instance, the smoother the ball and the smoother the surface of the ice, the farther the ball is perceived to roll under the influence of a given impulse: so that were this globe of a perfectly spherical surface, such as would oppose no resistance from friction to a ball put in motion upon it

and were the ball at the same time to meet with no retardation from the medium through which it rolls, or in consequence of the inequalities of its own surface we can assign no reason why motion should not be perpetual.

We are familiar too with the facts, that of two connected bodies at rest, when one is suddenly put in motion, the other remains unmoved; and of two

such bodies in motion, when one is suddenly stopped, the other goes on unchanged in velocity and direction, unless in as far as, in either case, the body untouched may be influenced by friction and gravity. Thus in the case of a pointed rod stationed in a hole of the ground, with a snuff-box, or some such object, poized upon its vertex, when the rod is struck suddenly, the snuff-box, it is well known, drops into

the hole beneath and in the case of a

:

person carrying a pitcher full of water, if the pitcher be suddenly stopped, it is well known that the water is spilled in the direction of the motion. These facts assume a variety of forms, and give rise to many amusing experiments.

(To be Continued.)

PRACTICAL PERSPECTIVE.

Sir, I should be extremely reluctant to take the field against your correspondent, M. H. S. as I have no doubt his intentions are good, but as the system of "Practical Perspective," advanced by him at page 377, vol. vi. appears to me fallacious, I think it advisable, rather than so many of your readers should be misled, to state my objections to it.

That M. H. S. and his author have both of them missed the true principles of the art, may be made sufficiently evident. For in the plan of the rectangular prism, fig. 2, p. 377, it is clear that the angle G, is onethird nearer to the spectator (who is supposed to be situated at S,) than the angle I. The altitude, therefore, of the perpendicular angle of

45

the prism or cube represented by I, should be proportionally diminished the well-known principle, that the in the picture, in accordance with apparent magnitude of an object decreases with its distance. On consulting the third diagram, however, which is intended by M. H. S. for the perspective representation of the cube, we find that these two perpendiculars have precisely the same altitude, the two horizontal lines, Ef, Ef, which connect them, being perfectly parallel.

Without particularly adverting to the ambiguity arising from the errors will proceed to point out some of the in the description of the diagrams, I fallacies of the system. By again referring to fig. 2, we shall see that the line I, N, which M. H. S. calls the intersecting line, is drawn parallel to one of the sides of the object, and oblique to the central line of vision. Now, sir, this line is supposed, by perspective draughtsmen, to represent a perpendicular plane of glass, through reasonable being would think of lookwhich the object is seen; and as no ing obliquely through a glass of any kind, to obtain a direct and clear view of an object, this part of the system is inconsistent, to say the least of it. In truth, however, it is so pregnant with error, that the representation or picture of an object, produced in this way, is indeed a graphic monster of the most distorted and unnatural proportions: for if you will also allow me to introduce a very simple diagram, (see the other side) it will be seen that if the equal spaces 1, 2, 3, 4, 5, 6, are viewed from C, through the medium of the plane A, B, which is parallel to them, their representations on the plane will also be equal to each other: because, if we suppose the plane to be moved gradually upward, in the direction of the central line of vision, C, D, without deviating from its parallelism, the spaces upon it will gradually increase until at length they coincide with the originals. Now, by examining this diagram, it will be found that the distance of the sixth space from the eye, (at C,) is precisely twice that of the first; its representation, there

46

fore, upon the perspective plane, instead of occupying an equal extent, should not, according to the true

principles of the art, occupy on the plane more than one fourth the space of the first.

B

The true mode of obtaining the representation of these six spaces, in correct perspective, is to place the plane at right angles to the central line of vision, as at E, F, in which case the spaces would occupy upon it their true perspective proportions; the most distant being, as above stated, not more than one fourth the length of the nearest.

It is an invariable rule in the art, that every object of a rectangular form, when represented in oblique perspective, should have two vanish ing points. M. H. S. has but one, and for this reason,-that upon his system it is impossible to obtain another. This one, too, is erroneous, in consequence of the oblique position of the perspective plane being considerably nearer than it should be to the object.

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Since writing the above, I perceive that problems 1 and 2, which I have been treating as examples in oblique perspective, are in reality entitled parallel perspective;" but that this is an erroneous, or at least a very arbitrary distinction, may be seen by comparing these problems with problem 3, which is under the head of " oblique perspective;" for in all three, the position of the spectator with respect to the object is as nearly as possible the same; and consequently the same rule should be used for their projection. I have shewn already the error, in these cases, of making the perspective plane parallel to one of the sides of the object; and by referring to fig. 16, page 504, in which a short ver

tical cylinder is represented by this method, the distortion of the figure will be immediately seen; its upper surface, instead of appearing circu lar, having all the appearance of an ellipsis of very considerable length in proportion to its width. An ob ject of a rectangular form is said to be in parallel perspective when one of its faces is at right angles to the central line of vision, and consquently parallel to the perspective plane, as in fig. 27, p. 522, in which it will be seen that the horizontal lines in this face are parallel to each other and to the ground line.

With the exception of figs. 16 and 17, which are constructed by the same rule as the two first problems, the examples in problems 3, 4, and 5, appear to be worked upon correct principles, although, from the nearness of the objects, and the large angle which they consequently form with the eye, their representations are in reality anamorphosis. In problem 6, the perspective plane is again partially misplaced, the result of which is a distorted elevation of the object; and in the concluding problem, which professes to describe the method of delineating a steam engine in parallel perspective, its representation is a palpable proof of the fallacy of the rule by which it was drawn, for no possible position of the object could warrant so great a deviation from proportion as is here exhibited in the cylinder and other parts of the engine.

To conclude: as I have already occupied too large a portion of your valuable columns, I would recom

mend such of your readers as are disposed to avail themselves of the information to be derived from the "Practical Perspective," to substitute the following (general rules, in lieu of those given by M. H. S, for the representation of all rectangular figures, of which the two nearest sides are visible to the eye from the point of view.

1. In order to avoid an anamorphosis or distorted representation, fix the point of view at such a distance from the object that the angle formed at the eye by the rays from the extreme points of the figure may not exceed 30 degrees, or the 12th part of a panoramic circle.

2. Having found on the plan the largest angle which the object subtends, by two lines drawn from its extreme angles on the right and left to the eye, bisect it, and draw another line through its centre from the point of view to the object. The central line of vision being thus obtained, place the perspective plane at right angles across it, and in contact with the nearest point of the object, continue this plane on each side until it meets two other lines drawn from the point of view, parallel with the two nearest sides of the object --the two points of intersection of these lines with the perspective plane will give the distance of the two vanishing points ;-having thus prepared the plan, the student may then proceed in other respects as described by M. H. S.

Your's, respectfully,
ALPHA BETA.*

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in your last number, I naturally felt desirous of a description of the chuck, but unfortunately Mr. Ibbetson has referred to two books which I find it rather difficult to get a sight of. Will you, Mr. Editor, be kind enough, through the medium of your useful magazine, to invite Mr. Ibbetson, or any of your intelligent correspondents, to give, in an early number, such a practical description as may enable an operative to construct one of the said Geometric Chucks.

I am, Sir, your's, &c.
I. E.

Sir,-Your correspondent, p. 552, vol. vi. has, I suppose, omitted the apparatus for shutting off the supply of steam when the piston descends, for surely he never could for a mo ment imagine that the steam at B, would raise up a weight, A, which afterwards is to be enabled, with the additional burden of a column of water at H, to overcome in its descent the pressure which forced it upwards.

The whole idea, sir, is, I conceive, so erroneous, that it needs no further comment to prove its total inefficiency.

From your's, &c.
C. S.

January 4th, 1827.

MR, IBBETSON'S GEOMETRIC CHUCK.

SIR, After an examination of the beautiful specimens of geometric turning by Mr. Ibbetson, as given

*We think Alpha Beta has done but scanty justice to the merits of M. H. S.'s Essays; we do but our duty, however, in giving a place to his remarks, and are convinced M. H. S. will not be sorry at having again occasion to address our readers on the subject. -EDIT.

SILK AND COTTON BRAID BONNETS.

An action was tried, in the court of King's Bench, on Wednesday last, for an enforcement of a patent, granted to Messrs. Brunton and Price, for manufacturing bonnets of silk and cotton braid. It appeared from the evidence, that this invention consisted of a mode of constructing bonnets of cotton or silk braid, knit or sewed together after the manner of the Leghorn bonnets, then stiffened by size, and, finally,

48

pressed on blocks into the desired shapes. The application of braid to this purpose, and in this manner, was alleged to be new and never adopted before the plaintiff's patent had been obtained. A Mrs. Susannah Crouch, however, proved that she had been thirty-one years in business, and upwards of twenty years ago, had made bonnets of the same descrip tion of materials, stiffened with isinglass, which were called infrivolity bonnets. The plaintiff was, therefore, nonsuited.

SKILL OF THE ATHENIAN MASONS.

If there be one thing more capable than another of giving us a correct idea of the rare skill acquired by the Athenian workmen, who were employed in constructing those buildings, which still constitute the glory of that industrious city, it is the perfection with which the drums, forming the parts of the largest columns, were fluted on their conical surfaces, and with which these different truncated cones were SO adapted to each other, that the grooves or fluting, when put together, were in complete unbroken continuity, from the capital to the base of the column.

Dupin's Geometry.

FECUNDITY OF FISHES.

It is asserted of the herring, that if suffered to multiply unmolested, and its offspring to remain undiminished during the space of twenty years, it would shew a progeny many times greater in bulk than the whole earth! And that a single cod-fish will produce at a birth, if they escaped depredation, a number equal to the whole population of England. -The Book of Nature Laid Open.

SINKING OF THE PARISIAN PANTHEON.

Perhaps no more striking illustration can be given of the necessity of having the surfaces of joints rigorously parallel in every part of an edifice, than what occurred in build

ing the Pantheon at Paris. In this edifice, a vast and lofty dome was to be supported by four groups of elegant columns. In order to give the columns the appearance of consisting only of a single stone, the drums or truncated conical pieces of which the shafts were formed, were hollowed out towards the centre, so that the edges of every two pieces might unite closely all round, and not leave the least visible separation. The aspect of these columns, when first erected, was beautiful; they appeared a chefd'œuvre of art; but when the immense weight of the arch was laid upon them, the edges of the drums which alone were in contact, not having sufficient surface to support the pressure, split and crumbled away, and the whole dome settled. down till all the surfaces of each joining came into contact. architect found it necessary to erect some large massy pillars in the centre of each group of columns which supported the dome, and the beauty of the structure disappeared. would have been preserved, had the joinings of the drums been surfaces applied to each other in every point. Geometry supplies us with the means of doing this in the most simple as well as the most complicated cases.Dupin's Geometry.

NOTICES

The

It

TO CORRESPONDENTS. Introductory notice to the Character of the London Mechanics' Institution in our next.

We are not sure of the real design of Civis's letter, and must therefore decline inserting it. We suspect there is a snake in the grass.

G. S. is not forgotten, but his drawings have rather puzzled our draughts

man.

Communications received from The

North Star-T. M. B.-Mr. ChildMr. Woolgar-R. F. C.-An old Subscriber-J. S.-J. Bateman-A. B. W. -L. U. F.-L. Masters-Mr. Weekes -Conductor-An old Coal Merchant.

Communications (post paid) to be addressed to the Editor, at the Publishers', KNIGHT and LACEY, 55, Paternoster Row, London. Printed by D. Sidney, Northumberland Street,

Strand.