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 | 1.80 | 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 | infi- nite. | —— |
Guns.—Calibres of European Guns, expressed in 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 weight of English Brass guns.
| Kind. | Length in | Weight. | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Calib. | ft. | in. | ct. | qr. | lb. | ||||||||
| 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 | |||||||
| Do. new | 13.000 | 6 | 3 | 24 | 0 | — | |||||||
| 18 | Light do. | 13.000 | 5 | 9 | 18 | 0 | — | ||||||
| 12 | - | Heavy | 24.659 | 9 | 0 | 31 | 2 | 8 | |||||
| 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 | |||||||
| * | Do. new | 13.000 | 5 | 0 | 12 | — | — | ||||||
| 6 | - | Heavy | 26.112 | 8 | 0 | 19 | 1 | 6 | |||||
| * | Desag’s. Med. | 22.876 | 7 | 0 | 12 | — | 24 | ||||||
| Med. | - | new | 18.500 | 6 | 0 | 8 | 3 | 27 | |||||
| reduced | 17.000 | 5 | 6 | 8 | 0 | 22 | |||||||
| * | Gen. 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 | |||||
| * | 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 | |||||||
| Gen. 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 | |||||||
The guns marked (*) are the only ones used by the British since 1795, on general service.
Length and weight of French brass guns, in their old weights and measures.[9]
| Kind. | Length in | W’t. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Calib. | ft. | in. | li. | lbs. | ||||||||
| 24 | Prs. | - | Siege | - | — | 9 | 11 | 5 | 5628 | |||
| 16 | — | — | 9 | 7 | — | 4111 | ||||||
| 12 | — | - | Garrison | - | — | — | — | — | 3184 | |||
| 8 | — | — | — | — | — | 2175 | ||||||
| 12 | — | - | Field | - | 18.0 | 6 | 6 | — | 1808 | |||
| 8 | — | 18. | 5 | 8 | — | 1196 | ||||||
| 4 | — | 18. | 4 | 6 | — | 590 | ||||||
| 1 | — | — | — | — | — | 266 | ||||||
[9] The French weights and measures have assumed new names, and are reduced to strict proportions since the revolution. The weights here referred to are the old. For the new French system of weights and measures, see the word [Weights].