Chapter 12 of 18 · 3948 words · ~20 min read

Part 12

_LEVELLING.—Table shewing the Difference between the True and Apparent Level._

+---------+----------+---------+-----------+ |Distance.|Difference|Distance.| Difference| | | of level.| | of level.| +---------+----------+---------+-----------+ | Yds. | Inches. | Mls. | Ft. In. | | | | | | | 100 | 0.026 | ¼ | 0 0½ | | 200 | 0.103 | ½ | 0 2 | | 300 | 0.231 | ¾ | 0 4½ | | 400 | 0.411 | 1 | 0 8 | | 500 | 0.643 | 2 | 2 8 | | 600 | 0.925 | 3 | 6 0 | | 700 | 1.260 | 4 | 10 7 | | 800 | 1.645 | 5 | 16 7 | | 900 | 2.081 | 6 | 23 11 | | 1000 | 2.570 | 7 | 32 6 | | 1100 | 3.110 | 8 | 42 6 | | 1200 | 3.701 | 9 | 53 9 | | 1300 | 4.344 | 10 | 66 4 | | 1400 | 5.038 | 11 | 80 3 | | 1500 | 5.784 | 12 | 95 2 | | 1600 | 6.580 | 13 | 112 2 | | 1700 | 7.425 | 14 | 130 1 | | | | 15 | 150 | | | | 16 | 175 | +---------+----------+---------+-----------+

This table will answer several useful purposes.

FIRST.—_To find the height of the apparent level above the true, at any distance._—If the given distance be contained in the table, the correction of level is found in the same line with it; but if the exact distance be not found in the table, then multiply the square of the distance in yards, by 2.57, and divide by 1,000,000, or cut off 6 places on the right, for decimals; the rest are inches: or multiply the square of the distance in miles, by 66 feet 4 inches, and divide by 100.

SECOND.—_To find the extent of the visible horizon, or how far can be seen from any given height, on a horizontal plane, as at sea_, &c.—The height of the observer’s eye above the horizon being known, the extent of his visible horizon is found in the column opposite, under the word _Distances_.

THIRD.—_To find the distance of any object when it first comes in sight, its height being, known._—For the distance of any object will be the extent of the visible horizon of the observer, added to the visible horizon of the point he observes. It is necessary in this case for the observer to know only the height of that part of the object which is kept from his view, by the curvilinear figure of the globe.—Knowing the distance of an object, its height may be found in the same manner.

If the height or distance exceed the limits in the table; then, first, if the distance be given, divide it by 2, 3 or 4, till the quotient comes within the distances in the table; then take out the height answering to the quotient, and multiply it by the square of the divisor for the height required. But when the height is given, divide it by one of these square numbers, 4, 9, 16, 25, &c. till the quotient come within the limits of the table, and multiply the quotient by the square root of the divisor.

_LOAD._—Artillery carriages, or waggons, are frequently loaded with 14 cwt. for 3 horses, and 20 cwt. for 4 horses. This, however it may answer on an English road, is a great deal too much for general service. No doubt a carriage of one construction will travel easier than of another, with the same weight; and where the mechanical advantage thus gained is greatest, the heaviest weight may be put, with the same number of horses; but in the carriages usually made for the service of artillery, 4 cwt. _per_ horse, beside the weight of the carriage, is the utmost they ought to be allowed to draw.

The French ammunition waggons, which are drawn by 4 horses, are always charged with 1200 pounds only.

The regulations for home service in 1798 state the load for a bread waggon at 2400 lbs. and for a cart of entrenching tools at 400 lbs. Men used to bear loads, such as porters, will carry from 150 to 250 pounds.

A horse will carry about 300 lbs. and a mule about 250 lbs.—See also the word _Horses_.

_MAGAZINES._—The present practice is not to make large powder magazines for batteries, but to disperse the barrels of powder, or cartridges _here_ and _there_ in small magazines, about 6 or 7 fathoms, in the rear of the battery; as it appears better to loose a small quantity from time to time, than to run the risk of the whole being destroyed, by a single shell falling into the magazine. These small magazines or entrenchments, will hold about one or two tons of powder; and are about 8 or 9 feet square. They ought to be well covered from the fire of the place, and always in the rear of one of the merlons. When they cannot be sunk in the ground, they should be secured by sand bags or gabions. They should be made with attention, as should the communication from them to the battery. Two magazines of this kind will be required for a battery of six pieces.

_Permanent Powder Magazines._—According to Vauban’s plan, powder magazines are commonly made 10 fathoms long, and 25 feet wide, in the clear. The foundation of the longest sides, is 9 or 10 feet thick, and 6 feet or more deep, according to the nature of the ground. The side walls raised upon these are 8 or nine feet thick; and if there is not to be an upper story, 8 feet will be sufficient height above the foundation. By this means the flooring maybe raised above the ground, free from damp, and there will remain 6 feet from the floor to the spring of the arch. The arch is formed of layers of bricks, arched one over the other, and ought to be 3 feet thick at the top. The exterior surface of the arch terminates with, an angle at top, like a roof; which angle must be of such magnitude as to make a thickness of 8 feet over the key stone of the arch. The foundation at the gable ends is 5 feet thick, and the same depth as the sides; these ends are built up 4 feet thick, from the foundation to the top of the roof. The long sides are supported by counterforts, 6 feet thick and 4 feet long; and placed 12 feet asunder. The ventilators are placed, one in the centre of each space between the counterforts, and are made with a die across them of 1½ feet. These ventilators are also closed with plates of iron. The magazine is lighted by a window in each end, high up, which are opened and shut by means of a ladder. These windows are secured, each by two shutters, made of plank 2 or 3 inches thick; and the outer one covered with sheet iron, and both fastened with strong bolts. The entrance to the is closed by two doors, one of which opens inwards, and the other outwards; the outward one is covered with sheet iron. The entrance of the magazine should, if possible, be placed towards the south. A wall of 1½ feet thick, and 10 feet high, is built round the magazine, at 12 feet distance. A magazine of the above dimensions will contain about 94,800 lbs. of powder, in piles of 3 barrels each; for a greater number piled above each other destroys the barrels, damages the powder, and occasions accidents.

_MATCH._—The slow match used by the English is made by contract: one yard of it will burn about 8 hours. The French slow match is usually made by soaking light twisted white rope for three days in a strong lye. It burns about 3 feet in 6 hours.

Slow match was made at Gibraltar, during the last siege, in the following manner: eight ounces of saltpetre were put into a gallon of water, and just made to boil over a slow fire; strong blue paper was then wetted with the liquor, and hung to dry. When dry, each sheet was rolled up tight, and the outward edge pasted down, to prevent its opening; half a sheet, thus prepared, will burn 3 hours.

_Quick Match._

_Compositions._

_Worsted Match._ Worsted 10 oz. Mealed powder 10 lbs. Spirits of wine 3 pints. Water 3 ” Isinglass ½ pint.

_Cotton Match._ Cotton 1 lb 12 oz. Saltpetre 1 8 Mealed powder 10 — Spirits of wine 2 quarts. Water 3 pints.

The worsted or cotton must be laid evenly in an earthen or other pan, and the different ingredients poured over it, and about half the powder: being left a short time to soak, it is afterwards wound smoothly on a reel, and laid to dry, remaining half of the powder is then sifted over it; and it is ready for use when dry.

=Note.= The French have lately made their slow match by soaking the rope in a solution of sugar of lead and rain water: in the proportion of ¾ of an ounce of sugar of lead to one pint of water; and this, they esteem as preferable to the old sort.

_MARCHING._—_The Quick step_, 108 paces _per_ minute, each of 30 inches; making 270 feet _per_ minute.

_Wheeling Step_, 120 _per_ minute, of 30 inches each; making 300 feet _per_ minute.

_Side Step._—12 inches—75 _per_ minute.

_Ordinary Step._—75 _per_ minute, 30 inches each.

DUNDAS.

The usual rate of marching for cavalry is 17 miles in 6 hours; but this may be extended to 21, or even 28 miles in that time.

D’ANTONI.

_Rates to be paid for Carriages on the March._

One shilling _per_ mile { with 5 horses, or for every carriage { with 6 oxen, or { with 4 oxen and 2 horses;

Nine pence _per_ mile for any cart with 4 horses, and so in proportion for less carriages; or a further sum, not exceeding 4d _per_ mile for every carriage with 5 horses, or with 6 oxen, or with 4 oxen and 2 horses; or 3d _per_ mile for every cart with 4 horses; and so in proportion for less carriages, as the same shall be fixed and ordered by the justices of the peace. The waggons, &c. not to carry more than 30 cwt.

_Regular_ ferries are only to be paid for on the march at half the ordinary rate.

_Mutiny Act._

_Marching Money._—Innkeepers are obliged to furnish troops on the march with diet and small beer, for the day of their marching in, and two days afterwards; unless one of the two days be a market day. For which the publican by the King’s warrant, 17th of March, 1800, is to receive 16d, and which is paid in the following manner:

Paid by Government, Cavalry 9d. Infantry 11d. ” by the soldier ” 6d. ” 4d. Soldiers beer money ” 1d. ” 1d. —— —— Total 16 16

_MEASURES._

_Long Measure._

12 Inches make 1 Foot. 3 Feet ” 1 Yard. 5½ Yards ” 1 Pole, or perch. 40 Poles ” 1 Furlong. 8 Furlongs ” 1 Mile. 4 Inches ” 1 Hand. 6 Feet ” 1 Fathom, or toise. 3 miles ” 1 League. 60 Nautical, or } geographical miles, or } ” 1 Degree. 69½ statute miles. }

_Square Measure._

144 Square inches make 1 Square foot. 9 Square feet ” 1 Square yard. 30¼ Square yards ” 1 Square pole. 40 Square poles ” 1 Square rood. 4 Square roods ” 1 Square acre.

_Solid, or Cubic Measure._

1728 Cubic inches make 1 Cubic foot. 27 Cubic feet ” 1 Cubic yard. 251 Cubic inches ” 1 Gallon, wine measure. 281 ” ” ” 1 Gallon, beer measure. 168⅗ ” ” ” 1 Gallon, dry measure.

_Dry Measure._

8 Pints make 1 Gallon. 2 Gallons ” 1 Peck. 4 Pecks ” 1 Bushel. 4 Bushels ” 1 Coom. 2 Cooms ” 1 Quarter. 5 Quarters ” 1 Wey. 2 Weys ” 1 Last.

_Avoirdupois Weight._

16 Drams make 1 Ounce. 16 Ounces ” 1 Pound. 25 Pounds ” ¼ of a hundred. 4 Quarters ” 1 Hundred. 20 Hundred ” 1 Ton. 14 Pounds ” 1 Stone.

_French Weights and Measures._

The toise is commonly used in France for military purposes, and is divided into 6 feet: each foot 12 inches; each inch 12 lines; each line 12 points. The pace is usually reckoned at 2½ feet.

_Poids de Mare_, ou _de Paris_.

24 Grains make 1 Den’r. 3 Den’rs ” 1 Gros. 8 Gros ” 1 Ounce. 8 Ounces ” 1 Marc. 2 Marcs ” 1 Pound.

The French have lately formed an entire new system of weights and measures: the following short account of them, and their proportion to the old weights and measures of France, and those of English standard, is extracted from _Nicholson’s Nat. Philosophy_.

_Reduction of the old French Weights and Measures to English; and the contrary._

1st. To reduce English Avoirdupois to Paris weight: The avoirdupois pound of 16 } ounces, or 7000 troy grains. = 8538 } Paris grains. The ounce = 533.6250 }

2d. To reduce Paris running feet or inches into } English, multiply by } ” ” English running feet or inches into} 1.065977 Paris, divide by }

3d. To reduce Paris cubic feet or inches into } English, multiply by } ” ” English cubic feet or inches into } 1.211278 Paris, divide by }

4th. To reduce the Paris pint to the English, } multiply by } ” ” the English pint to the Paris, } 2.0171082 divide by } LAVOISIER CH.

_German Measures._—The Rhinland rood is the measure commonly used in Germany and Holland, and in most of the northern states, for all military purposes. It is divided into 12 feet. The Rhinland rood is sometimes divided into tenths, or decimal feet, and the pace is made equal to 2 decimal feet, or ²/₁₀ of a rood.

_Proportion between the English Weights and Measures, and those of the principal Places in Europe._

+===========+================+=================+ | Places. | Foot in Parts. | Pound in Parts. | +-----------+----------------+-----------------+ |London | 1000 | 100 | |Paris | 1068 | 108 | |Amsterdam | 942 | 93 | |Rhinland | 1033 | 96 | |Antwerp | 946 | 98 | |Lovaine | 958 | 98 | |Middleburgh| 991 | 98 | |Strasburgh | 920 | 93 | |Bremen | 964 | 96 | |Cologne | 954 | 97 | |Frankfort | 948 | 93 | |Leipsig | — | 117 | |Hamburg | — | 95 | |Venice | 1153 | 151 | |Prague | 1026 | 106 | |Copenhagen | 965 | 94 | |Nuremburgh | 1006 | 94 | |Bavaria | 954 | — | |Vienna | 1053 | 83 | |Madrid | 1001 | 99 | |Toledo | 899 | 100 | |Bologne | 1204 | 127 | |Naples | 861 | — | |Florence | — | 123 | |Genoa | — | 142 | |Mantua | 1569 | 143 | |Turin | 1062 | — | |Dantzig | 944 | 119 | +===========+================+=================+

_Measures_—for gunpowder.

_Diameters and Heights of Cylindric Powder Measures, holding from 1 to 15 Ounces._

+======+=======+=======+=======+=======+=======+=======+ |Ounces| 0 | 1 | 2 | 3 | 4 | 5 | +------+-------+-------+-------+-------+-------+-------+ | 0 | 0 | 1.256 | 1.583 | 1.811 | 1.994 | 2.148 | +------+-------+-------+-------+-------+-------+-------+ | 1 | 2.706 | 2.793 | 2.876 | 2.953 | 3.027 | 3.098 | +======+=======+=======+=======+=======+=======+=======+

_Diameters and Weights of Cylindric Powder Measures, holding from 1 to 15 Pounds._

+=========+=======+=======+=======+=======+=======+=======+ | Pounds. | 0 | 1 | 2 | 3 | 4 | 5 | +---------+-------+-------+-------+-------+-------+-------+ | 0 | 0 | 3.165 | 3.988 | 4.565 | 5.024 | 5.412 | +---------+-------+-------+-------+-------+-------+-------+ | 1 | 6.890 | 7.039 | 7.245 | 7.442 | 7.628 | 7.805 | +=========+=======+=======+=======+=======+=======+=======+

The above are in inches and decimals.

_MECHANICS._—The whole momentum or quantity of force of a moving body, is the result of the quantity of matter, multiplied by the velocity with which it is moved; and when the product arising from the multiplication of the particular quantities of matter in any two bodies, by their respective velocities are equal, their momentum will be so too. Upon this easy principle depends the whole of mechanics; and it holds universally true, that when two bodies are suspended on any machine, so as to act contrary to each other; if the machine be put in motion, and the perpendicular ascent of one body multiplied into its weight, be equal to the perpendicular descent of the other, multiplied into its weight: those bodies, how unequal soever in their weights, will balance each other in all situations: for, as the whole ascent of the one is performed in the same time as the whole descent of the other, their respective velocities must be as the spaces they move through; and the excess of weight in one is compensated by the excess of velocity in the other. Upon this principle it is easy to compute the power of any engine, either simple or compound; for it is only finding how much swifter the power moves than the weight does, (_i. e._ how much further in the same time,) and just so much is the power increased by the help of the engine.

The simple machines usually called mechanic powers, are six in number, _viz._ the _Lever_, the _Wheel and Axle_, the _Pulley_, the _Inclined Plane_, the _Wedge_, and the _Screw_.

There are four kinds of _Levers_: 1st, Where the prop is placed between the weight and the power. 2d, Where the prop is at one end of the lever, the power at the other, and the weight between them. 3d, Where the prop is at one end, the weight at the other, and the power applied between them. 4th, The bended lever, which differs from the first in form, but not in property.

In the first and 2d kind, the advantage gained by the lever, is as the distance of the power from the prop, to the distance of the weight from the prop. In the 3d kind, that there may be a balance between the power and the weight, the intensity of the power must exceed the intensity of the weight, just as much as the distance of the weight from the prop exceeds the distance of the power from the prop. As this kind of lever is disadvantageous to the moving power, it is seldom used.

_Wheel and Axle._—Here the velocity of the power is to the velocity of the weight, as the circumference of the wheel is to the circumference of the axle.

_Pulley._—A single pulley, that only turns on its axis, and does not move out of its place, serves only to change the direction of the power, but gives no mechanical advantage. The advantage gained in this machine, is always as twice the number of _moveable_ pullies; without taking any notice of the _fixed_ pullies necessary to compose the system of pullies.

_Inclined Plane._—The advantage gained by the inclined plane, is as great as its length exceeds its perpendicular height. The force wherewith a rolling body descends upon an inclined plane, is to the force of its absolute gravity, as the height of the plane is to its length.

_Wedge._—This may be considered as two equally inclined planes, joined together at their bases. When the wood does _not_ cleave at any distance before the wedge, there will be an equilibrium between the power impelling the wedge, and the resistance of the wood acting against its two sides; when the power is to the resistance, as half the thickness of the wedge at the back, is to the length of either of its sides; because the resistance then acts perpendicular to the sides of the wedge: but when the resistance on both sides acts parallel to the back, the power that balances the resistance on both sides will be, as the length of the whole back of the wedge is to double its perpendicular height. When the wood cleaves at any distance before the wedge, (as it generally does) the power impelling the wedge will be to the resistance of the wood, as half the length of the back is to the length of either of the sides of the cleft, estimated from the top, or acting part of the wedge.

_Screw._—Here the advantage gained is as much as the circumference of a circle described by the handle of the winch, exceeds the interval or distance between the spirals of the screw.

There are few compound engines, but what, on account of the friction of parts against one another, will require a third part more power to work them when loaded, than what is required to constitute a balance between the power and the weight.

FERGUSON’S _Nat. Philosophy_.

_MILE._—Comparison of the different miles, in geometric paces, each of which is equal to 5 feet French royal, 5.6719 feet Rhinland, or 6.1012 English feet.

The mile of Sweden = 5761 geometric paces. ” ” ” Switzerland 4512 ” ” ” Denmark 4071 Common, of Germany 4000 ” ” Holland 3158 League of France 2400 ” ” Spain 2286 ” ” Scotland 1500 Mile of Italy 1000 ” ” England 868 Werste of Russia 575