peculiar claims to recommendation for its perfect equality of temperature, and for maintaining the heat an infinitely longer time than any other plan. To these likewise may be added another decided advantage, the great durability of this apparatus in comparison with others; for the large quantity of water which is employed, prevents the boiler ever approaching to a temperature which can injure it; and for horticultural purposes, the exemption from accident of the apparatus employed, is particularly important,-because the stoppage of its efficient working even for a single day, might cause the destruction of every plant in the building. This consequence appears almost inevitable, when any accident occurs to pipes worked on the high pressure plan; for not only would the plants suffer by the non-performance of the apparatus, but such is the expansive force of steam at a high pressure, that the smallest fissure happening in the pipes would instantly be followed by the rending asunder the whole of that part of the apparatus; the escape of steam completely destroying the plants, and not improbably the building also, by its uncontrollable violence." Mr. Fowler's present improvement in the hot water system consists, firstly, in dispensing with the circular pipes and brick tanks hitherto employed for the purpose, and substituting for them large channels of square, angular, and other forms, which present a much larger degree of heating surface than can be obtained by any other means; and secondly, in making provision, in the case of horticultural hot water circulators, for the occasional application of the vapour arising from the water to promote the growth of the plants. Fig. 1 is a sectional elevation of this new hot water circulator, as applied to a forcing house. It is made throughout of cast iron. A is the brick basement on which it stands; B B are the sides; C1 C2 C3 C4 C5 are five hollow ridges, three of a pyramidal, and two of an oblong form, LOSS OF THE IRON STEAMER which extend from end to end of the apparatus. The centre ridge C3 rises to the height of the cover, but the four others little more than half-way. The cover D is made of the indented or vandyke form, represented in the figure, or it may be made of any other analogous form, presenting an alternation of projecting and hollow points; the apex of the centre incut or recess resting upon the top of the centre ridge C3, and the peaks of the under side projecting as far downwards as the tops of the four lower ridges, C1 C2 C4 C5. All the five ridges are open at the bottom and ends. The spaces between these ridges, and between the outermost of them and the sides B B, as also the spaces immediately above them, between the lower peaks of the top plate, and between the outermost of these peaks, and the sides, as far up as the line ab, form the channels or passages through which the water circulates. The centre ridge C separates these passages into two distinct divisions or series, which are closed at each end. The water is conveyed by pipes from the boiler into one of these divisions, after traversing which it flows round through a curved pipe at the farther end into the other division, whence it is returned by pipes into the boiler. The spaces at top, above the line a b, are left vacant for the reception of the vapour arising from the hot water, and this vapour, when wanted for promoting the growth of plants, or any other useful purpose, may be let off from either side of the centre ridge by lifting vapourtight trap-doors of the construction separately represented in the plan and section figs. 2 and 3, and fixed at any convenient places in the top of the plate D, one on each side of the centre. The space between the cover D, and the top cd of the apparatus, may be either filled up with sand, as represented in fig. 1, on which potted plants, requiring to be forced, may be placed; or it may be filled with water for the purpose of evaporation; or it may be left open in order to give off heat to the surrounding atmosphere. Instead of the ridges being partly of a pyramidal and partly of an oblong form, they may all of them be of either of these forms; or instead of three of them being of the pyramidal, and two of the oblong form, the numbers of each sort be reversed, or otherwise varied at may pleasure. [We extract the following interesting particular of the loss of the Elberfeldt Iron Steamer, from an account of the disaster furnished to the Times by a writer who states that he derived his information from Captain Stranach of the General Steam Navigation Company, who commanded the vessel, and Mr. Bush the engineer, who was a passenger. The fate of this vessel may serve to teach certain railers against the Committee of Lloyds for the cautious course that they have pursued in regard to iron shipping, that the Committee were not so far wrong as has been alleged, when they insisted that evidence was wanting of iron ships being as safe as timber ones, under all sea-going circumstances. The question naturally suggests itself-Would any timber vessel have split so suddenly in two as the iron Elberfeldt? We think he would be a bold man who would give an answer in the affirmative. The case of the Elberfeldt is one which is evidently not met by the division of the vessel by bulk heads into different water-tight compartments. The great weight of the machinery amidships must have been the proximate cause of the calamity.] On "The Elberfeldt, under the command of Captain Stranach, sailed from the Brielle on the 22nd inst., at 50 minutes past 6 o'clock a.m., under light and variable winds. nearing the English coast, Mr. Bush remarked to Captain Stranach that the ship's working appeared to be different from when they left Brielle, and that there was a strong vibration of the vessel. Scarcely had these remarks been made when the suspicions of Mr. Bush were but too truly confirmed; he begged of Captain Stranach to order the boat to be in readiness, for he was convinced that the vessel, being constructed of iron, would afford but a few minutes to save themselves. Whilst this conversation was taking place an indication of a plain nature gave warning that their fears were well grounded; for about 10 minutes to 3 o'clock p.m. she broke completely in half in the middle. Mr. Bush rushed up-stairs ex-. claiming, "It is now all over, stop the engines and out boat," and himself and two others fell headlong into the boat at the moment she was launched; the wind at this time was blowing a brisk gale. Mr. Bush then took the rudder of the boat and kept her head to wind as she was rowed stern foremost towards the vessel to save the remainder of the crew, and to which nautical manoeuvre may be attributed the saving of those who were still upon the deck of the ill-fated vessel. The crew of the boat called out to Captain Stranach, who was on the after-part of the wreck, to save himself by springing with an oar into the sea, as her head and stern were collapsing. This was a dreadful moment to all: the wreck presented a most awful, yet grand spectacle ; the boiler, bursting by the collapse, threw up immense volumes of steam and fountains of water, and the vessel went down with a loud explosion. After her going down Mr. Bush looked around for the unfortunate crew, and one of the first he saw was Captain Stranach, struggling in the water, supported by a portion of the wreck. The captain and several others were with much difficulty taken into the boat. Three persons were unfortunately lost-two stokers was 13, including Mr. Bush and Captain Stranach, who, after experiencing the greatest hardships for hours in an open boat, were picked up by the Charlotte, Captain Moyes, who humanely supplied them with dry clothes, coffee, soup, &c. Captain Stranach and Mr. Bush described the whole occurrence as a dream, for from her breaking to her going down not more than five minutes elapsed; and what but a short time before was considered a beautiful model of naval architecture was sunk irrecoverably in the ocean." ON THE NUMERICAL SOLUTION OF EQUATIONS.-PART I. Sir,-Enquiries have been frequent in your pages as to an easier method of extracting the cube root than the usual cumbrous and almost impracticable process. These enquiries have received a certain share of attention, but little of practical value has been elicited. Now there exists a method by which not only the square and cube roots, but also roots of all dimensions whatsoever, may be extracted by means of a perfectly simple and purely arithmetical process. I conceive, therefore, I shall be rendering an essential service to many of your readers by placing within their reach, through the medium of your pages, such a powerful instrument of calculation, which is not as yet nearly so well-known as it deserves to be. The extraction of roots, in the ordinary sense of the term, is but a particular application of the method to which I refer. It is equally applicable to the numerical solution of equations of all orders; and it will conduce to perspicuity if I present it first, in this, its more general form.* I premise a few definitions. * The elements of the method have been known for 200 years; but it is to the late Mr. Horner, of Bath, that we owe the improvement by which it has been rendered practically useful; and it has accordingly received the name of "Horner's Method." A full and interesting history of the problem, from the lucid pen of Professor De Morgan will be found in the Companion to the Almanac for 1839. And I may add here that all the knowledge of the method I possess is derived from the article INVOLUTION AND EVOLUTION, by the same writer, in the Penny Cyclopædia. To that article I would refer such as wish for a more profound view of the subject than can, for various and sufficiently obvious reasons, be here attempted. P.S. Since the above note was written I have 1. An equation is designated as to order, degree, or dimension, according to the highest power of the unknown quantity which enters it.. Thus, equations in which x, x2, x3, &c., are the highest powers, are called equations of the 1st, 2nd, 3rd, &c., degrees, respectively. Equations of the first four degrees receive also the distinctive appellations of simple, quadratic, cubic, and biquadratic equations, respectively. 2. An equation that contains all the integral powers of x, from the highest that enters it down to ao, is called a complete equation of the order to which it belongs; but if any of the powers of are wanting, the equation is said to be incomplete. Thus, x+− 2 x3+4x2-2x+8=0, = is a complete equation of the 4th degree, since, a being always 1, the last term is 8 xo; and 2 x3-3x+7=0 is an incomplete cubic equation. In the application of Horner's method of solution, incomplete equations must be rendered complete, which is done by supplying the missing powers, with zero for their co-efficient. Hence, for this purpose the last equation would be written, 2 x3+0x2 −3x+7=0. 3. Any number which satisfies an equation, that is, which, when substituted in that equation for the unknown quantity, renders the left-hand member 0, is called a root of the equation. Thus, 5 is a root of the quadratic, x2+2x-35=0, and-7 is another. = read Mr. Horner's paper, which is reprinted, from the Phil. Trans., in the Ladies' Diary for 1838. It contains an excellent synthetic view of the method; but it will be found much less generally intelligible than the article above cited. |