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- SEPTENARY SYSTEM.

ment the rod B represents one of the assymptotes of the intended hyperbola, and the rod A is always parallel to the other.

The slide h moves along the rod A, and at the same time allows the flat bar G to move freely round the socket f, in which is placed the tracer.

Now, if motion be given to the bar G by the handle L, the tracer at f will describe the hyperbolic curve QWT.

It may not be improper to remark, that any other point in the bar G, except that where the tracer is fixed, describes a peculiar kind of curve, whose properties it may afford the mathematical reader a little pleasure in investigating.

The rod C is more essentially necessary when hyperbolas are drawn by this instrument under a different arrangement of its parts, or when used for describing other curves.

SEPTENARY SYSTEM.

Sir,-At p. 351, vol. x. I alluded to a case of motion in the septenary system, by which lines with a single cusp, resembling the cardioid, are described that case, I then stated had the line or locus of the cusps an ellipse. This intimation having exercised the ingenuity of Mr. R. C. jun. when he recently favoured me with a call, he inquired if it was to the rolling of an elliptical wheel upon another equal and similar to it that I had referred? Having stated that the primary principles of the septenary system are confined to the pole, the right line and the circle, I of course told him it was not by elliptic wheels that the motion, which I considered remarkable, was produced. Having, however, explained to him the case of double-crank motion, to which my mind had been directed, it immediately appeared that the motion of a surface was thus regulated in exactly the same way as it would be if attached to an elliptical wheel rolling around another equal and similar to it. These cases of harmony, which I had not anticipated, will, I trust, greatly facilitate a knowledge of the nature of the curves of the first division; some of which are now evi

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Let AB, AC, BD, and CD, (fig. 1.) be four pieces of wood, metal, or any other material, (the opposite sides being equal) connected together and moving freely on pins or centres at the angles. If the piece CD be fixed and the other three pieces be in motion, AB may be so moved that it will always be parallel to CD; but when AB comes to be in a right line with CD, the motion of it may be changed from parallel to angular, as in fig. 2. Fig. 2.

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fixed plane. From this diagram it will appear that the circumference of the ellipse or line of the cusps on the plane in motion continually coincides with the circumference of the ellipse or line of the cusps on the plane at rest; and that if elliptical wheels corresponding with these lines of the cusps are substituted for the four pieces, a plane attached to one, while it rolls against the other, will be regulated precisely in the same way as if attached to the bar AB, regulated by the two cranks AC and DB.

In fig 1, CD, one of the short

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Fig. 5.

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Here the continual intersections of DC and AB produced, will describe an hyperbola. The path of these intersections may be drawn either on a plane in motion attached to CA, or on a plane at rest, to which DB are fixed, and will be the line of the cusps in both cases. The circumferences of these hyperbolas on the two planes will always coincide; and if moulds be cut to the form, they may be substituted for the cranks, and will produce the same motion to a limited extent by rolling the one upon the other. But as the hyperbola is an ininite line, no mould, however extended, can contain the whole; therefore the whole of an hyperbolic epicycloid, although only a finite line, cannot be generated by hyperbolic

moulds, but it may be done by the double-cranks.

In former papers it has been stated that by double right-lined motion the same effect is produced as by the rolling of one circular wheel within another of a certain proportion; and we now see that by double circular motions the effects of cases both of elliptic and hyperbolic external epicycloidal motions are obtained.

As elliptical wheels are sometimes used in machinery, it may be worthy of consideration whether the cranks can be substituted with any advantage either for the wheels themselves or for rendering teeth in them unnecessary. If cranks are used, one elliptical wheel may be made to roll around another without teeth; but it

BREAKING INTO HOUSES ON FIRE.

may be perhaps necessary to have certain pins to prevent the cranks passing from the angular to the parallel motion.

I am, Sir, yours, &c.

JOSEPH JOPLING.

P. S. Since writing the above, some ideas have occurred which lead to the supposition that all the lines generated by the first division may be epicycloids of the lines of their

cusps.

BREAKING INTO HOUSES ON FIREBUILDING ACT.

Sir, I think Mr. Baddeley, jun. has taken, perhaps, a too hasty view of the notice I ventured to send of the practice of breaking open the lower part of a house as soon as it is discovered to be on fire.

Had Mr. B. not denied the motive which he appears to think I would lay to his charge for commenting upon my good intentions with such a spirit, I certainly should have supposed that manner could not have proceeded from the desire of preventing what he imagines now to be erroneous to pass unnoticed.

I say now, because Mr. B. at p. 309, vol. x. says, when a person in the street discovers a house on fire, "his first care should be to make its inmates and their neighbours aware of their danger. This being done, the alarm should be given to the nearest fire-engine station." Not a word about" breaking open the door." Nor could he with any propriety have introduced such a direction before either of the above.

Although Mr. B. has not spoken very respectfully of any of my plans, yet he has of my intentions. However, I find that one of them, which perhaps he overlooked, has found its way with some modification into the columns of "The Englishman's Almanac" for 1830. I allude to making a hole through the roof and ceiling of the attic (vol. ix. p. 68). In "The Englishman" this is stated to be " effectual method of escape," and "in the power of almost every description of persons." There it is stated that

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the inhabitant may, by getting upon a chair or table, &c., make these holes of escape for himself. The difficulties which may sometimes be met with are, however, greater than are there contemplated. When the roof is covered with slate boarding, it will require something more than "a bold thrust" to remove it: and the difficulty will be still greater, if a gutter or lead flat be in the way. Such holes of escape may of course be much sooner made by a person on the outside with proper tools; and this method ought not to be lost sight of.

I feel greatly obliged to Mr. B. for calling attention to my favourite plan to save life, when no other means of relief can be obtained; viz. "breaking a hole through the party-wall." The contemplated remodelling of the building-act offers an opportunity of rendering such a method legal, and if accompanied by an offer of reward, which Mr. B. has pointed out as an essential stimulus, would be every thing required; especially if the recommendation of Mr. Ainger and Mr. Elmes, that the upper part of partywalls may not be made unnecessarily thick, be attended to.

Such a method of escape is only required for upper rooms, where, of course, it must be obvious, that those holes about a foot square, would not have the same effect in fanning the flames in lower rooms as the breaking open the street door: which Mr. B. will not, I suppose, again find fault with me for objecting to, as the first step, if either the cry of fire, knocking at the door, or ringing the bell, will alarm the inhabitants, whose safety in every case ought to be the first consideration; and nothing, if possible to be avoided, ought to be done that will add to their danger.

Having alluded to the remodelling of the building-act, permit me to mention, that one of the gentlemen just named, considers that the rate of buildings ought not to be determined by the horizontal area, as is now the practice, but that it should be determined by the height. I think, however, that both ought to be taken into consideration; or, which is the same thing, either the inclined diagonal area of the loftiest story, or of all the

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reduced tithe to 24 per cent.-1-40-12; and triumphed."

"In the 479th year of the Hegira, and after the battle of Zaira, near Badajos, a coin of 12 dirhems was struck by Yousouf Ben-Taschfin, and was then adopted by sectarian Mahometans and several Christian states for a divisor. The see of Rome was so opposed to those Arabic divisions, that the Arabic cyphers were not generally employed throughout Europe until after the Reformation."

Here it may be asked, Why are the Chinese and the Japanese systems of reckoning conformable to St. Andrew's x, while the British is conformable to bad Mahometanism?

Dr. Lardner, as an historian, may say that Hindostan has been conquered from the Mahometans, for the inhabitants; but, as an arithmetician, he must acknowledge, that the inhabitants have not as yet discovered any difference between the bad Mahometan and the English system of reckoning.

When Mahomet declared the votolo of Mecca the standard weight of the faithful, he also declared, but most certainly not in the language of prophecy, that the relative value of silver to gold should be as 10 to 1; that is, the dinar, or dinero, for the tithe commutation of 20 dinars.

Christopher Columbus upset this relation; or, as the Chinese have it, the relation is all a tale. Just as our political journals have for the last three or four months been insisting that the United States make no more of 1000 Chinese cash than 6s. 8d.; though the United States reduced their system of reckoning one-sixth upon kicking the English, or Anglo-Mahometan system, out of every court of justice throughout the States.

The United States have acted right --because they have acted in obedience to the 25th chapter of Deuteronomy. In The Times of the 16th of May, a writer (" Americanus") exclaims, "How fortunate for unborn generations were the Duke of Wellington to assimilate the weights and measures of the world!" As a neighbouring people say (who, by the way, returned to the Christian standard in 1793)" Le premier pas se coute." This is the financial part for His Grace's history.

I am, Sir,

Your very obedient servant,
Dec. 11, 1829.

THE RAILWAY SYSTEM.

T.

Sir,-As your first, and consequently your oldest correspondent on railways (see Nos. 19 and 51 of your Magazine), I beg to transmit you the accompanying printed papers, and to solicit your particular attention to Circular No. 5.

These papers have been transmitted in all directions throughout the kingdom, and hundreds of them sent to Members of both Houses of Parliament.

Much speculative matter has been written upon friction or adhesion; and although it may appear very plausible in this early stage of the railway scheme, yet time, experience, and truth, will eventually show the errors of such writers.

I shall not now enlarge upon the subject, but only remark that had the good citizens seconded my petition to the Corporation of London, sent specially to Mr. Waithman in 1824, and inserted in the Morning Chronicles of

THE RAILWAY SYSTEM.

30th November, 1824, and Courier of 2nd Decemberthereafter,coal would have now been selling at 15s. per chaldron, instead of the present abominably high price.

But it is difficult to say, whether the Corporation of London or the inland proprietors of coal are most to blame. I remain, Sir, respectfully, Your obedient servant,

THOMAS GRAY, (the original projector of the railway scheme.)

Nottingham, Nov. 13, 1829.

P.S.-My work, "Observations on a General Iron Railway, &c., was published by Messrs. Baldwin, Cradock, and Joy, many years before any other individual had written a line upon the subject.

The papers transmitted to us by Mr. Gray, and the published work to which he refers in his postscript, establish very clearly the fact of his having laboured assiduously, as early at least as the years 1822 and 1823, to press on public attention the superiority of railways over turnpike-roads and canals, and the great gain to be derived from the substitution of steampower in lieu of horses.

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Mr. Gray's favourite project appears to have been the formation of Grand Trunk Railway" between London and Edinburgh, with branches extending to all the populous districts on both sides of the line. The numerous advantages likely to result from such a general railway are very well stated in the paper No. 3; but we have only room to give that part which serves to illustrate the paragraph in Mr. Gray's present letter respecting its favourable influence on the coal trade

"The coal annually consumed in London alone, amounts nearly to two million chaldrons; and there can be no doubt that were this article considerably reduced in price in the capital, that the consumption thereof would soon reach double this quantity. The collier averages, perhaps, a voyage in each month, and returns from London in ballast. The locomotive engine would impel a gang of coal waggons, carrying the full freight of a collier, from Newcastle to London in three days, and return with the waggons loaded for the different districts through which the railway might pass, making the whole journey from Newcastle to London and back again in one week, yielding annually the profits of fifty-two journeys in lieu of twelve voyages. The voyage by sea is about 500 miles, by the

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railway the distance will be reduced nearly to 200 miles."

The circular No. 5, to which Mr. Gray invites our particular attention, is of a recent date (August 1, 1829), and intended to show, first, that cograils are preferable to plain-rails; and, secondly, that neither a system of inclined planes with stationary engines, nor a series of reciprocating steam-engines, is half so good as a level railway with locomotive engines. We apprehend that the recent experiments on the Liverpool and Manchester railway-those particularly which we noticed in our last week's Number-must by this time have gone far to satisfy Mr.Gray, that on the first point he is much in error, and we shall therefore pass over for the present what he says in regard to it. The observations which he makes on the second matter in dispute have our entire concurrence, and we quote them with much pleasure

"I fear lest the public should be persuaded to follow the plans adopted in the collieries, by having recourse to inclined planes, stationary steam-engines, or the reciprocating steam-engine, all which may be useful in small private concerns, or where the coal-trade is the only business carried on; but, on railways for, national purposes, they should be avoided as much as possible, for this plain reason; the multiplicity of machinery-the consequent expense attending the annual waste of capital, and the accidents which would unavoidably occur from their general adoption on public lines of road, are quite sufficient to arrest the attention of companies in order to consider well before they commence laying down the rails.

"As there appears, however, a disposition to establish inclined planes, with stationary steamengines, rather than incur the expense of leveling the whole road in a direct line, it becomes my duty to offer a few more reinarks in opposition to this course, which would multiply the number of steam-engines in an excessive degree. It is my humble opinion that the number of engines likely to be required on the inclined planes would, if converted into locomotive engines, very shortly defray the expense of leveling the whole line of road in every direction. The question is not, what a stationary engine may do as an auxiliary, but how much more effective the power when employed as a locomotive engine? Moreover, the number of stationary engines required, should inclined planes be resorted to, would, if converted into locomotive engines, be sufficient for the commerce of the country.

"There will be other and more serious objections to inclined planes, besides those which present themselves on the first opening of these new communications between town and town; for, as the system becomes general, it will be found that the derangement of any of the multifarious machinery belonging to stationary steam engines, (which will occur at times, in the same manner as in all works of a similar nature,) would have the consequence of extending its effect throughout the whole line of communication with which they may be connected, As

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