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 | 1.46 | .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 | — |
| 24 | Heavy | 19.574 | 9 | 6 | 53 | 0 | 9 |
| Medium | 16.483 | 8 | 0 | 41 | 3 | 2 |
| Light | 10.302 | 5 | 0 | 16 | 3 | 13 |
| ” new | 13.000 | 6 | 3 | 16 | 3 | 13 |
| 18 | Light ” | 13.000 | 5 | 9 | 18 | 0 | — |
| 12 | Heavy | 24.659 | 9 | 0 | 31 | 2 | 8 |
| Gen. Desagulier’s | 19.468 | 7 | 6 | 22 | 1 | 21 |
| 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 | — | — |
| 6 | Heavy | 26.112 | 8 | 0 | 19 | 1 | 6 |
| Gen. Desag. Med.‡ | 22.876 | 7 | 0 | 12 | — | 24 |
| 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 |
| 3 | Heavy | 28.836 | 7 | 0 | 11 | 3 | 19 |
| Gen. Desagulier’s‡ | 24.717 | 6 | 0 | 6 | — | — |
| 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.