wheel back the rubbish which had been removed at the opening of the mine, and this is laid in one continued heap, to the amount of some hundred cart-loads, which securely blocks up both the passages into the mine. The door is then locked, as well as the door into the house, and all the men then leave the premises in a state of safety; for the mass of rubbish which is thus wheeled in at the larger door, dams up the small rill of water which usually flows through the mine, and this has the effect of flooding it completely. Thus, if an attempt. were made to break the house and enter the mine by that road, the robbers would find that the water had arisen to such a height as would drown any individual who should attempt to search for the ore.

From an examination of the exterior of the mountain, it appears that in former times various small shafts have been sunk for getting the black-lead; and the mine which they are now working was one of those which had been closed for a century, which was again opened in the year 1769, in consequence of another mine in the immediate vicinity having failed. The expense of raising the black-lead varies very much in different years, according to the size of the masses which the workmen happen to meet with: for instance, that which they found in the year 1778 was four yards in diameter, and twelve yards high; that of 1803 was twenty-one yards and a half high, two yards and a half in diameter, and perfectly round like a column; that which they found in 1812 was rather less than twenty yards in height, and only two feet in diameter; and what they are now getting is found only in a narrow string. The expenses of driving the level, of building the house, and working the mine, from the 23d of April 1798 to the 4th of April 1814, have amounted to 66371. 9s. 4d.; and during this period there have been produced 736 casks of fine black-lead, and 1816 casks of the coarse kind, amounting together to 2552 casks of about 112lb. each.

It might be a matter of difficulty to those who visit the mine, to conceive how these casks of black-lead can be conveyed with safety down the face of so steep a mountain. This is done by men who have been long accustomed to the task. The cask is fixed upon a light sledge with two wheels, and the man, who is well used to this sort of precipitous path, walks coolly down before the sledge, taking care that it does not acquire too great a momentum, and thus overpower him. The empty sledge he then carries back upon his shoulders, and takes another cask. All the black-lead is sent to

London, as I have already mentioned, where it is deposited in the warehouse of the proprietors, and afterwards disposed of by public auction held at Essex-street in the Strand, London. This happens on the first Monday of every month throughout the year; and the best kind usually sells for two guineas or more per pound. There are some considerable manufactories of pencils at Keswick, but I was told that the makers are under the necessity of sending to London for all the black-lead they use in the trade, although they reside so near the place of its production.

The propriety of this valuable mine is divided, as I understand, into two equal parts, one of which belongs to Henry Bankes, Esq. representative in parliameut for Corfe Castle in the county of Dorset; and the other moiety is divided into ten or twelve shares belonging to the executors of the late Sir Joseph Banks, Sir John Mitford, the executors of the late Mr Gilbert, and others. In some years the net produce of the black-lead has amounted to thirty or forty thousand pounds. Mr Otley has stated, that by an account drawn up in 1804 the stock of black-lead then on hand was valued at 54,000l., and the annual consumption about 3500.; the best blacklead was then sold at 35s. per pound; since that time the price has been from 30s. to 45s. and the consumption is much increased. It is remarkable that this mine, which was valued in making the grant of the manor of Borrowdale by King James I. at 15s. 4d., was on the last assessment for the property tax, estimated at 2700l. sterling a year. Some other particulars respecting this singular mine may be seen in the works quoted below.*

ART. XXXIV.-On a Simple Mechanical Method of Forming the Curves for Reflectors, and of illustrating the Principles of various Philosophical Instruments, &c. By Mr JOHN HART, Civil Engineer. Communicated by the Author. [Brewster's Jour. Sci.]

WHILE engaged in drawing a curve for a gage, to enable the workman to form the reflector of the lamp for illuminating the dials of the Tron steeple of this city, an idea occurred

* Robinson's Natural History of Westmoreland and Cumberland, 8vo, London, 1709, p 75; Colonel Thornton's Sporting Tour through the Northern parts of England, 4to, London, 1804, p. 282; Mr Otley in Memoirs of the Literary and Philosophical Society of Manchester, second series, vol. iii, pages 168-175.

to me of forming these curves, in a more simple manner than that usually practised. If a number of radii be drawn from a centre, on a sheet of paper, they will represent rays diverging from that centre; and if we fold them over in the direction that the light is required to take, the folds will represent the reflecting surface. Having found this method to answer upon trial, and to be more extensively applicable than I had at first supposed, I have sent it to you for insertion in your valuable Journal, under the impression that it may be of service to lecturers and teachers of youth, by affording a mechanical illustration of the properties of the conic sections, and other curves in the reflection of light or sound, &c. as well as to the practical mechanic, who may be unacquainted with geometry, but who may be employed in the construction of such instruments. The following is an abridgment of a paper read before the Glasgow Philosophical Society.

Before proceeding to curves, I shall give a few examples of its application to the angles of incidence and reflection, &c. 1st, a straight strip of paper simply folded, as shown in Plate III. Fig. 1st or 2d, will give a correct idea of the angle of incidence and reflection; the strip represents the light before and after reflection; and the fold the reflecting surface; if two or three lines of different colours be drawn upon the paper, it will show how the image is inverted after reflection, as is shown in the plate by dotted and continuous lines.

Fig. 3. shows the construction and principle of the optical toy, called the polemoscope; the paper again represents the light and the folds, the angle of the mirrors.

Fig. 4. represents two folds or reflections, to produce a right angle; or, the principle of Dr Wollaston's Camera Lucida. By holding the paper folded in this manner, between the eye and the light, the dotted lines will show how the object is erected by the second reflection in this beautiful little instrument, the folds, of course, represent the angle of the prism. The Circle. It is well known to geometers that rays of light falling on a spherical surface, (except from a luminous body placed in its centre,) will not meet in a point after reflection, but will have a number of distinct foci from every part of the circle: if a line be drawn through these foci, it will constitute a caustic curve. To illustrate this, take a piece of paper, see Figs. 5. and 6. and draw a number of parallel or diverging lines, about one-fourth of an inch asunder. From a point about the middle, describe a circle on both sides of the paper; then, with a knife, cut each alter

nate line, commencing with the cut a little within the circumference of the circle, and cutting to the end of the paper, these lines will represent parallel, or diverging rays of light: fold over the strips, making each fold upon the circumference of the circle: It will now be seen that these rays do not meet in a point, but cross each other in what geometers term caus

tic curves.

If all the parallel rays be folded so as to meet in the point where the first two rays crossed, as in Fig. 7. the curve formed by the folds will be a portion of a parabola.

The Ellipse.--If a luminous or sounding body be placed in the focus of an ellipse, the rays of light or sound will all be reflected to the other focus.

This may be shown by laying a narrow strip of paper from one of the foci, and folding it at any place upon the curve, it will point to the other focus. See Fig. 8.

Or by taking a few strips of paper of equal lengths, and pushing a pin through one end of them as a centre, and folding *them so that each fold joins the last, and the other end points to another centre, the folds will form an ellipse round these two centres; thus clearly showing that every point of the curve reflects light or sound from one focus to the other.

The Parabola.-In order to form a parabolic curve, or a gage for a reflector that will reflect the light of a luminous body placed in its focus in a parallel stream, such as lighthouse reflectors, &c., take a sheet of paper, see Fig. 9, and through the centre draw twelve or sixteen lines; let the centre represent a luminous point, (a candle for instance,) of course the lines will represent rays of light radiating from it. Take a knife, and cut each alternate line nearly to the centre, fold over one of the pieces, as in Fig. 10, making the fold at the same distance from the centre you want the focus of your curves to be, and the centre line of this fold to return over the centre of the radii, fold over the rest, making each successive fold to join with the last, observing always to make the centre line of each fold parallel to the centre line you first commenced with. The curve formed by these folds will be a parabola; the lines will represent the rays of light emanating from the luminous point, before and after reflection from the surface of the curve; or vice versa, parallel rays falling on this curve will be reflected to a point in the centre or focus.

The Hyperbola.-If the pieces be so folded, Fig. 11, that the lines be made to diverge, (so that if they were prolonged behind the curve they would meet in a point) the curve produced by the folds will be a hyperbola.

Therefore, if a luminous point be placed in the focus of this curve, the light will be reflected as if radiating from the point behind the curve, or its virtual focus.

It will be evident that parallel rays falling on this curve, will be reflected to its virtual focus; hence, if a hole be made through the centre of this reflector, and the virtual focus be placed close behind the curve, it will form an excellent burning mirror.

Reflectors for coach-lamps may be formed either of this curve, with a distant vertical focus to spread the light a little before the horses, or of the parabola. It will be evident, however, that the parabola will likewise spread the light a little, as the flame i necessarily larger than its focus.

It must be obvious to those conversant with optics, that in this manner Gregorian, Newtonian, and Cassegranian telescopes, and reflecting microscopes, may be explained to a popular or mixed class, affording them a better idea of the proper curves for the reflectors of these instruments, than by the usual method of diagrams.

Upon a board, for example, draw the two specula and cone of rays of a Gregorian telescope, then take twelve or more strips of paper, and nail them in the focus of the great speculum; spread them out (like the rays of a fan) so as to cover the large speculum; now fold them up parallel, beginning at the centre of the great speculum to represent the incident rays. Turn down the other ends, beginning likewise at the centre of the small speculum, but converging so as to meet at its focus before the eye-glass. The difference of curves produced by the folds from the spherical draught upon the board will now be apparent, especially if the telescope is drawn of a large aperture, the slips of paper will give a distinct idea of the path of the light.

I shall now give an example or two of its application in Acoustics, and in forming the teeth of wheels, &c.

A long strip of paper folded, as in Fig. 12, will illustrate the nature of the Speaking trumpet; that is, the proper angle of the conical tube, in proportion to its length, to give the. greatest number of echoes, or reflections, in lines, as nearly parallel as possible.

Fig. 13 is the converse of this principle, or the Ear trumpet ; it will be seen, by inspecting this figure, that the dotted part of the cone must be cut off, otherwise the sound, after another reflection, would return back. Drawing two or three converging lines, and folding a strip of paper from side to side, as