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a counterpart of the reverse side, and the effect of striking a mail between them is to bevel or round both the outer rim, and the interior holes. The number of dies contained in the holders is represented in the engravings as ten, but that number may be increased or diminished as convenience may suggest. The machine for working these dies (as to which I claim nothing new), is provided as usual with a supply tray for containing the mails to be struck, and a feeder, by which they are delivered to the dies; but these appendages are made proportionately larger than usual, to suit the greater number of mails struck at one time, and the tray channelled also, in order to keep the mails separate in their passage to the dies. Fig. 20, is a plan of the supply-tray, Q. Fig. 21, is a side elevation of that part of the machine which includes the supply tray and feeder R, and fig. 22, a plan thereof. The tray, Q, is placed in an inclined position, so as to ensure by the downward gravitation of the mails a constant supply of them to the feeder, R, which delivers them to the dies.

The whole of the tools before described are proposed to be worked by

steam.

MATHEMATICAL PERIODICALS.

(Continued from page 357.) XVIII.—The Diary Supplement. Origin. The same year which witnessed the premature decease of Burrow's Diary, gave birth to the "Diary Supplement," the first number of which was issued under the title of "A Supplement to the Ladies' Diary for the year 1788." Dr. Hutton, the "Diary Author of that period, appears to have been anxious to accommodate more of his correspondents, than the limited pages of the Ladies' Diary would permit, and hence he Sndertook"this Supplement at his own sole risk and expense, for the improvement of the Diary, and to oblige the more his learned and increasing contributors, by thus preserving a number of their ingenious compositions from being lost, from want of room to comprise them all in the narrow limits of the Diary; he (therefore) hopes all friends of that useful and amusing little work will extend the knowledge and sale of this Supplement as much as they can amongst their acquaintance." Notwithstanding the rather amusing admission at the close of this address, the worthy

doctor's appeal does not appear to have been made in vain, for the pages of the Supplement soon presented a numerous list of correspondents, such as few periodicals can boast; but, like most works of this class, its existence was doomed to be brief, and it closed its career with the number for 1806.

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Editor. Charles Hutton, LL.D., F.R.S., &c., &c., Professor of Mathematics in the Royal Military Academy, Woolwich.

Contents.-The usual contents of each number are-Additional Answers to the Enigmas, Charades, Rebusses, Queries, and Mathematical Questions proposed in the Ladies' Diary for the preceding year; Account of Eclipses, Occultations, &c., for the current year; New Enigmas, Charades, Rebusses, Queries, and Mathematical Questions proposed for solution in the following Supplement; &c., &c.

The first number contains an "Alphabetical List of all the Enigmas, with their numbers," from the commencement of the Diary to the year 1774; and in the second number is given a table of "All the Transits of Mercury over the Sun for 300 Years," viz., from 1605 to 1894 inclusive. A list of all the solar eclipses visible in England between the years 1769 and 1999, "computed by Mr. William Chapman, and adapted to the town of Foxton in Leicestershire," was announced on the title-page of the Supplement for 1790, but was not printed until 1793: it contains the dates, beginning, middle, end, duration, and the digits obscured for each eclipse, and appears to have been the last miscellaneous dissertation published in this work. No mathematical papers were admitted into the publication, if we except an improved solution to Question 865 in the Ladies' Diary for 1788, by Mr. John Burrow. The original solution, however, appears to have been considered satisfactory by Professor Leybourn; for he has omitted to include the improved one in his edition of the Diary. Many of the enigmas, &c., are worthy of commendation, and amongst the queries are numerous interesting and valuable discussions, well worthy the attention of the inquiring student. The late Dr. Dalton. of Manchester (then Mr. John Dalton, of Kendal), was a frequent contributor to the philosophical department, and in it are

Mr. Dalton's coming greatness; for in the Supplement for 1794, after an explanation of the phenomenon of "periodical winds," the editor announces, that "this ingenious gentleman intends soon to publish a work entitled 'Meteorological Observations and Essays,' containing several new improvements, particularly relative to the Theory of the Variation of the Barometer, of Rain, of the Trade Winds, &c., together with a full discovery (as he apprehends) of the cause of the Aurora Borealis." This was Dr. Dalton's first publication, and was issued almost simultaneously with the Diary and supplement in 1793: it was the avant courier of numerous essays in the transactions of various learned societies, and the well-known "System of Chemical Philosophy," which, in connection with the Atonic Theory, gained their author a more than European celebrity, and raised him from comparative obscurity, to a high and honourable position in the world of science.

Questions. The whole number of questions proposed and answered in the Supplement is 132, and a further selection of eight, was left unanswered on the discontinuance of the work. Besides these, each number contained several additional solutions to the questions in the Ladies' Diary for the current year; but, as the best of these have been incorporated with those given in the Diary itself, by Professor Leybourn in his edition, any further particulars respecting them are rendered unnecessary. The subjects of the questions embrace nearly the whole range of mathematical science as then understood, but since most of them are of a decidedly practical character, few points of interest present themselves; they would, no doubt, prove eminently useful to the teachers and students of that period, by furnishing them with a series of instructive examples for practice in numerical computation, and a selection might even now be made which would not by any means be without its utility. Dr. Gregory, Professor Leybourn, Colin Campbell, &c., were frequent and extensive contributors to this department: the lastnamed gentleman obtained the prize in 1794, and Dr. Gregory achieved the same honour in 1801. Question 15 cor

11, where he asserts that tan. 30° + tan. 22°-radius. Various analytical corrections are inserted in the next Supplement by Messrs. Burdon, Cook, and Haycock; and a geometrical construction determining two arcs having the stated property, is given by Mr. John Craggs, of Hilton, near Sunderland.

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Ques. 27 gives the radii R and r of the earth and moon, and the distance d of their centres, to find a point in this line from which equal portions of the luminaries will be visible. Several general formulæ are given in the next number, and the question was afterwards re-proposed as No. 40 in the Leeds Correspondent, where an elegant geometrical construction may be seen by Mr. John Whitley, under the signature of "Geometricus," of Rotherham. Ques. 35 relates to that "very curious problem,' "to divide a given circle into any proposed number of parts by equal lines, so that these parts shall be mutually equal both in area and perimeter." question was first solved by Dr. Hutton, and was most probably suggested to him, when considering the kindred problem respecting the division of the "grindstone," which was proposed as Ques. 9 in the Ladies' Diary for 1709. Both these problems ere inserted by Professor Young in his " Elements of Geometry," and some interesting particulars respecting their history and discovery are inserted in his "Notes," on these propositions from the third volume of Dr. Hutton's Tracts, where the property is shown to hold when an ellipse is substituted for the circle.

This

Ques. 42 gives the same data as No. 27, and requires the point from which the visible surfaces are a maximum. Mr. Charles Brady solves the problem in the next Supplement and deduces the elegant property that "the squares of the distances (from the luminaries) are as the cubes of the radii."

Ques. 47 requires "the odds, at the game of whist, that the dealer holds all the thirteen trumps in his own hand;" it was proposed by "J. B., Esq.," (query Byerley?) and solutions are printed from Colin Campbell, Esq., and the Rev. J. Ewbank.

Ques. 87 is a numerical example adopted to Problem 54 of Simpson's

whom refer to the original problem.

Ques. 127 requires the greatest octagon to be inscribed in a given square: various solutions are given. The next number, the last of which is a geometrical construction founded on a "remark to Prob. 59, p. 384, Dr. Hutton's Montucla," which determines the side of the octagon by bisecting the angle included between the diagonal of the square and the line joining the bisections of the opposite sides. Two other methods of determining the side may be seen in the solutions to Ques. 32 in No. II. of the "Western Miscellany," the first of which is the same as that given in Elliott's "Geometry and Mensuration," p. 61; and the second may be seen in Leslie's Geometry, Prop. XIV., p. 115, 4th edition.

Ques. 129 gives the area of a circle, and requires the length of a tether which, when fixed in the circumference, shall cut off a given portion of the area. The question was previously proposed as No. 170 in Burrow's Diary for 1788, but owing to the discontinuance of the work, no solution was published. It next appeared under a more general enunciation as Ques. 964 in the Ladies' Diary for 1793-4, to which a good solution was given by Mr. Buchanan, which included the question from Burrow's Diary as an example. The question was re-proposed in the Supplement, apparently to point out the advantages of applying the "Method of Double Position to such inquiries; and two solutions are given to it on these principles by Messrs. Gittens and Wiseman. It was again re-proposed as Ques. 186 of the Leeds Correspondent, in consequence of an anonymous correspondent having asserted that the "question could be solved without the assistance of Trial and Error;" but the editor, Mr. John Whitley, after examining the proposer's solution, which was stated to be "done pro forma," could "not refrain from pronouncing it erroneous." Solutions by approximation were, however, given by Messrs. Johnson and Baines, and an elaborate calculation of a similar question is given by Mr. Davidson in his "System of Mathematics." From what has been stated, it will be concluded that the question has attracted much more attention than it really deserves, nor should we

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'going the rounds" and form a sort of joint-stock test whereby the "knowing ones" in the provinces seek to prove the abilities of almost equally ignorant but more noisy pretenders.

Contributors.-Messrs. Adams, Barlow, Bearcroft, Bosworth, Brewer, Bruce, Burdon, Burrow, Campbell, Crosby, Dalton, Davis, Evans, Farey, Fildes, Furnax, Glendinning, Gregory, Hearding, Hellins, Holt, Howard, Leybourn, Lightbown, Lowry, Marrat, Mitchell, Nield, Pearson, Rowbottom, Rowe, Ryley, Scurr, Sewell, Smart, Squire, Surtees, Whiting, Woodhouse, &c., &c.

Publication. The publication took place annually; some of the earlier Supplements have no printer's name attached, but the latter ones were mostly "printed for G. G. and J. Robinson, Paternoster-row, London."

THOMAS WILKINSON.

Burnley, Lancashire, Nov. 14, 1849.

Corrigendum.

Instead of the clause beginning with " but it did not," &c., col. 2, p. 422; insert the following," it had previously been used by Mr. Lowry under the signature X. Y.,' in the solution to Ques. 224, in the Companion for 1812."

DAVIES'S PATENT ROTARY ENGINE.

Sir, I have just observed in No. 1317 of the Mechanics' Magazine, a description of Mr. Isaiah Davies's Patent Rotary Engine.

You state, generally, that it has been very successful, and, amongst other points, notice "the preservation of the parallelism of the shaft, and the equable motion of the piston."

It further appears, in No. 1318, that Mr. Davies originally constructed his engine with a single revolving piston, which he has since changed to a double one, by which means "the steam is made to act on opposite sides of the shaft at one and the same time .... A further advantage is, that as the steam has a double area of piston surface to act upon, the power of the engine is considerably increased without any corresponding increase in its bulk and weight."

I must now draw your attention to the fact that, in 1845, I described a doublerevolving piston engine (in the "Economy of the Marine Steam Engine"),

and enumerated its advantages in the same terms which I have quoted from your Magazine.

Mr. Davies's first patent was dated in 1844, and his subsequent patent for the double revolving piston was only dated in 1848.

In conclusion, I beg to say that I am gratified to find that my anticipations have been realized by the successful adoption, in Mr. Davies's engine, of the

principles of construction which I was the first to publish, and have always considered of the highest importance. I am, of course, not aware whether Mr. Davies had read my work before he patented his engine.

Trusting that you will give insertion to the above, I am, Sir, yours, &c., W. H. GORDON,

Ellon Castle, Nov. 14, 1849.

Lieut. R. N.

PADWICK'S GARDEN DRILL.

(Registered under the Act for the Protection of Articles of Utility. William Frederick Padwick, of the Manor House, Hayling Island, Southampton, Proprietor.)

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Fig. 1 is a side elevation of this implement; fig. 2, a cross section of the same on an enlarged scale, taken on the line ab of fig. 1; fig. 3 a plan of the seedbox, with the lid removed. A is a box or case, with a semicircular bottom; B, a disc, carrying a set of arms, CC, each of which is furnished at its outer end with a cup, a; D is an aperture by which the seed is introduced into the case; E is a hopper, into which the seed drops from the cups, aa, and from which it passes down through a pipe formed in the

coulter, F. G is a wheel, upon the periphery of which there is wound a quantity of line.

In using the implement, the end of the line is attached to some point at the end of the bed to be drilled, and the implement is then drawn forward by the handle, H, which causes the disc to revolve, and the cups, C, to rise up and deposit the seed in the hopper of the coulter. II are guides for conducting the seed into the cups.

DESCRIPTION OF A PLAN FOR VENTILATING COAL MINES BY MECHANICAL EXHAUSTION.

BY WM. BRUNTON, ESQ., C.E.

[We extract this description from a valuable pamphlet by Mr. Brunton, "On the Ventilation of Coal Mines," just published, (24 pp., 8vo., with plate, Nichols and Son); and very appropriately dedicated to Thomas Powell, Esq., of the Gear, Newport, "who at a season of extraordinary depression in the Coal Trade, generously incurred the expense of erecting the first Exhausting Ventilator with the view of testing its power of rarefaction, and making it publicly known." Mr. Brunton first describes in this pamphlet the ordinary means used to effect a rarefaction of the air in the upcast shaft of coal mines-namely, by a furnace or large open grate placed near to the shaft; next points out many insuperable objections to this system-its deficiency of power-liability to counteraction by changes in atmospheric pressure, &c. ; and then proceeds as follows.]

I will now describe the mechanical means I have substituted, and the particular advantages it possesses over the furnace as a ventilator.

I construct over the upcast shaft, or over a chamber immediately connected therewith,

a hollow drum, with curvilinear compartments, through which the air is discharged with that degree of force due to the velocity with which the drum revolves upon its axis. D, fig. 1, represents a drum, 22 feet exterior diameter, with curvilinear compartments: 16 feet being their mean diameter, the centrifugal force at 120 revolutions per minute will be 39.25, which, multiplied by the weight of 6 cubic feet of air =444 of a pound, will give a pressure of 17.5 pounds on the square foot, as the amount of rarefaction produced in the interior of the drum, and consequently in the upcast shaft, A, with which it is connected, which is much beyond what can be obtained by the furnace, yet greatly within the limits of the capability of this machine, as shown below.

Figs. 1 and 2 represent an elevation and plan of it, connected by a short tunnel (T), with the pump shaft (R), as the upcast closed at the top by a strong cover with a hole through which the pump rod works; the machine is driven by a steam engine (S) sufficiently powerful to increase the rarefaction to meet and overcome any sudden or extraordinary influx of carburetted hydrogen. The amount of rarefaction is governed by the speed of the engine, and is also under constant and visible inspection by a water or mercurial gauge: thus when the drum revolves

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In order better to understand the peculiar self-adaptation of this apparatus to all the circumstances that present themselves in the practice fo ventilation of collieries, let us suppose it altogether unconnected with any length of air-course, the air from the atmosphere having free access to the centre, and space for free discharge from the circumference, and a velocity given to it of 150 revolutions per minute, creating a rarefaction of 27 lbs. per square foot in the middle of the drum; then the velocity of the air through the machine would be 108 ft. per second, and the aggregate amounting to 8424 cubic feet per second, or 505.440 per minute.

Then let us suppose a state the very reverse of the above, viz., that no air be permitted to enter the drum at the centre part, of course none can be discharged at the cir

cumference; therefore, there being no resistance to the motion of the drum from discharge of air through the curvilinear compartments, but the power of the engine continuing the same, is consequently expended in increasing the velocity of the drum, and thereby the rarefaction. In the former case the effect is exhibited in the discharge of air; in the latter by the degree of rarefaction maintained in the middle of the drum.

From consideration of these two cases, it is manifest that the power required to work the machine will be as the quantity of air ascending the upcast shaft, and the amount of rarefaction required to draw it through the colliery; and such is the principle of self-adjustment of this apparatus, that if from any cause a less quantity or air is passed through the colliery at one time than

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