PART XII.
MATHEMATICS.
Characters, Marks, or Signs 265
REDUCTION 265
RULE OF THREE, OR SIMPLE PROPORTION 266
FRACTIONS 267
Reduction 268
Addition. Subtraction. Multiplication. Division 269
Rule of Three 270
DECIMALS.—Addition 270
Subtraction. Multiplication. Division 271
Reduction 272
Rule of Three 273
DUODECIMALS 273
TABLES OF WEIGHTS, AND MEASURES; English, and French 274
INVOLUTION, or Raising of powers 277
EVOLUTION, or Extracting roots 277
TABLE OF SQUARES, CUBES, AND ROOTS 280
PILING OF SHOT, AND SHELLS 281
To find the number of balls in a complete pile 281
number of balls in any pile, base not exceeding 21 282
in an incomplete pile 283
Table for computing the content of piles 284
CORDAGE.—To find weight, and strength of a rope 285
CHAINS.—To find the weight of chains 285
To find the weight that may be lifted by a chain 286
IRON RODS.—To find the weight of round, and square iron rods 286
To find the weight that may be sustained, or lifted, by round iron rods 286
TIMBER.—To find the area of a plank 287
content of timber 287
weight of a tree 287
TONNAGE.—Table of tonnage, and weight of carriages 288
To ascertain the tonnage of Sailing vessels 289
of Steam vessels 289
MECHANICS.—Mechanical powers 290
The Lever 291
The Wheel, and Axle 292
The Pulley. Tackles 293
Combination of pulleys 294
The inclined plane 295
The Wedge. The Screw 296
Compound machines 297
Friction. Unguents 298
Transverse strength of materials 299
Adhesion of Nails, and Screws 300
TRIGONOMETRY.—Definitions 301
Methods of resolving Triangles 301
Useful theorems, and corollaries 302
TRIGONOMETRY WITHOUT LOGARITHMS 303
Trigonometric ratios. Natural sines, and cosines 304
Application of trigonometry without logarithms 305
Table,—showing the reduction in feet, &c., upon 100 feet, at angles of elevation, and depression 306
Table, showing the rate of inclination of inclined planes, for angles of elevation 307
SURVEYING, AND RECONNOITRING.—HEIGHTS, AND DISTANCES 307
Methods of ascertaining Heights 307
1. By means of a pocket sextant 307
2. ” a portable barometer, and thermometer 308
3. ” the Reconnoitring protractor 308
4. By the shadow of the object 310
5. Where there is no shadow 310
6. By the tangent scale of a gun 310
7. By means of two pickets 310
Methods of ascertaining Distances 311
1. By means of the sextant 311
2. ” a pocket sextant 311
3. ” the prismatic compass 312
4. ” the Reconnoitring protractor 312
5. 6, 7, & 8. Pickets 312–4
9. ” the tangent scale of a gun 314
10. ” the peak of a cap 314
11. ” the report of fire-arms 314
To traverse Roads— By means of the Reconnoitring protractor, or other instrument 315
SOUND.—Velocity of, &c. 315
To ascertain the distance, by the report of fire-arms 316
GRAVITY 316
Specific gravities of bodies 317
To find the magnitude, weight, or specific gravity of a body, or a fluid 318
Quantities of two ingredients in a compound 319
Diameter of a sphere, or globule 319
Table showing the weight of a cubic foot of materials 319
MOTION, FORCES, ETC. Body 319
Density. Velocity. Momentum. Force. Gravity 320
Momentum. Amplitude. Time of flight. Time of descent 321
PRACTICAL GEOMETRY. Definitions 322
To divide a line into two equal parts. To bisect an angle 324
To erect a perpendicular. To let fall a perpendicular 324
To draw a line parallel to a given line 324
To divide an angle 324
To find the centre of a circle 325
To describe an equilateral triangle, a square 325
To inscribe a square in a circle 325
” an octagon in a circle 325
On a line to describe all the polygons 325
To inscribe in a circle an equilateral triangle 325
” a hexagon, or a dodecagon 326
To inscribe a pentagon, hexagon, or decagon, in a circle 326
To find the angles at the centre, and circumference of a polygon 326
To inscribe a polygon in a circle 326
To circumscribe a circle about a triangle, or a square 327
” a square about a circle 327
To reduce a Map, or Plan 327
MENSURATION OF PLANES 327
To find the area of a parallelogram 327
” of a triangle 328
” of a trapezium, or of a trapezoid 329
” of an irregular figure 329
” of a figure, having a part bounded by a curve 329
To measure long irregular figures 330
To find the number of square acres, &c. in preceding figures 330
” the area of a regular polygon 330
” diameter, and circumference of a circle 331
” the area of a circle 331
” the area of a circular ring 332
” the length of any arc 332
” the area of a sector 332
” of a segment, of a semicircle 333
” of an ellipsis, of a parabola, &c. 333
MENSURATION OF SOLIDS.—Definitions 334
To find the superficies of a prism, or cylinder 334
” surface of a pyramid, or cone 335
” surface of the frustrum of a pyramid, or cone 335
” solid content of a prism, or cylinder 335
” content of the solid part of a hollow cylinder 336
” solidity of the frustrum of a cylinder 336
” content of a pyramid, or cone 336
” solidity of the frustrum of a cone, or pyramid 336
” surface of a sphere, or any segment 337
” solidity of a sphere, or globe 337
” ” hemisphere 337
” solid content of a spherical segment 337
” diameter of a sphere 338
” weight of an iron shot 338
” weight of a leaden ball 338
” diameter of an iron shot 338
” diameter of a leaden ball 339
” weight of an iron shell 339
” quantity of powder a shell will contain 339
” size of a cubical box to contain powder 340
” quantity of powder to fill the chamber of a mortar, or howitzer 340
” quantity of powder to fill a rectangular box 340
” quantity of powder to fill a cylinder 340
” size of a shell to contain a given weight of powder 341
” length of a cylinder, or bore of a gun to be filled by a given weight of powder 341
To find the content, and weight of a piece of ordnance 341
” content of a cask 341
EPITOME OF MENSURATION 342
Of the Circle; Cylinder; Sphere, &c. 342
Of the Square; Rectangle; Cube, &c. 343
Table of the Surfaces, and Solidities of bodies 344
Of Triangles; Polygons, &c. 344
Table of the Areas of regular Polygons 345
Of Ellipses; Cones; Frustrums, &c. 345
PUBLICATIONS,
REFERRED TO, OR EXTRACTED FROM.
The Infantry Manual.
Field Exercise, and Evolutions of the Army.
Instruction of Musketry.
Bombardier, and Pocket Gunner {Captain Adye. {Major Elliott.
British Gunner Captain Spearman.
Artillery Mr. J. Landmann.
{Lieut.-General Sir H. Douglas, Bart. Naval Gunnery {Captain Stephens. {Lieut. Beauchant.
Instructions for the Exercise, and Service of Great guns, and Shells, on board Her Majesty’s ships.
Field battery Exercise, and Movements.
The Horse, with a treatise on draught.
Directions for the guidance of the Farriers of } the Royal Artillery } Mr. C. Percivall.
Instructions, and Regulations for the Service, and Management of Heavy Ordnance, &c.
Fortification {Lieut.-General Pasley. {Mr. J. Landmann.
{Mr. Lochée. Field fortification {Captain Malorti. {Captain Macaulay.
Military Surveying Lt.-Col. Basil Jackson.
Treatises on Attack, and Defence Lt.-Colonel Jebb.
Artificial fireworks Mr. G. Mortimer.
{Dr. Hutton. Mathematics {Dr. O. Gregory. {Mr. Trotter.
Practical Geometry Mr. J. Landmann.
Natural Philosophy Dr. Fergusson.
The practical Mechanic’s guide.
The practical Engineer’s guide.
The Engineer’s, and Contractor’s pocket-book
Tables Mr. Beardmore.
&c. &c. &c.
THE ARTILLERIST’S MANUAL, AND BRITISH SOLDIER’S COMPENDIUM.