PART X.

BRIDGES, AND PONTOONS.—SCALING LADDERS.
Bridges.—To find number of planks to form a float[250]
To find number of casks to form a raft[250]
To find the number of Boats, or Pontoons required to support a given weight[250]
Pontoons.—Large pontoons[251]
Small pontoons[252]
Scaling Ladders[253]

PART XI.

FIREWORKS.
Candles, Roman, Blue. Crackers[254]
Earthquake, artificial. Fires of various colours. Wildfire. Gerbes[255]
Iron filings. Iron sand[256]
Leaders. Marroons. Mealing gunpowder. Paste for representing animals[257]
Portfires for illuminations. Rain, gold, or silver. Rockets, line[258]
Rockets, signal[259]
Saltpetre pulverized[260]
Serpents, or squibs. Shells. Showers of fire[261]
Speckie. Spur fire. Suns, or wheels[262]
Touch paper. Wheels, pin, or Catherine[264]

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]