Rates to be paid for Carriages on the March.

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.

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:

MEASURES.

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.

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.

• (A) = Proportion of the principal measures between themselves and
• the length of the Meridian.
• (B) = Value of the principal measures in the ancient French measures.
• (C) = Value in English measures.

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

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.

Measures—for gunpowder.

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

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

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.

MINE.—The excavation formed by the blowing up of a mine is found by experiment to be nearly a paraboloid. It was formerly supposed that the diameter of the entonnoir, or excavation, was always equal to only double the line of least resistance; but experiments have proved, that the diameter of the excavation may be increased to six times the line of least resistance; and that the diameter of the globe of compression may be increased to eight times that line; this is called the maximum of a mine, or the greatest effect that can be produced by a globe of compression. In any mine intended to produce an effect within this extent, the effects will be nearly as the charges.

The globes are to each other as the cubes of their radii. Their radii are the hypothenuses of rightangled triangles, of which the line of least resistance, and the semi-diameter of the excavation, are the other two sides. Therefore, to find the charge to produce any required diameter of the excavation, the following will be the rule, the radius being found as above:

Table for the Charges of Mines,
according to Valiere.

This table is calculated upon a supposition that the excavation of the mine is a paraboloid, having a base double the line of least resistance; and that 10 lbs. 10 oz of powder is sufficient for raising one cubic fathom of earth, by making the line of least resistance of the required globe only equal to the radius of the globe of compression.

The charges thus found by means of this table, being only for one nature of soil; viz. light earth and sand, (that for which the table is calculated) must be augmented according to the following table of Vauban’s, by one, four, five, seven, or nine elevenths of the charge found.

Table of the Quantity of Powder
required to raise a Cubic Fathom,
according to the Soil.

The following rule is however laid down by Belidor, and generally adopted, if it be intended that the mine shall produce its maximum or greatest effect: Multiply the line of least resistance, expressed in feet, by 300, the product will be the charge in pounds.

In making mines of any kind, the following remarks may be of service.

The best form for the chamber would be spherical; but from the difficulty of its construction, it is always made a cube, of one inch larger dimensions than the box to contain the powder.

The chamber must not be made in the prolongation of the branch of the mine, but at one side, and lower than the level of the branch, if the soil be dry; but higher if it be wet.

One cubic foot will contain 75 lbs. of powder; upon which principle the size of the case to contain the powder must be regulated. The auget is generally one inch square interior dimensions, and the end of it must reach the centre of the chamber; where the saucisson must be fastened, to prevent its being easily pulled out.

The branch of the mine to be sprung must be closed in the strongest manner by doors well secured by props, and must be stopped with earth or rubbish to a distance, taken in a straight line, equal to 1½ times the line of least resistance.

In proportioning the length of saucisson, in order that any number of mines may be fired at the same instant, a return of a right angle is generally reckoned equal to 4 inches in a right line.

The first step in making a mine, whether for attack or defence, is to sink a shaft to the depth of the bottom of the gallery, having two of its sides in the direction of the sides of the gallery. These shafts should be where the galleries are to cross each other, or in the centre of the length of gallery to be made. These shafts should never be further apart than 40 or 50 fathoms; for it is found, that the air is not fit for respiration in the larger galleries at a greater distance from the shaft than 25 fathoms; at 20 fathoms in those of medium dimensions; and at 15 in the smallest.

The rectangular frames used in sinking a shaft are commonly placed 4 feet asunder; and in the galleries they are only 3 feet. A gallery intended to be lined with masonry, must be 7 feet high, and 6 feet wide, in order that it may be, when finished, 6 feet high, and 3 feet wide.

Temporary galleries are only made 4½ feet high, and 2½ or 3 feet wide.

The branches, at the ends of which the chambers are to be placed, are only made 2½ or 3 feet high, and 2 feet, or 2 feet 3 inches wide.

The first of these is dug on the knees; the second sitting or lying.

The miners are divided into brigades of 4 each; and the rate of work for each brigade is 3 feet of the temporary gallery in 4 hours. The first brigade is relieved by a second, after having worked 4 hours, or laid one frame; which second brigade is again relieved by the first, at the expiration of the same time.

In the most easy ground to work, a miner may be heard to the distance of 14 or 15 fathoms under ground; and the noise made by fixing the frames of the galleries may often be heard as far as 20 or 25 fathoms. A drum braced, standing on the ground, with a few peas or other round substances on the head, will be very sensibly affected by an approaching miner.

It is of the most essential consequence to place the entrances to the countermines beyond the reach of any surprise from the enemy.

To prevent an enemy gaining possession of the galleries of the countermines, they should be well secured by strong doors, at every 15 fathoms. These should be musquet proof.

A glacis, properly countermined, and every advantage taken of it to retard the besiegers, may, with proper management, prolong a siege at least 2 months; and if the rest of the works are also countermined, and properly defended, they may add another month to the siege. Every system of countermines must depend upon the system of fortification to which they are to be adapted; the general principle for their regulation is, that the galleries should occupy situations, from which branches can be most readily run out under the most probable points of the besieger’s batteries and approaches. The general system of countermines commonly used in a place prepared beforehand, is as follows:—The principal or magistral gallery runs all round the work, under the banquette of the covert way, and across the places of arms, having the entrances at the re-entering places of arms. Nearly parallel to this at 20, 25, or 30 fathoms distance is another gallery, called the envellope. These two galleries are connected by galleries of communication, under the gutters of the re-entering parts of the glacis, and under the ridges of the salient parts. From the envellope are run out about 15 or 16 fathoms, galleries, in directions parallel to the capitals of the works, and at 23 fathoms distance from each other. These are called listeners.

Sometimes, shafts are sunk from the ends of these listeners, and by connecting these shafts, a second envellope formed. Behind the escarps of the different works, galleries are likewise made, about the level of the bottom of the ditch; from whence branches may be run out into or under the foundations of the walls; and if the ditch be dry, galleries of communication may be made from these to the magistral gallery; and from which communications branches may be run out for chambers to annoy the besiegers in their passage of the ditch. The entrances to the escarpe galleries are by means of posterns, which descend from behind the interior slope of the rampart.

If a place be not countermined before hand, a great deal may be done, even after the investment of the place, to prolong the siege by countermines. In this case, the first thing to be done immediately that the place is invested, to sink a shaft in each of the places of arms of the covert way; one in each branch of the covert way, opposite that part of the bastion where the breach will most probably be made; and one in the flanked angle of each bastion. Those on the covert way will be on the banquette, and sunk to about 18 inches below the bottom of the ditch. Those in the bastions to about 12 feet below the bottom of the ditch. Thus prepared, the moment the side on which the attack is to be made can be ascertained, galleries must be carried on from these shafts on the side attacked along the capitals, in the form of tressles; or double T; and advanced as far into the country as the time will admit. Communication galleries may likewise be driven between these different works on the covert way, and from them to the work in the bastion; which will prevent the enemy gaining possession of their entrances. All these works may be carried on after the investment of the place; and be in sufficient forwardness by the time the enemy gains the third parallel.

The following rules are given by Vauban for fougasses, or small mines, having the diameter of the excavation equal to double the line of least resistance: The side of the chamber must be exactly a sixth part of the depth of the shaft. The side of the box to hold the powder exactly a ninth part of the depth of the shaft.

These remarks respecting mines are principally extracted from the General Essay on Fortification before mentioned, written in French, and published at Berlin, 1799.

MORTARS.—Weight and Dimensions of English Mortars.

French Mortars, in their own Weights and Measures.

Ranges with a 10 Inch Sea Mortar, at
21 Degrees, on a Horizontal Plane.

Ranges with Sea Service, Iron Mortars, at 45 Degrees,
upon a Horizontal Plane. 1798

Ranges with French Mortars, at 45 Degrees,
in French Weights and Measures.

Medium Ranges with Land Service Iron Mortars,
at 45 Degrees. 1798.

Medium Ranges with Brass Mortars,
at 45 Degrees. 1780.

Ranges with a 5½ inch Brass Mortar,
at 15 Degrees.