284 SOLUTIONS OF ALGEBRAIC QUESTIONS in regard to these ancient time-marks; but the defence is incomplete, for in the list of Saints' days omitted, because their commemoration does not in the least degree influence the proceedings of the present time, there are several which do influence" the proceedings of the present time" most decidedly, inasmuch as they regulate the holding of Fairs, where people assemble in hundreds and thousands to traffic in rural commodities. Is it to be characteristic of The British Almanac to supply information which is useful only to lawyers and landlords, and withhold equally useful information from the honest yeomanry of the country? There is also the promised article on the tides by J. W. L (ubbock) Esq., F. R. and L. S. which more than confirms all that we advanced in our review of the almanac in regard to the author's fitness for the task he has undertaken. It is as elaborate a piece of mathematical priggism as ever came under our critical notice; composed of English not always intelligible, Latin scraps quoted for mere parade, and the signs and symbols instead of any of the body and substance of scientific talent. We hope to be able in the course of a week or two to unravel this web of absurdity. Meanwhile we may observe, that from an authoritative paper to which a Member of the Committee of Superintendence subscribes his name, we learn, 1st. That the tide-table of servations are decidedly and essentially inaccurate, being scarcely ever to be re lied upon within ten or fifteen minutes! Bravo!! Mr. Lubbock, Fellow of the Tide Royal and Linnæan Societies, de Dif computer to the "Society for fusion of Useful Knowledge Better far it would have been had your brother superintendents trusted to the virtue of the "guinea-fee," and preferred a mathematical-usher, with his grey stockings, to all the Lubbocks of Lombard street. SOLUTIONS OF MR. MACKINNON'S ALGEBRAIC QUESTIONS, PROPOSED IN NO. 294. Question First: filiw By Mr. Mathew Forster, Pupil at Mansion- House School, Hammersmith. Given r+y+y2=52, and xy+ =8. From the 2nd equation we have 2 + 8 Agupid -.. by substitution the 1st equation becomes x+x+8+ y +16x+64 =52. Clearing of x2 fractions, &c. 3-28x+640, and this equation by decomposition becomes (x-4) (3x-16)=0.4, 2; also 3a2=16..=£ and 4 = 4 33: hence y 10 Question Second. +8 The British Almanac" for 1830, does not relate to London Bridge, as has been usual, but to the London Docks. 2nd. That the Society are in great dudgeon (p. 26) because the computers of tide-tables withhold the secret of their art from their generous rivals-rivals +6, or 3. who first pirated the calculations of these computers, and then pretended that there was nothing in them worth spirating! 3rd. (p. 36) That the times of high-water given in "The British Almanac" for 1829, are all wrong; though the encomiasts of the Society persisted in affirming in every newspaper and publication to which they could get access, that they were right. 4th. (p. 59) That the times of high-water in "The British Almanac" for 1830, are computed from inadequate data, (which is exactly what we asserted before this Companion" appeared,) and that (p. 62) the Society cannot vouch for their accuracy. And, 5th. That the results obtained present a very remarkable coincidence between theory and observation" (p. 64); but that, nevertheless, (p. 62) ALL the ob By Mr. Thomas Hughes, Pupil at the above School. The ingenious proposer of the three preceding problems requires that they shall be solved by simple equations, although they are all evidently of the biquadratic form. Had no such con'ditions been imposed, they might have been all solved by quadratics. The method of solving the two first in that way is perfectly obvious from this, that the final equations 3x4-28 x2+ 640, and 47x4—4504x2-19600=0. The third question, which is a little more difficult, may be solved as folHlows: & Since x4-2x3+x=132; add to both sides of the equation .. x4-2x3 Extracting the square 2 root x2 + 2. 529 11. Completing the square x2-x+ root 7 7 or43. 285 In poser, that this demonstration has been intended for young beginners, my humble opinion, such an exercise is quite sufficient to puzzle many who may be styled even veterans in the mathematics." There must be some truth, we suspect, in this remark; for though the question has been now three months before our readers, have received but one answer to itfrom Mr. J. Gilbert, jun. That answer, however, is very elaborate-and correct; and but for its great length, we should at once lay it before our readers. It seems to us that it may, without difficulty, be brought within the limits of half a page; and if Mr. Gilbert will favour us with such an abridgment of it, we shall gladly give it a place. 1 ON THE PROMOTION OF COMBUSTION BY FORCING AIR THROUGH FIRE, AND THE ECONOMICAL APPLICATION OF THE HEAT THUS PRODUCED TO THE GENERATION OF STEAM BY MR. WILLIAM GILMAN, CIVIL ENGINEER. (Concluded from our last Number, p. 261.)′′ The preceding plans and their modifications open a wide field for ingenious, useful, and valuable appropriations of the heat that has hitherto been almost entirely neglected. Of sóme which have been actually carried into effect, I will proceed to give an account; but I must first observe, that as the plans are applicable to all high-pressure engines, whether worked by pure vapour or by the compound elastic fluid, after such steam or fluid has performed its office in an engine, it may be applied most advantageously to the purposes of heating, drying, &c. This I have put in practice at an extensive papermill, drawing and card-board manufactory, a short distance from London, where the steam from the eductionpipe of a ten-horse engine that I lately erected on the premises, is delivered by an appropriate apparatus to the steam-pipes, which convey it to the work-rooms and drying-lofts, containing many hundred feet surface of pipes, most of them in detached buildings, and at considerable distance from the engine. The steam is also successfully, T ±or ±√43 = 4 or −3 or 4 THE ALGEBRAIC EXERCISE, NO. 316, A mathematical friend writes to us of this Exercise in these terms: "I could scarcely refrain a smile at the enunciation of A, the ingenious pro 97 286 PROMOTION OF COMBUSTION BY FORCed air. applied to boil the paste at upwards of one hundred feet distance, to heating the stuff in the vats, the cylinders of the paper-drying machine, &c.; all this is performed, and the pressure of the steam regulated to the greatest nicety, at a loss of less than one-tenth of the power of the engine. Hence at this small cost the whole of the steam passing through the engine, or, in other words, steam equal to the power of ten horses, is rendered available to such purposes as those abovementioned. The resistance indeed of the steam to the action of the engine, when thus applied, seems to be less than what, by calculating the difference between the pressure of the steam in the pipes and that of the atmosphere, the engine really ought to feel. The circumstance may be accounted for thus:-the steam issuing from the eduction-pipe is resisted by the air in a greater degree than the mere atmospheric weight, on account of the velocity with which it makes its exit; but the steam, though it may be a few pounds above atmospheric pressure, being subject to continual condensation throughout the whole length of pipes, cylinders, &c. a regular flow is consequently the result, Hence the resistance of the steam to the piston is comparatively less than when exposed to atmospheric resistance; and it may be a question whether if, were it not for the unavoidable number of elbows in the pipes, and the steam being much wiredrawn in some places, through inch and three-quarter inch gas pipes and cocks fixed in the buildings many years ago, the resistance would not be so much less, that steam of three pounds above atmospheric pressure would scarcely be felt, if at all, by the engine. And when it is considered that the resistance of the steam so appropriated causes no additional stress on the working gear of the engine, but that such stress is wholly confined to the two sides of the piston, it will readily be perceived that there is no difficulty in applying the plan to any existing high-pressure engine for the purpose of effecting the same objects, or for boiling water, or any of the like purposes. Any small loss of power by such appropriation, is of course easily made up by generating the steam in the boiler at a few pounds per inch higher. I will now proceed to the manner of appropriating the heat arrested at the termination of the flues in the several modifications. The elastic. fluid generated in the separate vessel of water into which the products of combustion are directly forced, as described in the first modification, may be applied to the greatest advantage to work the blowing-apparatus, independent of the engine, as this will carry on combustion and keep up the steam during any temporary stoppage of the engine. In this case, however, there ought to be such a length of flue intervening between the generator and water-vessel as would take up all but a sufficiency of heat to generate a fluid of adequate power to work such apparatus; and the fluid when it has performed its office may be applied to heating and other useful purposes in the manner abovedescribed. By this arrangement pure. condensible steam is procured, from which the utmost profit steam can give may be obtained by using it expansively in a high-pressure condensing-engine of one steam cylinder. Of the second modification I scarcely need observe, that it is capable, like the above, of generating either high or low condensible steam; and the vapour and heated air arising from the water in which the flue terminates is also capable of being ap propriated to most of the purposes of heating, drying, &c., to which the steam from the eduction-pipe of an engine is applicable at low pressures, if circumstances require. The first modification, by the supposed additional intervening flue between the generator and vessel of water, may be considered to merge into the second modification; but the form as first described, and referred to in the drawings, is the form in which it was used. What has been said of the capabilities of the second applies likewise in a great measure to the last modification; for though the creating a partial vacuum over the surface of the water in which the flue terminates neces sarily causes the compound fluid rising PROMOTION OF COMBUSTION BY FORCED AIR. therefrom to be of an elasticity inferior to that of the atmosphere, yet with the assistance of the exhaustingapparatus it may be rendered applicable to most of the above-described purposes. The value of the heat obtained from the steam after passing through the engine, and the elastic fluid at the termination of the generator or boilerflue, must depend of course entirely on the necessities of the establishment in which the engine is erected; but without taking this at all into account, I think it will be manifest that the several plans are capable of generating power with the smallest quantity of fuel possible, and possess the pre-eminent quality of destroying the smoke and rendering a chimney totally unnecessary. The mode adopted in the last modification of obtaining a draught by an exhausting-apparatus, is particularly adapted to the purpose of destroying the smoke of existing furnaces where there is an engine by which the apparatus can be kept in action; and as I believe it to be entirely free from the objections to which most of the plans hitherto proposed for effecting so desirable an object is liable, it merits the particular attention of the proprietors of the numerous establishments, especially in London and other large towns, whose immense volumes of smoke render them at present a nuisance to the whole neighbourhood in which they are situated. Yours, &c. WILLIAM GILMAN. 7, Ratcliffe-highway. P. S.-I perceive I have omitted to state, that it is not absolutely necessary that the exhausting apparatus should be placed immediately over the surface of the water, as described in the last modification, as such apparatus may be fixed under the enginebeam, and worked thereby, or by a crank in any other convenient situation, and connected to the chamber above the water-surface by a suctionpipe also, that if the heated water, in which either of the flues terminates, is required for any purpose for which it is not fitted by reason of its impurity through its retention of the carbonacious matter, such impurity may 2870 be in a great measure remedied, by causing the vapour and gases rising from its surface to flow into a second vessel, in like manner to that of the first; which water may be used for feeding the boiler, and many other purposes. The loss of heat, by using the second vessel, will be insignifi cant. [We mentioned generally last week the obvious similarity between Mr. Gilman's plans and those of Messrs. Braithwaite and Ericsson. This similarity is not confined to the plan of gaining heat by means of forced air, but extends also to the mode of producing a draught or current of air by means of an air-exhausting apparatus at the end of the furnace-flue. In the specification of Messrs. Braithwaite and Ericsson's patent, it is stated that their invention "consists in generating steam in a boiler, wherein the capacity of the flue is too small to allow a sufficient quantity of heated air to pass through in a given time by the mere agency of what is commonly. called atmospheric draught, and to which flue therefore we attach either an air-forcing apparatus at the furnace end, (as in "The Novelty,") or an airexhausting apparatus at the other end of the flue, in order by these mechanical means to compel the required quantity of heated air to pass throngh the flue in a given time." With whom the merit of priority lies we do. not presume to say, and have not, in truth, the means before us of determining; for though Messrs. Braithwaite and Ericsson's patent is, we believe, of a more recent date than the invention described by Mr. Gilman, it is not always from the date of a patent that the date of the discovery included in it, is to be inferred. Messrs. Braithwaite and Ericsson will probably favour us with some farther information on the subject.-EDIT. M. M.] MINOR CORRESPONDENCE. The Almanacs for 1830.-Sir, In the list of the magistracy of London, given in "The British Almanac," page 46, after the "Recorder, Newman Knowlys, Esq.," there appears the "Common Sergeant, T. Denman, Esq." I believe this is the first time the Common Sergeant has been included in such a list; but as be sometimes acts magisterially, I am not disposed to: 288 MISCELLANEOUS NOTICES. question the propriety of the addition. If it is, however, right to include the Common Sergeant, on this account would it not have been still zmore so to include the Deputy Recorder, Mr. Sergeant Arabin? And what good reason can the compilers of "The British" assign for giving the one a place and excluding the other? Surely it cannot be because Mr. Common Sergeant happens to be a member of the Committee of Superintendence, under whose auspices this almanac is issued to the world; or because Mr. Sergeant Arabin happens to be the rival of Mr. Denman for the reversion of the Recordership! I wait for a reply. I am, &c. CIVIS Ward of Farringdon Within, Dec. 2, 1829. [The suppression of Mr. Sergeant Arabin's name is certainly very indecorous; but we must stafe at once our firm conviction, that neither the Common Sergeant nor the Committee of which he is a member have had any thing what ever to do with it. Mr. Denman, in particular, is by far too high-minded and honourable a man to countenance so underhand a method of keeping a rival's pretensions out of public view: it is evidently the device of some tool, who thinks by this means to curry favour with his employers. EDIT. M.-M.] Almanacs for 1830.-Sir, Relying on your as sertion that the Englishman “contains at least one-third more matter than the British," I re, solved that the Englishman should be my almanac for the ensuing year; but after purchasing a copy, I was surprised to read in a critical notice of both almanacs, which appeared in that respectable journal, The Times, that the " arrange. ment" of the British is fully better than the other, and its articles of information "more numerous." I immediately concluded (will you pardon me?) that you had given a false character of your favourite;" but to make sure how the fact stood, I put it in my pocket, and called on friend who takes in the Britisk, and every thing published by the Useful Knowledge So, ciety, in order to make a fair comparison of the one with the other. We have accordingly gone through them page by page, and the result, which it is but fair you should be made acquainted with, is briefly this:-The number of distinct "articles of information" in the British is eighty five; in the Englishman-two hundred and seven!!! The Times has no doubt been imposed upon by the artful manner in which the table of contents in the British has been drawn up. The Calendar, for example, which passes for one article in the Englishman (as it ought), is there split into twelve! Sir, your constant reader, I am, PETER PARTICULAR. the Tradesman's and Mechanic's Almanac there is a notice of that excellent establishment the National Repository, the merits of which are thus abruptly disposed of:-" This would have been an admirable institution for the commence. ment of the eighteenth century!" The writer might at least have favoured his readers with a reason for this presumptuous assertion. I am, &c. L. U. T. [The writer of the notice in the Traderman is quite correct. The Repository is, at the very feast, a hundred years too late.-EDIT. M. M.) Jackson's Studs for Boots and Shoes.-" Wm. Kingsnorth, of 31, Smith-street, Northamptonsquare, Carpenter," desires to corroborate by his testimony the great durability and economy of shoes provided with these studs, which he pro. nounces from experience to be greatly superior to either metal heels, nails, or sparables. We know Mr. Kingsnorth to be an old and respect. able member of his craft, and attach great. weight to his recommendation, INTERIM NOTICES. -Ingenious but Poor." The mode and ex pense of taking out a patent for a medicine are the same as for any thing else, Next Session of Parliament will probably decide whether there is to be any reform in either respect. Mr., Steele promises to send us shortly a letter ou a subject which he justly describes as one of "great general importance, not merely to Great Britain and Ireland, but to every country in Europe that sends ships on the Atlantic towards the United States of America, as well as to the American States: themselves" namely, "the formation of an ASYLUM HARBOUR at Carrickaholt, near the mouth of the Shannon."It is inatter of notoriety that a great many ships are lost annually for the want of such a port of refuge. We overlooked the concluding part of Mr. Hopwood's last letter till it was too late to do as be directed. The series of papers offered by Brackstone will be acceptable. ,,:་ T. F. M. deserves great praise. We shall give his letter and the explanations he requests in an early number. We presume that Mr. Murdoch and Mr. HopWood will agree with us in thinking that the letters, inserted in our 329th Number, from Mr. Gilman and R. C. jun., render any farther exposition of the fallacy of the plan for a Selfacting Railway Carriage unnecessary Communications received from Mr. Thomas Davy-A. B.-J. R.-Caleb Mainspring-Investigator-Mr. W. Rickett-C. B-J. P. W. -Mr. Day-James C-EW. G.--Mr. Badde ley-G. F. S.-Mr. Hebert. Errata. In the description of the coachmakers' klam, vol. xi. p. 328, the bow is described as 5 feet 8 inches; it should have been of an inch. P. 205, col. 1, 1. 8, for Ba," read" BE." 7, 1. 9 and 10, for 602" read " DCs." SP. 258, col. 2, 1. 38, for "experiment," read "expedient." P. 260, col. 1. 1. 19, for "the nitrogen thus charged with heat," read" the heat thus ab. sorbed by the nitrogen." |