Part 10

+--------+------------------------+-------------------------+------+ |Nature. | Fuze Diameter. | Composition. |Drove | | +--------+-------+-------+---------+-------+-------+by one| | | below |at the | at the|Diameter.|Length.|Time it|man in| | |the cup.|bottom.| cup. | | |burns. |1 day.| +--------+--------+-------+-------+---------+-------+-------+------+ |Inches. | Inch. |Inches.|Inches.| Inch. | Inch. | ″ | Nᵒ. | | 13 | 2.1 | 1.575 | 2.49 | .5 | 8.4 | 35 | 25 | | 10 | 1.8 | 1.35 | 2.13 | .438 | 7.2 | 33 | 25 | | 8 | 1.3 | 1.25 | 1.78 | .375 | 6.37 | 29 | 30 | | 5½ | 1.1 | .825 | 1.3 | .275 | 4.4 | 18 | 50 | | 4⅖ | 1.0 | .75 | 1.18 | .25 | 3.5 | 15 | 700 | |Grenades| 0.8 | .6 | .9 | .2 | 2.25 | | 1000 | +--------+--------+-------+-------+---------+-------+-------+------+

Diameter inside the cup is 3 diameters of the bore.

Depth of the cup 1½ do.

Thickness of wood at bottom of the bore, 2 diameters.

_To find the Length of Fuzes for any Range._

The 13 and 10 inch fuzes of the same length burn so nearly equal, that one common length answers both, as do the 8 inch, 5½ and 4⅖. Therefore, to find the length of fuze for any range, multiply the time of flight by .22 for the 13 and 10 inch, and by .24 for the 8, 5½, and 4⅖; which is the decimal part of an inch a fuze burns in a second. Fuzes are thought to keep better by being painted; and for field service, are often marked off by black lines into seconds and ½ seconds.

_GABIONS._—Small gabions of 3 feet high, and 2 feet diameter, are made with least trouble, and are easiest carried. The pickets for them must be 1½ or 2 inches thick, and 4 feet long. Large gabions are 6 feet high, and 3 feet in diameter; and require two men to carry them. The smallest gabions or baskets are formed of pickets, 1 inch in thickness, and 1 foot long: they are 12 inches in diameter at top, and 10 at bottom. The small gabions have 7 or 8 pickets, the large ones 9 or 10.

_To make them._—The pickets are first to be fixed in the ground in a circle, the size of the bottom of the intended gabion; then a few twigs are to be wove through the upper ends, to keep them from flying out; afterwards the work must be begun at the bottom and continued upwards; and the whole being well driven down with a mallet, the edges must be secured by twigs, wattled up and down. The twigs of willow, birch, hazle, alder, poplar, and beech are proper for this purpose. The top of the gabion must be made very even, because that becomes the bottom when finished. Four men are usually employed on each gabion, with a billhook, a mallet, a spade, and two axes. Two collect the wood, while the other two form the gabion. A 3 foot gabion ought to be made in half an hour.

_GIN Triangle._—Length of arms of the gin 16 feet 4½ inches. Roller, 6 feet long. Tackle fall, 78 feet of 3 inch white rope. Sling, 6 inch white rope.

For the different exercises of the gin, see the word _Exercise_.

_GRAVITY.—Table of the Specific Gravity of several Solid and Fluid Bodies._

Platina 23400 Nitre 1900 Fine gold 19640 Ivory 1825 Standard gold 18888 Brimstone 1810 Quicksilver 11325 Solid gunpowder 1745 Fine silver 11091 Sand 1520 Standard silver 10535 Coal 1250 Copper 9000 Boxwood 1030 Copper halfpence 8915 Sea water 1030 Gun metal 8784 Common water 1000 Cast brass 8000 Oak 925 Steel 7850 Gunpowder, close stacken 937 Iron 7645 ” in loose heap 836 Cast iron 7425 Ash 800 Tin 7320 Maple 755 Crystal glass 3150 Elm 600 Marble 2700 Fir 550 Common green glass 2600 Charcoal Flint 2570 Cork 240 Common stone 2520 Air 1.232 Clay 2160 Brick 2000 Common earth 1984

The several sorts of wood are supposed dry.

This table also contains the weight of a cubic foot of each body in avoirdupois ounces; from whence results the following rules:

1. _To find the Magnitude of any Body from its Weight._

As the tabular specific gravity of the body Is to its weight in avoirdupois ounces, So is one cubic foot, or 1728 cubic inches, To its content in feet or inches respectively.

2. _To find the Weight of a Body from its Magnitude._

As one cubic foot, or 1728 cubic inches, Is to the content of the body, So is the tabular specific gravity To the weight of the body.

_GRAPE SHOT._—See the word _Shot_.

_GRANADES._—Hand granades may be thrown to the distance of 13 fathoms. For their dimensions, see the word _Shell_.

_GUNNERY._—By the assistance of good tables of practice, and the tables of amplitudes, sines, tangents, and secants, all the cases in gunnery in a nonresisting medium may be easily solved; and perhaps the solution may be sufficiently correct for practice, if the initial velocity of the projectile be not so great as to make the air’s resistance considerable.

For the tables of ranges with ordnance, see the different natures, as _Gun_, _Mortar_, &c. and for the tables of amplitudes, sines, tangents, and secants, see pages 151 and 152.

_Upon Horizontal Planes._

1. The greatest range is at 45° nearly.

2. The ranges with different elevations with the same charge, are as the double sines of the angles of elevation.

3. Any angle and its complement give the same range nearly.

4. The times of flight, are as the sines of the angles of elevation.

5. The altitude of the curve, at any elevation, is found by this proportion: as

Radius : tangent of angle of elevation :: range : altitude. ----- 4

6. The time of flight at 45° is equal the square root of the range in feet, divided by 4, or more nearly = √(quotient)² of the range in feet, divided by 16.1, or the space passed through in the first second by gravity.

Having the first graze with a given elevation and charge, to determine the charge for any other first graze and elevation, multiply the known charge and elevation into the proposed first graze; also the proposed elevation into the known first graze, and divide the first product by the last, for the charge required.

_Upon inclined Planes, at 45° Elevation._

_Case 1st. Given the charge and inclination of the plane, to find the range._

Multiply the horizontal range with this given charge, (found in the tables of ranges) by the number found opposite the angle of inclination of the plane, in the first column of multipliers, in the table of amplitudes, under the head _Ascents_, if it be inclined above the horizon; and _Descents_, if below the horizon, for the range required.

_Case 2d. Given the range and inclination of the plane, to find the charge._

Multiply the number found in the abovementioned table opposite the angle of inclination of the plane, in the second column of multipliers, under the head _Ascents_, or _Descents_, according as it is above or below the horizon, by the given range; for the range on a horizontal plane at 45°, the charge for which may be found from the tables of ranges.

_Upon Inclined Planes, at any Elevation._

There are always two elevations with which any range, (less than the greatest) may be made; and these elevations are always the complements of each other. The greatest range upon a horizontal plane is at 45°; or when the direction bisects the angle formed by the horizontal and vertical plane; also the greatest range upon any plane is made with that direction which bisects the angle between the plane and the zenith; and all other directions which make equal angles with this direction, (on each side of it) will also make equal ranges on the said plane; for the direction that bisects the angle between any plane and the zenith is the same with respect to that plane as the direction at 45° is with respect to the plane of the horizon.

_Rules._—1st. The elevation which gives the greatest range on a given ascent, is equal to half the sum of 90° added to the ascent.

2d. The elevation which give equal ranges on a given ascent, are the complements of each other added to the ascent.

3d. The elevation which gives the greatest range on a descent, is equal to half the complement of the descent.

If the range and inclination be given, the least charge that will reach the object, may be found as follows: multiply the tangent of the proper elevation into the proposed range, for the horizontal range whose charge is required.

WILLIAMS’S _Gunnery_.

_Table of Amplitudes._

+--------+-----------------+---------------+ |Degrees.| Ascents. | Descents. | | | Multipliers. | Multipliers | +--------+--------+--------+--------+------+ | |1st.cl. | 2d.cl. |1st.cl. |2d.cl.| | 1 | .983 | 1.02 | 1.02 | .983 | | 2 | .966 | 1.03 | 1.04 | .966 | | 3 | .949 | 1.06 | 1.05 | .950 | | 4 | .932 | 1.07 | 1.07 | .932 | | 5 | .916 | 1.09 | 1.09 | .916 | | 6 | .900 | 1.11 | 1.11 | .900 | | 7 | .884 | 1.13 | 1.13 | .884 | | 8 | .868 | 1.15 | 1.15 | .868 | | 9 | .852 | 1.18 | 1.17 | .853 | | 10 | .836 | 1.20 | 1.19 | .836 | | 11 | .821 | 1.22 | 1.22 | .821 | | 12 | .805 | 1.24 | 1.24 | .805 | | 13 | .789 | 1.27 | 1.27 | .789 | | 14 | .774 | 1.29 | 1.29 | .774 | | 15 | .758 | 1.32 | 1.31 | .763 | | 16 | .742 | 1.35 | 1.34 | .745 | | 17 | .726 | 1.38 | 1.37 | .730 | | 18 | .711 | 1.40 | 1.39 | .720 | | 19 | .693 | 1.45 | 1.42 | .704 | | 20 | .677 | 1.48 | 1.45 | .690 | | 21 | .660 | 1.52 | 1.48 | .675 | | 22 | .643 | 1.56 | 1.52 | .662 | | 23 | .625 | 1.60 | 1.55 | .645 | | 24 | .607 | 1.64 | 1.58 | .633 | | 25 | .589 | 1.70 | 1.62 | .617 | | 26 | .570 | 1.76 | 1.66 | .603 | | 27 | .550 | 1.82 | 1.69 | .592 | | 28 | .530 | 1.86 | 1.73 | .578 | | 29 | .510 | 1.96 | 1.78 | .562 | | 30 | .488 | 2.05 | 1.82 | .549 | | 31 | .466 | 2.14 | 1.87 | .534 | | 32 | .442 | 2.26 | 1.92 | .526 | | 33 | .418 | 2.41 | 1.97 | .508 | | 34 | .393 | 2.55 | 2.02 | .495 | | 35 | .366 | 2.73 | 2.08 | .488 | | 36 | .338 | 2.96 | 2.13 | .470 | | 37 | .309 | 3.24 | 2.20 | .455 | | 38 | .278 | 3.60 | 2.26 | .443 | | 39 | .245 | 4.09 | 2.33 | .430 | | 40 | .210 | 4.80 | 2.40 | .417 | | 41 | .173 | 5.78 | 2.48 | .404 | | 42 | .134 | 7.46 | 2.56 | .390 | | 43 | .092 | 10.90 | 2.64 | .380 | | 44 | .045 | 22.22 | 2.73 | .370 | | 45 | .000 |infinite| 2.83 | .360 | +--------+--------+--------+--------+------+

_Table of Natural Sines, Tangents, and Secants._

+--------+------+---------+--------+ |Degrees.|Sines.|Tangents.|Secants.| +--------+------+---------+--------+ | 1 | .018 | .018 | 1.000 | | 2 | .035 | .035 | 1.000 | | 3 | .052 | .052 | 1.001 | | 4 | .070 | .070 | 1.002 | | 5 | .087 | .087 | 1.004 | | 6 | .105 | .105 | 1.006 | | 7 | .122 | .123 | 1.008 | | 8 | .139 | .141 | 1.010 | | 9 | .156 | .158 | 1.012 | | 10 | .174 | .176 | 1.015 | | 11 | .191 | .194 | 1.019 | | 12 | .208 | .213 | 1.022 | | 13 | .225 | .231 | 1.026 | | 14 | .242 | .249 | 1.031 | | 15 | .259 | .268 | 1.035 | | 16 | .276 | .287 | 1.040 | | 17 | .292 | .306 | 1.046 | | 18 | .309 | .325 | 1.051 | | 19 | .326 | .344 | 1.058 | | 20 | .342 | .364 | 1.064 | | 21 | .358 | .384 | 1.071 | | 22 | .375 | .404 | 1.079 | | 23 | .391 | .424 | 1.086 | | 24 | .407 | .445 | 1.095 | | 25 | .423 | .466 | 1.103 | | 26 | .438 | .488 | 1.112 | | 27 | .454 | .510 | 1.122 | | 28 | .469 | .532 | 1.133 | | 29 | .485 | .554 | 1.143 | | 30 | .500 | .577 | 1.155 | | 31 | .515 | .601 | 1.167 | | 32 | .530 | .625 | 1.179 | | 33 | .545 | .649 | 1.192 | | 34 | .559 | .675 | 1.206 | | 35 | .574 | .700 | 1.221 | | 36 | .588 | .727 | 1.236 | | 37 | .602 | .754 | 1.252 | | 38 | .616 | .781 | 1.269 | | 39 | .629 | .810 | 1.287 | | 40 | .643 | .839 | 1.305 | | 41 | .656 | .869 | 1.325 | | 42 | .669 | .900 | 1.346 | | 43 | .682 | .933 | 1.367 | | 44 | .695 | .966 | 1.390 | | 45 | .707 | 1.000 | 1.414 | | 46 | .719 | 1.036 | 1.440 | | 47 | .731 | 1.072 | 1.466 | | 48 | .743 | 1.111 | 1.494 | | 49 | .755 | 1.150 | 1.524 | | 50 | .766 | 1.192 | 1.556 | | 51 | .777 | 1.235 | 1.589 | | 52 | .788 | 1.280 | 1.624 | | 53 | .799 | 1.327 | 1.662 | | 54 | .809 | 1.376 | 1.701 | | 55 | .819 | 1.428 | 1.743 | | 56 | .829 | 1.483 | 1.788 | | 57 | .839 | 1.540 | 1.836 | | 58 | .848 | 1.600 | 1.887 | | 59 | .857 | 1.664 | 1.942 | | 60 | .866 | 1.732 | 2.000 | | 61 | .875 | 1.804 | 2.063 | | 62 | .883 | 1.881 | 2.130 | | 63 | .891 | 1.963 | 2.203 | | 64 | .899 | 2.050 | 2.281 | | 65 | .906 | 2.145 | 2.366 | | 66 | .914 | 2.246 | 2.459 | | 67 | .921 | 2.356 | 2.559 | | 68 | .927 | 2.475 | 2.669 | | 69 | .934 | 2.605 | 2.790 | | 70 | .940 | 2.747 | 2.924 | | 71 | .946 | 2.904 | 3.072 | | 72 | .951 | 3.078 | 3.236 | | 73 | .956 | 3.271 | 3.420 | | 74 | .961 | 3.487 | 3.628 | | 75 | .966 | 3.732 | 3.864 | | 76 | .970 | 4.011 | 4.134 | | 77 | .974 | 4.331 | 4.445 | | 78 | .978 | 4.705 | 4.810 | | 79 | .982 | 5.145 | 5.241 | | 80 | .985 | 5.671 | 5.759 | | 81 | .988 | 6.314 | 6.392 | | 82 | .990 | 7.115 | 7.185 | | 83 | .993 | 8.144 | 8.206 | | 84 | .995 | 9.514 | 9.567 | | 85 | .996 | 11.430 | 11.474 | | 86 | .998 | 14.301 | 14.336 | | 87 | .999 | 19.081 | 19.107 | | 88 | .999 | 28.636 | 28.654 | | 89 | .999 | 57.290 | 57.299 | | 90 | 1.000|infinite.| ———— | +--------+------+---------+--------+

_GUNS.—Calibers of English and Foreign Guns, expressed in English Inches._

+---------+---------+---------+---------+---------+---------+ |English. | French. | Spanish | Dutch. | Russian.| Portug. | +---------+---------+---------+---------+---------+---------+ |Pr. Inch.|Pr. Inch.|Pr. Inch.|Pr. Inch.|Pr. Inch.|Pr. Inch.| |42 |7.018| — | — | — |— | — | — |36 |6.86 |48 |7.49 | |32 |6.41 |36 |6.9 |36 |6.84 |32 |6.4 |30 |6.47 |36 |6.8 | |24 |5.823|24 |6.03 |24 |6.03 |24 |5.92 |24 |6. |24 |5.93 | |18 |5.292|16 |5.26 |18 |5.52 |18 |5.45 |18 |5.45 |18 |5.4 | |12 |4.623|12 |4.78 |12 |4.8 |12 |4.76 |12 |4.76 |12 |4.7 | | 9 |4.200| 8 |4.18 | 9 |4.2 | 8 |4.13 | 8 |4.17 | 9 |4.3 | | 6 |3.668| — | — | — | — | 6 |3.78 | 6 |3.78 | 6 |3.75 | | 4 |3.204| 4 |3.315| — | — | — | — | — | — | — | — | | 3 |3.913| — | — | — | — | — | — | — | — | — | — | | 1 |2.019| — | — | — | — | — | — | — | — | — | — | +---------+---------+---------+---------+---------+---------+

_Length and Width of English Brass Guns._

+-----------------------+-----------------+-------------+ | Nature. | Length in | Weight. | +-----------------------+-----------------+-------------+ | |Calib’rs.|Ft. In.|Ct. qrs. lbs.| | 42 Pounders | 16.244 | 9 6 | 66 — — | | 32 ” | 18.721 |10 0 | 55 2 — | +----+------------------+-----------------+-------------+ | |Heavy | 19.574 | 9 6 | 53 0 9 | | |Medium | 16.483 | 8 0 | 41 3 2 | | 24 |Light | 10.302 | 5 0 | 16 3 13 | | | ” new | 13.000 | 6 3 | 24 0 — | +----+------------------+-----------------+-------------+ | 18 |Light ” | 13.000 | 5 9 | 18 0 — | +----+------------------+-----------------+-------------+ | |Heavy | 24.659 | 9 0 | 31 2 8 | | |Gen. Desagulier’s | 19.468 | 7 6 | 22 1 21 | | 12 |Medium, old | 16.872 | 6 6 | 21 3 — | | |Medium, new‡ | 16.872 | 6 6 | 18 — — | | |Light | 12.978 | 5 0 | 8 3 4 | | | ” new‡ | 13.000 | 5 0 | 12 — — | +----+------------------+-----------------+-------------+ | |Heavy | 26.112 | 8 0 | 19 1 6 | | |Gen. Desag. Med.‡ | 22.876 | 7 0 | 12 — 24 | | 6 |Med. new | 18.500 | 6 0 | 8 3 27 | | | ” reduced | 17.000 | 5 6 | 8 0 22 | | |General Belford’s‡| 16.342 | 5 0 | 5 2 21 | | |Light, common | 14.706 | 4 6 | 5 — 18 | +----+------------------+-----------------+-------------+ | |Heavy | 28.836 | 7 0 | 11 3 19 | | |Gen. Desagulier’s‡| 24.717 | 6 0 | 6 — — | | 3 |Light, common‡ | 14.418 | 3 6 | 2 2 27 | | |Light infantry | 12.358 | 3 0 | 1 3 16 | | |General Pattison’s| 12.358 | 3 0 | 1 2 19 | +----+------------------+-----------------+-------------+ | 1 | Pr. Amuzette | 29.7 | 5 0 | 2 2 12 | | | Do. | 35.6 | 6 0 | 3 0 11 | | | Do. | 41.5 | 7 0 | 3 1 12 | +----+------------------+-----------------+-------------+

NOTE. The guns marked (‡) are the only ones now used on general service.

_Length and Weight of French Brass Guns, in their own Weights and Measures._

+---------------------+-----------------------+------+ | Nature. | Length in |Weight| +---------------------+---------+-------------+------+ | |Calibers.| Ft. In. Li. | lbs. | | 24 Prs. Siege | — | 9 11 5 | 5628 | | 16 ” | — | 9 7 — | 4111 | +---------------------+---------+-------------+------+ | 12 ” Garrison | — | — — — | 3184 | | 8 ” | — | — — — | 2175 | +---------------------+---------+-------------+------+ | 12 ” | 18.0 | 6 6 — | 1808 | | 8 ” Field | 18. | 5 8 — | 1196 | | 4 ” | 18. | 4 6 — | 590 | +---------------------+---------+-------------+------+ | 1 ” | — | — — — | 266 | +---------------------+---------+-------------+------+

_Length and Weight of English Iron Guns._

+----------+-----------------+---------+---------------+ | | | | Proportion | | Nature. | Length in | Weight. | between shot | | | | | and gun.[8] | +----------+---------+-------+---------+---------------+ | |Calibers.|Ft. In.| Ct. Qr.| | | | | | | | | 42 Prs. | 17.098 | 10 — | 67 — | | | | 16.244 | 9 6 | 65 — | 170 | | | | | | | | 32 ” | 18.721 | 10 — | 58 — | | | | 17.725 | 9 6 | 55 — | 193 | | | | | | | | | 20.604 | 10 — | 52 — | | | 24 ” | 19.574 | 9 6 | 49 2 | 231 | | | 18.542 | 9 — | 47 2 | | | | | | | | | 18 ” | 21.542 | 9 6 | 42 — | | | | 20.408 | 9 — | 40 — | 249 | | | | | | | | | 24.659 | 9 6 | 34 — | | | 12 ” | 23.361 | 9 — | 32 — | | | | 22.063 | 8 6 | 31 2 | | | | 19.468 | 7 6 | 29 1 | 294 | | | | | | | | 9 ” | 21.4 | 7 6 | 24 2 | 305 | | | 19.9 | 7 — | 23 — | | | | | | | | | 6 ” | 26.2 | 8 — | 22 — | | | | 19.6 | 6 — | 16 2 | 411 | | | | | | | | 4 ” | 22.4 | 6 — | 22 1 | 343 | | | 20.6 | 5 6 | 11 1 | | | | | | | | | 3 ” | 18.6 | 4 6 | 7 1 | 270 | +----------+---------+-------+---------+---------------+

[8] This column expresses the number of pounds of metal in the guns, to each pound in the shot.

_French Iron Guns, in English Weights, &c._