or Gunners CALLIPERS, is an instrument wherein a right line is so divided as that the first part being equal to the diameter of an iron or leaden ball of one pound weight, the other parts are to the first as the diameters of balls of two, three, four, &c., pounds are to the diameter of a ball of one pound. The caliber is used by engineers, from the weight of the ball given, to determine its diameter or caliber, or vice versa.
The gunners callipers consist of two thin plates of brass joined by a rivet, so as to move quite round each other: its length from the centre of the joint is between six inches and a foot, and its breadth from one to two inches; that of the most convenient size is about nine inches long. Many scales, tables, and proportions, &c. may be introduced on this instrument; but none are essential to it, except those for taking the caliber of shot and cannon, and for measuring the magnitude of salient and entering angles. The most complete callipers is exhibited Plate CXXXIII. The furniture and use of which we shall now briefly describe. Let the four faces of this instrument be distinguished by the letters A, B, C, D: A and D consist Caliber.
On the circular head adjoining to the leg of the face A are divisions denominated *shot diameters*; which show the distance in inches and tenths of an inch of the points of the callipers when they are opened; so that if a ball not exceeding ten inches be introduced between them, the bevil edge E marks its diameter among these divisions.
On the circular bevil part E of the face B is a scale of divisions distinguished by *lb., weight of iron shot*. When the diameter of any shot is taken between the points of the callipers, the inner edge of the leg A shows its weight in avoirdupois pounds, provided it be lb. \( \frac{1}{2}, 1, \frac{3}{4}, 2, 3, 4, \frac{5}{4}, 6, 8, 9, 12, 16, 18, 24, 26, 32, 36, \) or \( 42 \); the figures nearest the bevil edge answering to the short lines in the scale, and those behind them to the longer strokes. This scale is constructed on the following geometrical theorem, viz. that the weights of spheres are as the cubes of their diameters.
On the lower part of the circular head of the face A is a scale of divisions marked *bores of guns*; for the use of which, the legs of the callipers are flipped across each other, till the steel points touch the concave surface of the gun in its greatest breadth; then the bevil edge F of the face B will cut a division in the scale showing the diameter of the bore in inches and tenths.
Within the scales of *shot* and *bore* diameters on the circular part of A, are divisions marked *pounders*: the inner figures \( \frac{1}{2}, \frac{1}{4}, 3, \frac{5}{4}, 8, 12, 18, 26, 36 \), correspond to the longest lines; and the figures, 1, 2, 4, 6, 9, 16, 24, 32, 42, to the short strokes. When the bore of a gun is taken between the points of the callipers, the bevil edge F will either cut or be near one of these divisions, and show the weight of iron shot proper for that gun.
On the upper half of the circular head of the face A are three concentric scales of degrees; the outer scale consisting of 180 degrees numbered from right to left, 10, 20, &c. the middle numbered the contrary way, and the outer scale beginning at the middle, with 0, and numbered on each side to 90 degrees. These scales serve to take the quantity of an angle, either entering or salient. For an entering or internal angle, apply the legs of the callipers so that its outward edges coincide with the legs of the given angle, the degree cut by the bevil edge F in the outer scale shows the measure of the angle sought; for a salient or external angle, slip the legs of the callipers across each other, so that their outward edges may coincide with the legs forming the angle, and the degree marked on the middle scale by the bevil edge E will show the measure of the angle required. The inner scale will serve to determine the elevation of cannon and mortars, or of any oblique plane. Let one end of a thread be fixed into the notch on the plate B, and any weight tied to the other end: apply the straight side of the plate A to the side of the body whose inclination is sought; hold it in this position, and move the plate B, till the thread falls upon the line near the centre marked *perp.* Then will the bevil edge F cut the degrees on the inner scale, showing the inclination of that body to the horizon.
On the face C near the point of the callipers is a little table showing the proportion of troy and avoirdupois weights, by which one kind of weight may be easily reduced into another.
Near the extreme of the face D of the callipers are two tables showing the proportion between the pounds weight of London and Paris, and also between the lengths of the foot measure of England and France.
Near the extreme on the face A is a table containing four rules of the circle and sphere; and geometrical figures with numbers annexed to them: the first is a circle including the proportion in round numbers of the diameter to its circumference; the second is a circle, inscribed in a square, and a square within that circle, and another circle in the inner square: the numbers 28, 22, above this figure exhibit the proportion of the outward square to the area of the inscribed circle; and the numbers 14, 11, below it, show the proportion between the area of the inscribed square and the area of its inscribed circle. The third is a cube inscribed in a sphere; and the number 89\(\frac{1}{2}\) shows that a cube of iron, inscribed in a sphere of 12 inches in diameter, weighs 89\(\frac{1}{2}\)lb. The fourth is a sphere in a cube, and the number 243 expresses the weight in pounds of a sphere inscribed in a cube whose side is 12 inches; the fifth represents a cylinder and cone of one foot diameter and height: the number in the cylinder shows, that an iron cylinder of that diameter and height weighs 364.5 lb, and the number 121.5 in the cone expresses the weight of a cone, the diameter of whose base is 12 inches, and of the same height: the fifth figure shows that an iron cube, whose side is 12 inches, weighs 464lb, and that a square pyramid of iron, whose base is a square foot and height 12 inches, weighs 154\(\frac{1}{2}\)lb. The numbers which have been hitherto fixed to the four last figures were not strictly true; and therefore they have been corrected in the figure here referred to; and by these the figures on any instrument of this kind should be corrected likewise.
On the leg B of the callipers, is a table showing the weights of a cubic inch or foot of various bodies in pounds avoirdupois.
On the face D of the circular head of the callipers is a table contained between five concentric segments of rings: the inner one marked *Gun* shows the nature of the gun or the weight of ball it carries; the two next rings contain the quantity of powder used for proof and service to brass guns, and the two outermost rings show the quantity for proof and service in iron cannon.
On the face A is a table exhibiting the method of computing the number of *lbs* or *balls* in a triangular, square, or rectangular pile. Near this is placed a table containing the principal rules relative to the fall of bodies, expressed in an algebraic manner: nearer the centre we have another table of rules for raising water, calculated on the supposition, that one horse is equal in this kind of labour to five men, and that one man will raise a hoghead of water to eight feet of height in one minute, and work at that rate for some hours.
N.B. Hogheads are reckoned at 60 gallons.
Some of the leading principles in gunnery, relating to *firing* in cannon and mortars, are expressed on the face B of the callipers. Besides the articles already enumerated, enumerated, the scales usually marked on this sector are laid down on this instrument; thus the line of inches is placed on the edge of the callipers, or on the straight borders of the faces C, D: the logarithmic scales of numbers, fines, versed fines, and tangents, are placed along these faces near the straight edges: the line of lines is placed on the same faces in an angular position, and marked Lin. The lines of planes or surfaces are also exhibited on the faces C and D, tending towards the centre, and marked Plan. Finally, the lines of solids are laid on the same faces tending towards the centre, and distinguished by Sol.