Part 81

In the formation, however, of tables of logarithms, it has been found convenient to adopt a ten-fold progression, as the geometrical progression, and the series of natural numbers as the arithmetical progression. It will be remarked, that, in respect to the latter, the ratio, or common measure of increase, is always unity, while the former has the advantage of being adapted to the mode of notation which is in universal use. The following, therefore, are the progressions chosen:

1 . 10 . 100 . 1000 . 10000 . 100000 . 1000000 0 . 1 . 2 . 3 . 4 . 5 . 6

It follows from the nature and correspondence of these progressions, that, as often as the ratio of the former may have been used as a factor in the formation of any one of the terms of that progression, so often will the ratio of the second progression have been added to form the corresponding term of this identical second progression. For instance, in the term 10000, the ratio 10 is 4 times a factor, and in the term 4 the ratio is added 4 times.

If any two terms of the geometrical progression be intermultiplied, and if the corresponding terms of the arithmetical progression be added, the product and the sum will be two terms which will correspond with each other in the same progressions.

Upon this principle it is, that, by the simple addition of any two or more terms of the arithmetical progression, we can ascertain the product of the corresponding terms of the geometrical progression.

For instance, by adding the terms 2 and 3 which answers to 100 and 1000, I have 5, which answers to 100000; whence I conclude that the product of 100 by 1000 is 100000, which in fact it is.

It is always easy to ascertain the logarithm of unity followed by any given number of ciphers; for such logarithm will invariably be expressed by as many units as there may be ciphers in the given number. In order to extend this practice to the formation of intermediate logarithms, it may be conceived, that, although any given number, for instance 3, may not apparently form any part of the geometrical progression 1 . 10 . 100, yet if we were to insert a great number of geometrical means, suppose 1,000,000, between the two first terms, we should either find the number 3 itself, as one of such means, or a number of very near approximation to it. The intermediate terms between 10 . 100 and between 100 . 1000 might be found in like manner, as well as a corresponding number of intermediate terms, in arithmetical proportion, between 0 and 1, and between 1 and 2, 2 and 3, &c. The whole of the geometrical terms being then arranged upon the same line, and the whole of the arithmetical terms upon another line, under the former, it is obvious that the lower series would contain units, or decimal fractions, corresponding with the numbers in the upper series, or, in other words, the logarithmic relation of the two series would be complete and exactly similar to that of the fundamental progressions.

It is thus, that, in the tables most in use, the number of decimal places in the logarithmic quantities is 7, than which, however, many more are used by men of science with a view to the attainment of a corresponding degree of precision. Nevertheless, in certain tables which were made a few years ago for the use of accompting houses, the number of decimal places is reduced to 5, and the rather, as a greater degree of precision is not necessary in those calculations of business which do not require more than approximate results.

It should be remarked, in respect to the tables of logarithms, that the first figure to the left of each logarithm is called _the characteristic_; since it is that figure which denotes the class of the geometrical progression which comprises the number to which the logarithm relates. For instance, if the characteristic of a number be 2, I know that it relates to the second class, or the hundreds, the logarithm of 100 being 2; and, as that of 1000 is 3, every number from 100 to 999 inclusively, cannot have any other logarithm than 2 and a decimal fraction.

Thus, the characteristic of a logarithm is a number corresponding to the natural numbers, namely, 1 to 10, 2 to 100, 3 to 1000, 4 to 10000, &c. &c. The characteristic of the logarithm of any number under 10 is 0.

It happens by this progressive correspondence, that a number being 10 times, 100 times, or 1000 times greater than another number, has the same logarithm as the lesser number, as far as relates to the decimal fractions of each. The characteristic alone is susceptible of variation, as will be seen by the logarithms of the following numbers:

Numbers Logarithms 3 0,47712 30 1,47712 300 2,47712 3000 3,47712

the characteristics of which are separated by a comma, being 0, 1, 2, 3.

It is this property by which the extraction of logarithms is facilitated, since, if we know the logarithm of the number 30, and are desirous of finding that of 300, of 3000, or of 3, it is requisite merely to add to the characteristic of 30, or to deduct from it, as many units as there may be more or less ciphers in the number whose logarithm is sought.

LOGEMENT, _Fr._ means generally any place occupied by military men, for the time being, whether they be quartered upon the inhabitants of a town, or be distributed in barracks. When applied to soldiers that have taken the field, it is comprehended under the several heads of huts, tents, &c.

LOGIS, _Fr._ Quarters.

_Marquer les_ LOGIS, _Fr._ To mark the officer’s rooms according to their respective ranks.

LOGEMENT _d’une attaque_, _Fr._ See _Lodgment_ in FORTIFICATION.

LONG BOAT, the largest boat belonging to a ship: it serves to bring goods, provisions, &c. to or from the ship, to land men, to weigh the anchor, &c.

_Le long de la Côte_, _Fr._ Along the coast.

_Tout du long de l’année_, _Fr._ All the year round.

_Long à la guerre_, _Fr._ An expression used in the French service.

_Faire long-bois_ signifies to leave a considerable opening between the ranks.

_Prendre le plus long_, _Fr._ To go the furthest way about, as _L’armée fut obligee de prendre le plus long pour éviter les défilés_, the army was under the necessity of going the furthest way about in order to avoid the defiles.

LONGER, _Fr._ A French military phrase. _Longer la riviere._ To move up or down the river. It is frequently found necessary to attack an enemy’s post, in order to have a free passage on the river, _pour longer la riviere_.

_Longer le bois_, _Fr._ To march by the side of a wood.

_Faire une_ LONGUE _marche_, _Fr._ To make a long march.

_Epee de longueur_, _Fr._ A sword of a proper length to serve as a weapon of defence. This term is used to distinguish it from the short swords, which are worn for mere dress or parade.

_Longs-costes_, _Fr._ Those sides are so called, which belong to places that are irregularly fortified, and contain indiscriminately eighty toises and upwards. In which cases they are usually strengthened by a flat bastion in the centre, or by several flat bastions, which are constructed, according to the extent of the sides, at intermediate distances.

LONGIMETRY, (_Longimetrie_, _Fr._) The art of measuring lands and distances, whether the extent or space be accessible as in a road, or inaccessible as in a river, or branch of the sea.

LONGITUDE _of the earth_, denotes its extent from west to east, according to the direction of the equator.

LONGITUDE _of a place_, in _geography_, its distance from some first meridian, or an arch of the equator intercepted between the meridian of the place, and the first meridian. See GEOGRAPHY.

LONGITUDE _of motion_, according to some philosophers, is the distance which the centre of any moving body runs through, as it moves on in a right line. See MOTION.

LONGRINES, _Fr._ Pieces of wood or branches which are laid along the extent of a sluice, and make part of its grating.

_To_ LOOK, a word frequently used in the British service to express the good or bad appearance of a corps, &c. viz. such a regiment looks well or ill under arms.

_To_ LOOK _at_. To go down the front of a regiment, &c. without requiring that the troops should be put through the different evolutions. A general officer frequently looks at a regiment in this manner. Sometimes indeed the expression bears a more extensive meaning: it is usual, for instance, to say--It would be ridiculous to think of looking at a strong place for the purpose of attacking it, without having sufficient force to carry its works.

_To be_ LOOKED _at_, in a military sense to be distantly observed by an enemy who has a design of attacking you; or to be seen by a general officer, whose duty is to enforce any established system. The latter must be considered as a mere cursory inspection. It is common to say--We are to be seen or looked at, but not regularly reviewed.

LOOP, in a _ship-carriage_, made of iron, fastened one on the front of a fore axle-tree, and two on each side, through which the ropes or tackle pass, whereby the guns are moved backwards and forwards on board of ships.

LOOP, a small iron ring or staple, by which the barrel of a gun is affixed to the stock.

LOOP is likewise used to signify an ornamental part of a regimental hat.--Every officer in the British service, when dressed in his uniform, is directed to wear a hat, the loop of which is made of scaled silver or gold, if in the cavalry; and of gold lace if in the infantry. General officers wear the scaled loop.

LOOP-_holes_, (_Crénaux_, _Fr._) In fortification, are small holes in the walls of a castle or fort, through which the garrison may fire. In field fortification, loop-holes are frequently resorted to.

_To_ LOOSEN, to separate, to make less coherent. In a military sense it implies to open ranks or files from close order. In marching by files, the officers and non-commissioned officers should be particularly attentive to their men, especially when any particular manœuvre requires a compact and solid movement. To loosen is, in fact, to lose that firm continuity of line or perpendicular adherence, which constitutes the true basis of military operations. The lock step was introduced for the purpose of counteracting the mischievous effects of loose marching, but it produced a greater inconvenience, and has therefore been laid aside; and the equal pace and marked time corrects both.

LOOT. Indian term for plunder or pillage.

LOOTIES or LOOTEES, _Ind._ A term in India to express a body of irregular horsemen, who plunder and lay waste the country, and harass the enemy in their march. They may be compared to the Hulans of Europe, and other free-booters.

LOOTYWALLOW, _Ind._ A term Of the same import as Looties.

_To_ LOT _for men_, a phrase peculiar to military arrangements. When recruits join they should be lotted for with the strictest impartiality. If some troops or companies should be less effective than others, they must be first completed to the strength of other troops or companies, and then the whole must lot equally.

LOUIS, _or Knight of St. Louis_, the name of a military order in France, instituted by Louis XIV. in 1693. Their collars were of a flame color, and passed from left to right: the king was always grand master.

LOUIS d’OR. A French coin first struck in the reign of Louis XIII. in 1640; but laid aside since the revolution.

LOUP, _Fr._ literally signifies a wolf.

LOUP _des anciens_ was an iron instrument, made in the shape of a tenaille, by means of which they grappled the battering rams and broke them in the middle. See CROWS-FEET.

LOYAL. By a misapplication of terms has been perverted from its true signification, a person faithful to the _law_, _loi_, is _loyal_; it is made to signify, a person who, whether he regarded the _law_ or not, was called loyal if he supported a king. Hence during the revolutionary war a regiment was formed, called _Loyal American_.

LOYALISTS. During the American war several Americans who betrayed their country, served in the British army; and at the conclusion of it many went over to England and received compensations for their perfidy to their country. The allowances made on this occasion were not, however, confined to those that had served; several families had their cases taken into consideration, and were provided for by the British government. These compensations did not however give any right to a military man to avail himself of the allowance on the score of half-pay; many of these persons have been since used as spies.

LUMIERE, _Fr._ Vent, touch-hole, aperture.

LUMIERE _des pieces d’artillerie, des armes à feu, et de la plûpart des artifices_, _Fr._ the vent or aperture through which fire is communicated to cannon, fire-arms, and to almost every species of artificial fireworks. In the making of cannon, it is of the utmost consequence to pay minute attention to the vent or touch-hole. It is in this part that pieces of ordnance are generally found defective, from the vent being too much widened by repeated firing, and the explosion of the gunpowder being necessarily weakened.

LUNETTE _d’approche_, _Fr._ a telescope. The French sometimes call them _Lunettes de Galilèe_, from the perspective glass or telescope having been invented by Galileo.

LUNETTE _à facettes_, _Fr._ a multiplying glass.

LUNETTE _polyèdre_. _Fr._ a magnifying glass.

LUNETTE _à puce_, _Fr._ a microscope.

LUNETTES, in _fortification_, are works made on both sides of the ravelin: one of their faces is perpendicular to half or two thirds of the faces of the ravelin; and the other nearly so to those of the bastions.

LUNETTES, are also works made beyond the second ditch, opposite to the place of arms: they differ from the ravelins only in their situation. See FORTIFICATION.

LUNETTONS, are a smaller sort of _lunettes_.

LUNGER-CONNA. A poor-house or hospital is so called in India.

LUNT. The matchcord with which cannon, &c. are fired.

LUNULÆ. (_Lunules_, _Fr._) In geometry a half moon or crescent, which is made by the arcs of two intersecting circles. If you inscribe a triangle-rectangle within a half circle, the diameter of which becomes the hypothenuse; and if upon each side that compresses the right angle, as its diameter, you describe a half circle, the space in shape of a half moon, closed in by the circumference of each of these two circles, and by a part of the circumference of the great half circle, will form the figure called Lunula.

LUTTE, _Fr._ Struggle. An exercise of the body, which consists in a full exertion of all its muscular powers to overcome another body, that resists with equal force and pertinacity. This sort of exercise was much encouraged among the ancients. The wrestlers or _lutteurs_, were distinguished by the name of athletics.

LUXHEBAR. The Indian name for Thursday.

LUZERNE, _Fr._ Spanish trefoil, called likewise in English _Lucerne_. A species of hay, which is cultivated for the subsistence of horses. It bears a violet colored flower.

LYCANIANS, (_Lycaniens_, _Fr._) A militia that was formerly raised in Sclavonia, the troops of which resemble the _Pandours_ and _Warasdins_. It derives its name from being quartered in the neighborhood of the lordship of _Lyka_.

LYING, to be actually stationed or quartered in a given place.

_In_-LYING. This term is peculiarly applicable to pickets. A picket is said to be an _In-lying picket_ when it is confined within the immediate lines of entrenchments belonging to a camp, or within the walls of a garrisoned town.

_Out_-LYING _picket_, is that which does duty without the limits of a camp or garrisoned town; that is, beyond the immediate sentries belonging to either. Those pickets are likewise called _In-line_ and _Out-line_ pickets.

_Out_-LYERS, the same as faggots in the line, or among the regulars. The term out-lyers was a term, however, peculiarly understood among the guards; and consisted of a certain number of men from each company, who were permitted to work, on condition that the whole of their pay was left in the hands of the captain, for the time they were so employed. This sum the officer appropriated to his own use, and was thereby enabled not only to increase his pay, but to keep a handsome table whenever he mounted guard. During the winter months the money arising from out-lyers amounted to a considerable sum. This was allowed as a sort of compensation for the expence the captain incurred by the dinner he gave to his subalterns; and for his contribution to the support of a regimental hospital. The custom is now abolished, as a table is kept by the king, and copiously paid for out of the civil list. The following anecdote, which is related to have occurred in the company that once belonged to the British general Gansell, (whom Junius notices in his letters) will shew the absurdity of the old custom, and the wisdom of its abolition:--A general muster being ordered, it was remarked that a soldier dressed in new regimentals, and perfectly unknown to every man in the company, stood to have his name called over: on being asked to whose company he belonged, he replied, to general Gansell’s: (it must be here observed, that the general had quitted the guards for some time.) Who is the present captain? was the next question, or who are the other officers? To which he briefly replied, I only know the pay-serjeant. The fact was, that he had been some years in the guards, and had constantly been an out-lyer.

It was a common practice and continues to be, though not to so great an extent as formerly, to place the names on the muster rolls of the children of officers, often their illegitimate children, and instances have occurred of girls, receiving men’s pay as _out-lyers_.

M.

MAALER, _Ind._ A certificate, which is attested by the principal inhabitants of a town or village.

MACE. A heavy blunt weapon, having a metal head: a club.

MACHICOULIS, or _Masse-coulis_, _Fr._ In ancient, and sometimes in modern fortification, that upper part of the wall which is sustained by brackets or corbels, jets out and overlooks the gate or ditch.

When a place is besieged, detached parties of the garrison may be posted in the several machicoulises. Through the intervals of the corbels, or supporting brackets, they may easily observe every thing that passes at the foot of the wall; and if the besiegers should be hardy enough to penetrate as far, they may easily overwhelm them by throwing down large stones, combustible materials, hand-grenades or bombs. These brackets or supporters, which in ancient fortification were of a slight construction, might be made of solid materials. The machicoulis, in fact, is susceptible of great improvement; and in many instances might be adopted in order to defend the lower parts of angular forts or turrets.

MACHINES. _Machines_, _Fr._

MACHINES _used in war by the ancients_. Every species of instrument or machine, which was employed before the invention of fire-arms, for the purpose of demolishing the fortifications of an enemy, or of rendering them accessible to the besieger, came under the denomination of machine. For a full and elaborate explanation of the different machines that were adopted by the ancients, we refer our military readers to the second volume of the _Recueil Alphabetique_, page 73.

MACHINES _Infernales_, _Fr._ Infernal machines. Although the first idea of these machines has been attributed to France, the invention, nevertheless, is by no means new. Frederic Jambelli, an Italian engineer, was the first that used them, when Alexander, of Parma, besieged Antwerp. The prince of Orange likewise had recourse to the destructive effects of an infernal machine, in order to bombard Havre-de-Grace, and to set it on fire. The Dutch and English, in conjunction, attempted to destroy St. Malo by the same means. The first instance, however, upon record, in which the French made use of this machine, was when Louis the XIVth ordered a vessel, carrying an enormous shell, full of every species of combustible matter, to be dispatched to Algiers, for the purpose of demolishing its harbor. This, the English say, suggested to other nations the adoption of fire-ships, and other destructive machines, which have frequently been used against maritime places, although they had been in use a century before.

The author of _Oeuvres Militaires_, tom. xxii. page 222, speaking of the infernal machines, observes, that if he were to be in a situation which required the use of so dreadful an explosion, especially to destroy a bridge, he would prefer having the machine made simply with different strong pieces of wood joined together, so as to be in the shape of an egg, or of a cone reversed. The whole must then be made compact with cords twisted round it. This method, in his opinion, is not only the best, but can be executed in the most easy and expeditious manner. He further adds, that in order to burn and blow up wooden bridges, and even to destroy such as are constructed upon arches, several sorts of barges or boats might be used, which should be filled with fireworks, bombs, petards, &c. It would likewise be extremely easy to construct these machines upon floating rafters, carrying several thousand pounds weight of gunpowder, which might be confined within strong pieces of wood, put together in the manner already described.

These machines should be piled one above the other, and long iron bars must be thrown across the floats, or be fixed like masts, so that when the whole of the combustible materials is beneath the centre of the bridge, the rafters may be stopped. Great care must be taken to dispose the matches in such a manner that no fire may be communicated to the gunpowder before the machine reaches the exact spot which is to be destroyed.

MACHINE, in _general_, whatever hath force sufficient to raise or stop the motion of a heavy body.

MACHINES are either simple or compound: the simple ones are the seven mechanical powers, viz. lever, balance, pully, axis, and wheel, screw, and inclined plane. See MECHANICAL POWERS.

If the given power is not able to overcome the given resistance when directly applied, that is, when the power applied is less than the weight or resonance given; then the thing is to be performed by the help of a _machine_, made with levers, wheels, pullies, screws, &c. so adjusted, that when the weight and power are put in motion on the _machine_, the velocity of the power may be at least so much greater than that of the weight, as the weight and friction of the _machine_, taken together, is greater than the power; for on this principle depends the mechanism or contrivance of all mechanical engines used to draw or raise heavy bodies, or overcome any other force; the whole design of these being to give such a velocity to the power, in respect of the weight, as that the momentum of the power may exceed the momentum of the weight: for if _machines_ are so contrived, that the velocity of the agent and resistant are reciprocally as their forces, the agent will just sustain the resistant, but with a greater degree of velocity will overcome it. So that if the excess of motion or velocity in the power is so great as to overcome all that resistance which commonly arises from the friction or attraction of contiguous bodies, as they slide by one another, or from the cohesion of bodies that are to be separated, or from the weights of bodies that are to be raised: the excess of the force remaining, after all these resistances are overcome, will produce an acceleration of motion thereto, as well in the parts of the _machine_, as in the resisting body.