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Britain. We have no wish to depreciate the labors from the common screws only in this, that its of Bernouilli, Euler, and others, of whom we have threads or rifles are less deflected, and approach already spoken in terms of commendation; more to a right line; it being usual for the and upon whose genius and attainments we often threads with which the rifled barrel is indented reflect with pleasure. Yet had it not been for to take little more than one turn in its whole the practical iurn given to the investigation by length. The numbers of these threads are not Robins, and so incessantly kept in mind, and so determinate, skilfully and elaborately carried out to its pro The usual method of charging these pieces is fessional applications by Dr. Hutton, the prin- this :— The proper quantity of powder being put ciples of gunnery would at this moment have down, a leaden bullet rather larger than the bore been little better than a collection of barren of the piece is forcibly driven home to the powspeculative rules, calculated to mislead, rather der; and in its passage acquires the shape of the than direct, the intelligent engineer.

inside of the barrel, so that it becomes part of

a male screw, exactly answering to the indents In the notice we have taken of Robins's ex- of the rifle. The rifled barrels made in Britain periments, we do not perceive that we have are often contrived to admit the charge and shot described his celebrated ballistic pendulum. It at the breech; and the ball acquires the same consists of a large block of wood, annexed to the shape in its expulsion that is given to it by the end of an iron stem, strongly framed, and capa- ' more laborious operation of driving it in at the ble of oscillating freely upon a horizontal axis. muzzle. From the whirling motion communiThis machine being at rest, a piece of ordnance cated by the rifles, it happens that, when the is pointed directly towards the face of the block, piece is fired, that indented zone of the bullet at any assigned distance, as twenty, thirty, forty, follows the sweep of the rifles, and thereby, be sixty, &c., feet, and then fired; the ball dis- sides its progressive motion, acquires a circular charged from the gun strikes and enters the motion round the axis of the piece; which cirblock, communicating to it a velocity, which is cular motion will be continued to the bullet after to the velocity with which the ball was moving its separation from the piece; and thus a bullet at the moment of impact as the weight of the discharged from a rifled barrel is constantly made ball to the sum of the weights of ball and pen- to whirl round an axis which is coincident with dulum. Referring this velocity to the centre of the line of its flight. By this whirling on its oscillation of the pendulum, it will rise through axis, the aberration of the bullet, which proves an appreciable arc of vibration till such velocity so prejudicial to all operations in gunnery, is is extinguished. The measure of that arc will almost totally prevented : and accordingly such lead to the determination of the velocity, be- pieces are much more to be depended on, and cause it is evidently equal to the velocity which will do execution at a much greater distance, a body would acquire by falling freely through than the other. But as it is in a manner imposthe versed sine of the arc shown by the experi- sible entirely to correct the aberrations arising ment.

from the resistance of the atmosphere, even the Robins's largest ballistic pendulum weigbed rifled barrelled pieces cannot be depended upon only ninety-seven pounds; being employed to for more than one-half of their actual range at ascertain the velocities of balls weighing about any considerable elevation. It becomes therefore an ounce each. The smallest pendulum con a problem very difficult of solution, to know, structed by Dr. Hutton weighed 600 pounds; even within a very considerable distance, how and, as he pursued his experiments, the new far a piece will carry its ball with any probabipendulums were made successively larger and lity of hitting its mark, or doing any execution. larger, till at last they reached the weight of The best rules hitherto laid down on this subject about 2600 pounds. He also made several im- are those of Robins. provements in their construction, especially in Of Carronades.—Mr. Gascoigne's improved their manner of suspension, and in that of gun, called a carronade, was, in June 1779, by measuring the semi-arc of vibration; employing the king in council instituted a standard navythis curious apparatus in ascertaining the velo- gun, and ten of them appointed to be added cities of balls varying in weight from one pound to each ship of war, from a first-rate to a sloop. to six, and propelled with nearly all possible The carronade is mounted upon a carriage with modifications of charge. It appears farther, a perfectly smooth bottom of strong plank, withfrom Annales de Chimie et de Physique, tome out trucks; instead of which there is fixed on 5, that in recent experiments at Woolwich, con- the bottom of the carriage, perpendicular from ducted by Dr. Gregory and the select committee the trunnions, a gudgeon of proper strength, of artillery officers, a ballistic pendulum, weigh- with an iron washer and pin at the lower end. ing 7400 pounds, was employed in determining This gudgeon is let into a corresponding groove the velocities of six, twelve, eighteen, and twenty- cut in a second carriage, called a slide-carriage; four pounders.

the washer supported by the pin overreaching Of Rifled-barrelled Guns.--The greatest irre- the under edges of the groove. This slide cargularities in the motion of bullets are owing to riage is made with a smooth upper surface, upon the whirling motion on their axis, acquired by which the gun-carriage is moved, and by the the friction against the sides of the piece. The gudgeon always kept in its right station to the best method hitherto known of preventing these port; the groove in the slide-carriage being of a is by the use of pieces with rifled barrels. These sufficient length to allow the gun to recoil and be pieces have the insides of their cylinders cut loaded within board. The slide-carriage, the with spiral channels, as a female screw, varying groove included, is equally broad with the fore

part of the gun-carriage, and about four times pieces. They are made of cast-iron ; and are not the length; the fore part of the slide-carriage is bored like the common pieces, but have the fixed by hinge-bolts to the quick-work of the rifles moulded on the core, after which they are ship below the port, the end lying over the fill, cleaned out and finished with proper instruments. close to the outside plank, and the groove reach- Guns of this construction, which are intended ing to the fore end; the gudgeon of the gun- for the field, ought not to be made to carry a carriage, and consequently the trunnions of the ball of above one or two pounds weight at most; gun, are over the fill of the port when the gun a leaden bullet of that weight being sufficient to is run out; and the port is made of such breadth, destroy either man or horse. A pound-gun, of with its sides bevelled off within board, that the this construction, of good metal, need not weigh gun and carriage may range from bow to quarter. above 100 lbs., nor its carriage above 100 lbs. The slide-carriage is supported from the deck at more. It can therefore be easily transported the hinder end, by a wedge or step-stool ; which from place to place, by a few men; and a couple being altered at pleasure, and the fore end turn- of good horses may transport six of these guns ing upon the hinge-bolts, the carriage can be and their carriages, if put into a cart. But this constantly kept upon an horizontal plane, for the kind of ordnance has never been extensively more easy and quick working of the gun when used, we believe, in the British service. See the ship lies along. But see Sir Howard Dou- our article ARTILLERY, for the latest official reglas's remarks on this piece, already given. gulations for the proportion and disposition of

Of Rifled Ordnance.--In 1774 Dr. Lind, and the ammunition attached to the field pieces of captain Alexender Blair of the sixty-ninth regi- our army: as also for the guns attached to the ment of foot, invented a species of rifled field- brigades of artillery. See also Cannon.

E

The PROJECTION OF THE SPHERE is a perspec

Fig. 1. tive representation of the circles on the surface of

G

HdF the globe; and is variously denominated, according to the different positions of the eye and plane of projection. There are three principal kinds of projection; the stereographic, the orthographic, and gnomonic. In the stereographic projection, the eye is supposed to be placed on the surface of the sphere; in the orthographic it is supposed to be at an infinite distance; and in the gnomo nic projection the eye is placed at the centre of the sphere. Other kinds of projection are, the globular, Mercator's developement, &c. The chief application of the doctrine of these

B projections is to the constructing of maps and dials. In our article Maps we have, therefore, entered at length into the principal projections ; produced, and consequently to the line of meai. e. 1. By development; 2. The orthographic; sures : hence the given circle will be projected 3. The stereographic ; 4. The globular; and 5. into that section ; that is, into a straight line Mercator's.

passing through d, perpendicular to Cd. Now In that of DIALLING the gnomonic is involved. Cd is the cotangent of the angle Cd A, the inSee that article. It may, however, be thus ex- clination of the given circle, or the tangent of the hibited more formally.

arch C D to the radius AC. The eye, in this projection, is in the centre of Corol. 1. A great circle perpendicular to the the sphere, and the plane of projection touches plane of projection is projected into a straight the sphere in a given point parallel to a given line passing through the centre of projection ; circle : the plane of projection will represent and any arch is projected into its correspondent the plane of a dial, whose centre being the pro- tangent. jected pole, the semi-axis of the sphere will be the 2. Any point, as D, or the pole of any circle, stile or gnomon of the dial.

is projected into a point d, whose distance from Prop. I. THEORY I.-Every great circle is the pole of projection is equal to the tangent of projected into a straight line perpendicular to the that distance. line of measures ; and whose distance from the 3. If two great circles be perpendicular to centre is eqnal to the cotangent of its inclination, each other, and one of them passes through the or to the tangent of its nearest distance from the pole of projection, they will be projected into pole of the projection.

two straight lines perpendicular to each other. Let BAD, hg. 1, be the given circle, and let 4. Hence if a great circle be perpendicular to the circle C BED be perpendicular to BAD, several other great circles, and its representation and to the plane of projection : whose intersection pass through the centre of projection; then all CF with this last plane will be the line of mea- these circles will be represented by lines parallel sures. Now, since the circle CBE D is per- to one another and perpendicular to the line of pendicular both to the given circle B A D and to measures, for representation of that first circle. the plane of projection, the common section of Prop. II. TueoR. II. If two great circles the two last planes produced will therefore be intersect in the pole of projection, their repreperpendicular to the plane of the circle C BED sentations will make an angle at the centre of the

plane of projection, equal to the angle made by ing as the distance of its most remote point is these circles on the sphere.

less, equal to, or greater than, 90°. For, since both these circles are perpendicular 2. If I be the centre, and K, k, l, the focus of to the plane of projection, the angle made by the ellipse, hyperbola, or parabola ; then HK= their intersections with this plane is the same as Ad-Af for the ellipse ; Hk=

Ad+Af the angle made by these circles,

for 2

2 Prop. III. Theor. III. Any less circle the hyperbola ; and fn being drawn perpendiparallel to the plane of projection is projected

in E + F f into a circle whose centre is the pole of projec- cular to A E fl=

for the parabola.

2 tion, and its radius is equal to the tangent of the distance of the circle from the pole of projec- fig. 1, Plate PROJECTION OF THE SPHERE, bę

Prop. V. Theor. V. Let the plane TW, tion. Let the circle PI (fig. 1) be parallel to the BCD a great circle of the sphere in the plane

perpendicular to the p.ane of projection TV, and plane G F, then the equal arcbes PC, CI, are TW. Let the great circle B E D be projected projected into the equal tangents. GC, CH; into the straight line bek. CQ$ perpendicular and therefore C, the point of contact and pole of to bk, and Cm parallel to it and equal to CA, the circle P I and of the projection, is the centre and make Qs equal to Qm; then any angle of the representation G, H.

Corol. If a circle be parallel to the plane of QSt is the measure of the arch Qt of the proprojection, and 45° from the pole, it is projected jected circle. into a circle equal to a great circle of the sphere; the angle QCm equal to QC A, each being a

Join AQ: then, because Cm is equal to CA, and therefore may be considered as the primitive right

angle, and the side QC common to both Prop. IV. Theor. IV. A less circle not triangles; therefore Qm, or its equal QS, is parallel to the plane of projection is projected equal Qa. Again, since the plane AC Q is into a conic section, whose transverse axis is in perpendicular to the plane TV, and bQ to the the line of measures; and the distance of its intersection CQ;

therefore 6 Q is perpendicular nearest vertex from the centre of the plane of both to AQ and QS: bence, since A Q and QS projection is equal to the tangent of ils nearest the same points as the equal angles at A. But

are equal, all the angles at S cut the line 6 Q in distance from the pole of projection; and the by the angles at A the circle BÈ D is projected distance of the other vertex is equal to the tan- into the line 6Q. Therefore the angles at S are gent of the great distance.

Any less circle is the base of a cone whose the measures of the parts of the projected circle vertex is at A, fig. 2; and this cone being pro

bQ; and S is the dividing centre thereof.

CoRoL. 1. Any great circle 6 Q t is projected

into a line of tangents to the radius SQ. Fig. 2.

2. If the circle b C pass through the centre of LIK

projection, then the projecting point A is the dividing centre thereof, and Cb is the tangent of its correspondent arch C B to C A, the radius of projection.

PROP. VI. Theor. VI. Let the parallel circle GLH, fig. 1, be as far from the pole of pro

jection C as the circle FN I is from its pole ; and E

let the distance of the poles C P be bisected by the radius A0; and draw bAD perpendicular to AO; then any straight line Qt drawn through b will cut off the arches k, l, F, n, equal to each other in the representations of these equal oireles in the plane of projection.

Let the projections of the less circles be de duced, its intersection with the plane of projec- scribed. Then, because B D is perpendicular to tion will be a conic section. Thus the cone A 0, the arches BO, DO, are equal; but, since DAF, having the circle D F for its base, being the less circles are equally distant each from its produced, will be cut by the plane of projection respective pole, therefore the arches FO, OH, in an ellipse whose transverse diameter is df; are equal; and hence the arch BF is equal to and Cd is the tangent of the angle CAD, and the arch DH. For the same reason the arches Cf the tangent of CAF. In like manner, the BN, DL, are equal; and the angle FBN is cone AFE, having the side A E parallel to the equal to the angle L DH; therefore, on the line of measures df, being cut by the plane of sphere, the arches FN, H L, are equal. And projection, the section will be a parabola, of since the great circle BNLD is projected into which f is the nearest vertex, and the point into the straight line bQnl, &c., therefore n is the which E is projected is at an infinite distance. projection of N, and l that of L: hence fn, hly Also the cone AFG, whose base is the circle the projections of FN, I L, respectively, are FG, being cut by the plane of projection, the equal. section will be a hyperbola; of which f is the Prop. VII. THEOR. VII. If Fnk, hlg, fig. nearest vertex; and GA being produced gives 2, be the projections of two equal circles, whereof d the other vertex.

one is as far from its pole P as the other from COROL. 1. A less circle will be projected its pole C, which is the centre of projection; and into an ellipse, a parabola, or hyperbola, accord- if the distance of the projected poles C, p, be di.

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