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._
+---------------+-------------------+------------+
| Nature. | Length in | Weight. |
+---------------+----------+--------+------------+
| |Calibers. |Ft. In. |Ct. Qr. lbs.|
| | | | |
| 36 Pounders | 16.18 | 9 8 | 74 3 — |
+---------------+----------+--------+------------+
| 24 ” | 18.18 | 9 1½ | 51 — — |
+---------------+----------+--------+------------+
| | 21.01 | 9 7 | 42 — — |
| 16 ” | 18.45 | 8 4 | 43 2 — |
| | 16.92 | 7 8½ | 35 — — |
+---------------+----------+--------+------------+
| | 21.54 | 8 7 | 31 2 — |
| 12 ” | 20.5 | 8 2 | 20 3 — |
| | 17.14 | 6 10 | 28 — — |
+---------------+----------+--------+------------+
| 8 ” | 24.64 | 8 7 | 24 1 — |
| | 17.22 | 6 — | 16 — — |
+---------------+----------+--------+------------+
| 4 ” | 17.19 | 4 9 | — — — |
+---------------+----------+--------+------------+
_Ranges of Brass Guns, with one Shot. 1793._
+----------------------+--------+-------------------------------+
| | Charge |To the first graze of the Shot.|
| Nature. | +-----+----+----+----+----+-----+
| | |P. B.| 1° | 2° | 3° | 4° | 5° |
+----------------------+--------+-----+----+----+----+----+-----+
| | lb.oz. | Yds.|Yds.|Yds.|Yds.|Yds.|Yds. |
+----------------------+--------+-----+----+----+----+----+-----+
| Heavy | 8 0 | 473| 781|1032|1405|1585|1710 |
|24 Medium | 8 0 | 488| 757|1103|1425|1557|1745 |
| Light | 3 0 | 162| 364| 606| 722| |1390 |
+----------------------+--------+-----+----+----+----+----+-----+
| Heavy | | | | | | | |
|12 Medium | 4 0 | | 705| 973|1189| | |
| Light | 3 0 | | 601| 816|1063| | |
+----------------------+--------+-----+----+----+----+----+-----+
| Desagulier’s | 2 0 | | 646| 966|1325| | |
| 6 Feet | 2 0 | | 683| 948|1327| | |
| 6 5 : 6 Medi. | 2 0 | | 775|1003|1444| | |
| 5 : 6 Red’d. | 2 0 | | 642| 976|1150| | |
| 5 Feet | 1 8 | | 587| 825| 950| | |
| 4 : 6 Feet | 1 8 | | 628| 804| 991| | |
+----------------------+--------+-----+----+----+----+----+-----+
| 3 Desagulier’s | 1 0 | | 679| 883| 918| | |
| Ammuzette of 5 feet| 0 8 | | 604| 800| | | |
| ” of 7 feet| 0 8 | | 656| 830|1000| | |
+----------------------+--------+-----+----+----+----+----+-----+
_Ranges from Brass Guns, with Two Shot. 1793._
+-------------------+--------+----------+--------------------+
| Nature. |Charge. |Elevation.| Medium first Graze.|
+-------------------+--------+----------+----------+---------+
| |lbs. oz.| 1° 30′ | 1st Shot.| 2d Shot.|
| | | | | |
|12 Pounder, Medium | 4 — | 1 30 | 607 | 706 |
| 6 : Desagulier’s | 2 — | 1 30 | 621 | 739 |
| 6 : of 5 feet | 1 8 | 1 30 | 586 | 732 |
| 3 : Desagulier’s | 1 — | 1 30 | 523 | 638 |
+-------------------+--------+----------+----------+---------+
_Ranges from Brass Field Guns, with small Charges. 1798._
+-------+------+----------------------------------+------------------+
| | | First Graze with | |
|Nature.|Charge| different Elevations. | Extreme Range. |
+-------+------+---+---+---+---+---+----+----+----+------------------+
| | | 1°| 2°| 3°| 4°| 5°| 6° | 7° | 8° | |
+-------+------+---+---+---+---+---+----+----+----+------------------+
|12 Pr. |10 oz.|199|290|390|385|597| 716| 695| 788|From 800 to 1000.|
| | 1 lb.|280|416|729|777|966|1090|1054|1295|From 1200 to 1500.|
+-------+------+---+---+---+---+---+----+----+----+------------------+
| 6 Pr. | 5 oz.|111|222|376|432|618| 625| 650| 788|From 800 to 1000.|
| | 8 oz.|277|401|754|826|925| 980|1103|1100|From 1000 to 1300.|
+-------+------+---+---+---+---+---+----+----+----+------------------+
=N. B.= The above was a 12 Pr. Medium, and a 6 Pr. Desagulier’s. The
Distances are given in Yards.
_Effects of Case Shot from a Battalion Gun.—Light 6 Pr. Length 5
feet—Weight 5 cwt. 3 qrs. 21 lbs. against a Target 8 feet high, and 90
feet long._
+--------+-----------------+----------+------------+------------+
|Distance| | |Nᵒ. put |Nᵒ. put |
| of | | |into the |into the |
| Target.|Nature of Charge.|Elevation.|height of 6 |height of 8 |
| | | |feet, or the|feet, or the|
| | | |height of |height of |
| | | |_Infantry_. |_Cavalry_. |
+--------+-----------------+----------+------------+------------+
| Yards. | | Deg. | | |
| |12 Balls, 8 oz. | 1 | 3 | 3 |
| 500 | each, 3 in a | 1½ | 3 | 4 |
| | tier, 1¼ lb. | | | |
| | powder. | 2 | 3 | 4 |
+--------+-----------------+----------+------------+------------+
| | | 1 | 6 | 6 |
| 400 |Same Charge. | 1½ | 4 | 5 |
| | | 2 | 4 | 5 |
+--------+-----------------+----------+------------+------------+
| | | ½ | 6 | 7 |
| 300 |Same Charge. | 1 | 3 | 3 |
| | | 1½ | 4 | 6 |
+--------+-----------------+----------+------------+------------+
| |34 Balls, 3 oz. | P. B. | 10 | 12 |
| 400 | each, 7 in a | ½ | 9 | 10 |
| | tier, 1¼ lb. | 1 | 6 | 8 |
| | powder. | | | |
+--------+-----------------+----------+------------+------------+
| | | P. B. | 11 | 13 |
| 300 |Same Charge. | ½ | 12 | 15 |
| | | 1 | 7 | 9 |
+--------+-----------------+----------+------------+------------+
=N. B.= There were three rounds fired at each change, but they were all
so nearly alike that it has been thought necessary to put down only one
of them.—1802.
_Ranges with Sea Service Iron Guns. 1796._
+------------------------------------------------------------------+
| Nature of Guns 32, 24, and 18 Pounders. |
+----------+----------+------------------------------------+-------+
|Elevation.|Proportion| Nature of Shot. | Range.|
| |of powder.| | |
+----------+----------+------------------------------------+-------+
| Deg. | | |Yards. |
| 2 | ⅓ |With single Shot to the first graze.| 1200 |
| 2 | ¼ | Do. Do. | 1000 |
| 2 | ¼ |2 Shot, ranged close together, to | 500 |
| 4 | ⅓ |Single Shot | 1600 |
| 4 | ¼ | Do. | 1500 |
| 7 | ⅓ | Do. | 2150 |
| 7 | ¼ | Do. | 2020 |
+----------+----------+------------------------------------+-------+
| | |One round shot, and 1 round | |
| 2 | ¼ | of grape, will range with | 600 |
| | | effect together, to | |
+----------+----------+------------------------------------+-------+
| 4 | ¼ |One round of grape shot, alone, to | 1000 |
+----------+----------+------------------------------------+-------+
| | |One double headed, or bar shot, | |
| 2 | ¼ | will range to the first graze | 800 |
+----------+----------+------------------------------------+-------+
_Ranges with 5½ Inch Shells, from a 24 Pounder Iron Gun, Length of Gun
9½ Feet—Weight 49 ct. 26 lbs._
+----------+-----------------------++-----------------------+
| | 2 Pounds. || 2 lbs. 8 oz. |
| +-------+---------------++-------+---------------+
| | | Range to || | Range to |
|Elevation.|Flight.+------+--------+|Flight.+------+--------+
| | |First |Extreme.|| |First |Extreme.|
| | |Graze.| || |Graze.| |
+----------+-------+------+--------++-------+------+--------+
| Deg. | Sec. |Yards.| Yards. || Sec. |Yards.| Yards. |
| 1 | 1 | 213 | 1139 || 2¾ | 562 | 1456 |
| 2 | 1¾ | 384 | 1267 || 1½ | 442 | 1413 |
| 3 | 2¾ | 565 | 1413 || 2½ | 647 | 1553 |
| 4 | 2¼ | 750 | 1479 || 3¾ | 896 | 1639 |
| 5 | 3¾ | 836 | 1670 || 4 | 915 | 1510 |
| 6 | 4 | 896 | 1495 || 5 | 1140 | 1657 |
| 7 | 6½ | 1180 | 1492 || 6 | 1205 | 1481 |
| 8 | 6¾ | 1305 | 1526 || 6½ | 1259 | 1544 |
| 9 | 7½ | 1329 | 1527 || 7 | 1341 | 1561 |
| 9½ | 6¾ | 1229 | 1453 || — | —— | —— |
+----------+-------+------+--------++-------+------+--------+
| | 3 Pounds. |
| +-------+---------------+
| |Flight.| Range to |
|Elevation.| +------+--------+
| | |First |Extreme.|
| | |Graze.| |
+----------+-------+------+--------+
| Deg. | Sec. |Yards.| Yards. |
| 1 | 1 | 277 | 1424 |
| 2 | 1¾ | 526 | 1464 |
| 3 | 2¼ | 740 | 1600 |
| 4 | 3½ | 880 | 1679 |
| 5 | 5 | 1182 | 1733 |
| 6 | 6¼ | 1384 | 1787 |
| 7 | 6¼ | 1410 | 1749 |
| 8 | 7 | 1520 | 1744 |
| 9 | 7¾ | 1722 | 1938 |
| 9½ | 8½ | 1748 | 1881 |
+----------+-------+------+--------+
_Ranges with 4⅖ Shells from a 12 Pounder, Medium._
+----------+-----------------------++-----------------------+
| | 8 Ounces. || 12 Ounces. |
| +-------+---------------++-------+---------------+
|Elevation.|Flight.|First |Extreme ||Flight.|First |Extreme |
| | |Graze.| Range. || |Graze.| Range. |
+----------+-------+------+--------++-------+------+--------+
| Deg. | Sec. |Yards.| Yards. || Sec. |Yards.| Yards. |
| 1 | 1½ | 156 | || | | |
| 2 | 2 | 293 | || 2½ | 350 | |
| 3 | 2½ | 363 | From || 3½ | 355 | From |
| 4 | 3½ | 462 | 800 || 4 | 679 | 1100 |
| 5 | 4 | 587 | to || 3½ | 641 | to |
| 6 | 4 | 621 | 1200 || 5 | 941 | 1300 |
| 7 | 4½ | 898 | || 6 | 1020 | |
| 8 | 5 | 781 | || | | |
+----------+-------+------+--------++-------+------+--------+
| | 1 lb. 8 oz. |
| +-------+---------------+
|Elevation.|Flight.|First |Extreme |
| | |Graze.| Range. |
+----------+-------+------+--------+
| Deg. | Sec. |Yards.| Yards. |
| 1 | | | |
| 2 | | 707 | |
| 3 | | 758 | From |
| 4 | | 849 | 1400 |
| 5 | | 1075 | to |
| 6 | | 1150 | 1600 |
| 7 | | 1300 | |
| 8 | | | |
+----------+-------+------+--------+
_Ranges with French Brass Field Guns, with Round Shot._
+-------+----------+-----------------------+-------+
| | | Elevation. | |
| | +-------------+---------+ Range |
|Nature.| Charge. | Lines of | | in |
| | |Tangt. Scale.|Deg. Min.|Toises.|
+-------+----------+-------------+---------+-------+
| | | L. M. | — 58 | 300 |
| | | 2 | 1 3 | 350 |
| 12 Pr.| 4 lbs. | 10 | 1 39 | 400 |
| | | 14 | 1 49 | 450 |
| | | 16 | 1 56 | 480 |
+-------+----------+-------------+---------+-------+
| | | L. M. | — 58 | 300 |
| | | 6 | 1 24 | 350 |
| 8 Pr. | 2½ lbs. | 12 | 1 51 | 400 |
| | | 16 | 2 8 | 450 |
| | | 20 | 2 24 | 480 |
+-------+----------+-------------+---------+-------+
| | | L. M. | — 58 | 250 |
| | | 4 | 1 20 | 300 |
| | | 8 | 1 40 | 350 |
| 4 Pr. | 1½ lbs. | 12 | 2 — | 400 |
| | | 16 | 2 20 | 450 |
| | | 18 | 2 40 | 480 |
+-------+----------+-------------+---------+-------+
The above are in French weights and measures.
_GUNPOWDER.—Proportions of the different Ingredients for making
Gunpowder, by different Powers in Europe_:
+---------+------+--------+------+--------+--------+--------+
| | Eng. | France.| Swed.| Poland.| Italy. | Russia.|
+---------+------+--------+------+--------+--------+--------+
|Saltpetre| 75 | 75 | 75 | 80 | 76½ | 70 |
|Sulphur | 10 | 9½ | 9 | 8 | 12½ | 11½ |
|Charcoal | 15 | 15½ | 16 | 12 | 12½ | 18½ |
+---------+------+--------+------+--------+--------+--------+
| Pounds | 100 | 100 | 100 | 100 | 100 | 100 |
+---------+------+--------+------+--------+--------+--------+
_Proofs of Powder._—The first examination of powder in the king’s
mills, is by rubbing it in the hands to find whether it contains any
irregular hard lumps. The second is by blasting 2 drams of each sort
on a copper plate, and in this comparing it with an approved powder;
in this proof it should not emit any sparks, nor leave any beads or
foulness on the copper. It is then compared with an approved powder, in
projecting an iron ball of 64 lbs. from an 8 inch mortar, with a charge
of 2 ounces. The best cylinder powder generally gives about 180 feet
range, and pit 150; but the weakest powder, or powder that has been
redried, &c. only from 107 to 117 feet.
The merchants’ powder, before it is received into the king’s service,
is tried against powder of the same kind made at the king’s mills;
and it is received if it gives a range of ¹/₂₀ less than the king’s
powder with which it is compared. In this comparison both sorts are
tried on the same day, and at the same time, and under exactly the same
circumstances.
The proof of fine grained, or musquet powder, is with a charge of 4
drams from a musquet barrel, to perforate with a steel ball a certain
number of ½ inch wet elm boards, placed ¾ inch asunder, and the first
39 feet 10 inches from the barrel: the king’s powder generally passes
through 15 or 16, and restoved powder from 9 to 12. The last trial
of powder is by exposing about 1 pound of each sort, accurately
weighed, to the atmosphere for 17 or 18 days; during which time, if the
materials are pure, it will not increase anything material in weight,
by attracting moisture from the atmosphere.
In this exposure 100 lbs. of good gunpowder should not absorb more than
12 oz. or somewhat less than one per cent.
_Powder Marks._—The different sorts of powder are distinguished by the
following marks on the heads of the barrels.
--------+-------------+-----------------------
Nᵒ. ½ | |
L G | Cylinder |
--------+-------------+
Nᵒ. 2 | |
S G | Cylinder | Marked in Red.
--------+-------------+
Nᵒ. 3 | |
F G | Cylinder |
--------+-------------+-----------------------
S A—The dust from Nᵒ. 3, and F G cylinder.
R A—For rifle arms.
----------------------------------------------
⁴/₇ Cylinder mixed—Marked white L G.
³/₇ Restoved