mechanics is founded on the same principles as the application of algebra to geometry. It consists principally in representing by equations the curves described by bodies in motion, by determining the equation between the spaces which the bodies describe when actuated by any forces, and the times employed in describing them. As a familiar instance, we may refer to the article ACCE. LERATION, where the perpendiculars of triangles represent the times, the bases the velocities, and the areas the spaces described by bodies in motion, a method first invented by Galileo. As lines and figures may be treated of algebraically, it is evident in what way the principles of geometry and algebra may be applied to mechanics, and indeed to every branch of mixt mathematics. APPLICATION of mechanics to geometry consists in the use that is made of the centre of gravity of figures for determining the contents of solid bodies described by those figures.

APPLICATION of geometry and astronomy to geography consists in determining the figure and magnitude of the earth; in determining the positions of places by observations of latitudes and longitudes; and in determining by geometrica! operations the positions of such places as are not far distant from one another.

APPLICATION of geometry and algebra to natural philosophy was invented chiefly by Sir Isaac Newton, and upon this application are founded all the mixed sciences of mathematical and natural philosophy. Here a single observation or experiment will frequently produce a whole science, or branch of science. Thus, when it is proved by experiment that the rays of light, in reflecting, make the angle of incidence equal to the angle of reflection, we deduce the whole science of catoptrics; for this fact being established, catoptrics becomes a science purely geometrical, since it is reduced to the comparison of angles and lines given in position.

APPOINTEE, in heraldry, the same as aguisée: thus we say, a cross appointée, to signify that which has two angles at the end cut off, so as to terminate in points.

APPORTIONMENT, in law, the division of a rent into parts, in the same manner as the land out of which it issues is divided: for example, if a person leases three acres of land for a certain rent, and afterwards grants away one acre thereof to another: the rent shall be apportioned between them.

APPOSITION, in grammar, the placing two or more substantives together, in the same case, without any copulative conjunction between them; as, ardebat Alexim delicias domini.

APPRAISING, the valuing or setting a price on goods. This is usually done by a sworn appraiser, who, if he values the goods too high, is obliged to take them at the price appraised.

APPREHENSION, in logic, the first or most simple act of the mind, whereby it perceives, or is conscious of some idea: it is more usually called perception.

APPRENTICE, a young person bound by indenture to some tradesman, in order to be instructed in the mystery or trade. By the laws of England, a master may be indicted for not providing for, or for turning away his apprentice: and upon complaint from a master, that he neglects his duty, an apprentice may be committed to Bridewell, or be bound over to the sessions. Apprentices may be bound to husbandmen, or even to gentlemen of fortune and clergymen, who, as well as tradesmen, are compellable to take the children of the poor, under a penalty of 101. And the church-wardens and overseers, with the consent of two justices, may bind them till the age of 21 years. Justices may compel certain persons under age to be bound apprentices, and on refusal may commit them. Apprentices may be discharged on reasonable cause, either at their own request or that of their masters. If any, whose premium has been less than ten pounds, run away from their masters, they are compellable to serve out the time of absence, or give satisfaction for it, any period within seven years after the expiration of the original contract. Indentures are to be stamped, and are chargeable with several duties by act of parliament.

APPRENTICESHIP, denotes the servitude of an apprentice, or the duration of his indenture. The competition in several employments is restrained to a smaller number, than would otherwise be disposed to enter into them, partly by the limitation of the number of apprentices, which attends the exclusive privilege of incorpo rated trades; and partly by the long term of apprenticeship, which increases the expense of education. Seven years seem formerly to have been, all over Europe, the usual term established for the duration of apprenticeships in the greater number of incorporated trades. Such incorporations were anciently called universities,

which is the proper Latin name for any incorporation whatever. The university, of smiths, the university of tailors, &c. are expressions commonly occurring in the old charters of ancient towns. When those particular incorporations, which are now peculiarly called universities, were first established, the term of years during which it was necessary to study, in order to obtain the degree of Master of Arts, appears evidently to have been copied from the term of apprenticeship in common trades, of which the incorporations were much more ancient. As to have wrought seven years under a master properly qualified, was necessary to entitle any person to become a master, and to have himself apprentices, in a common trade, so to have studied seven years under a master properly qualified, was necessary to entitle him to become a master, teacher, or doctor (words anciently synonymous) to study under him. By the 5th of Elizabeth, commonly called the statute of apprenticeship, it was enacted, that no person should, for the future, exercise any trade, craft, or mystery, at that time exercised in England, unless he had previously served to it an apprenticeship of seven years at least; and thus, what before had been the bye-law of many particular corporations, became in England the general and public law of all trades carried on in market-towns. To country villages the term of seven years apprenticeship doth not extend; but the limitation of this statute to trades exercised before it was passed, has given occasion to several distinctions, which, considered as rules of police, appear as foolish as can well be imagined. A coachmaker, for instance, has no right to make, or employ journeymen for making, coach-wheels but he must buy them of a master wheel-wright, this latter trade having been exercised in England before the 5th of Elizabeth. But a wheel-wright, though he has never served an apprenticeship to a coachmaker, may, by himself or journeyman, make coaches, because this trade, being of a later origin, is not within the statute. Thus also the manufactures of Manchester, Birmingham, and Wolverhampton, are, many of them, upon this account, not within the statute, not having been exercised in England before the 5th of Elizabeth.

The regulations of apprenticeship in Ireland are upon a different footing, and somewhat less illiberal than in England. Prohi bitions similar to those of the statute of the

5th of Elizabeth, obtain in all corporate towns, by authority of bye-laws of the several corporations: but these prohibitions extend only to natives of Ireland; for by a regulu. tion made by the lord lieutenant and privycouncil having in this instance, by 17 and 18 Car. II. the force of a law, all foreigners and aliens, as well persons of other religious persuasion as Protestants, who are merchants, traders, artificers, &c. shall, upon coming to reside in a city, walled town, or corporation, and paying twenty shillings, by way of fine to the chief magistrate and common-council, or other persons authorized to admit freemen, be admitted to the freedom of that city, &c. and to the freedom of guild's of their respective trades, with the full enjoyment of all privi leges of buying, selling, working, &c.; and any magistrate refusing to admit foreigners so applying, shall be disfranchised.

In Scotland, there is no general law which regulates universally the duration of apprenticeships. The term is different in different corporations; where it is long, a part of it may generally be redeemed by paying a small fine. In most towns, too, a very small fine is sufficient to purchase the freedom of any corporation. The weavers of linen and hempen cloth, the principal manufactures of the country, as well as all other artificers subservient to them, wheelmakers, reel-makers, &c. may exercise their trades in any town corporate, without paying any fine. In all towns corporate, all persons are free to sell butchers' meat upon any lawful day of the week. Three years are, in Scotland, a common term of apprenticeship, in some very nice trades; and, in general, there is no country in Europe in which corporation laws are so little oppressive. In France the duration of apprenticeships is different in different towns, and in different trades. In Paris, 5 years are the term required in a great number; and before any person can be qualified to exercise the trade as a master, he must, in many of them, serve 5 years more as a journeyman. During this latter time he is called the companion of his master, and the term itself is called his companionship. The institution of long appren ticeships, says Dr. Smith, can give no security that insufficient workmanship shall not frequently be exposed to sale; nor has it any tendency to form young people to industry. Apprenticeships were altogether unknown to the ancients: the Roman law is perfectly silent with regard to them. There is no Greek or Latin word which expresses the

idea we now annex to the word appren

tice.

Long apprenticeships are altogether unnecessary. The arts, which are much superior to common trades, such as those of making clocks and watches, contain no such mystery as to require a long course of instruction. In the common mechanic trades, the lessons of a few days might certainly be sufficient. The dexterity of hand, indeed, even in common trades, cannot be acquired without much practice and experience. But a young man would practise with much more diligence and attention, if from the beginning, he wrought as a journeyman, being paid in proportion to the little work which he could execute, and paying, in his turn, for the materials which he might sometimes spoil through aukwardness and inexperience. His education would generally in this way be more effectual, and always less tedious and expensive. The master, indeed, would be a loser; he would lose all the wages of the apprentice, which he now saves for seven years together. In the end, perhaps, the apprentice himself would be a loser: in a trade so easily learnt he would have more competitors; and his wages, when he came to be a complete workman, would be much less than at present. The same increase of competition would reduce the profits of the masters, as well as the wages of the workmen: the trades, the crafts, the mysteries would all be losers; but the public would be a gainer, the work of all artificers coming in this way much cheaper to market.

We cannot conclude this article better than by inserting an admirable paper on the subject of apprentice laws, drawn up, and printed for private circulation, by a gentleman of high legal authority, and member of parliament, entitled "A few Opinions of some great and good Men, and sound Lawyers, on the Apprentice Laws of Queen Elizabeth, applicable to the Era of 1806-7."

Lord Mansfield, in his arguments on the case, Rennard and Chase, brewers. 1 Bur. Rep. p. 2, says, "It hath been well observed that this act (viz. 5 Eliz. chap. 4.) is,

1. A penal law.

2. It is a restraint on natural right.

3. It is contrary to the general right given by the common law of this kingdom.

4. The policy upon which this act was made, is from experience become doubtful. Bad and unskilful workmen are rarely prosecuted. This act was made early in the

reign of Queen Elizabeth, when the great number of manufacturers, who took refuge in England after the Duke of Alva's prosecution, had brought trade and commerce with them, and enlarged our notions. The restraint introduced by this law was thought unfavourable; and the judges, by a liberal interpretation, have extended the qualification for exercising the trade much beyond the letter of it, and confined the penalty and prohibition to cases precisely within the express letter." Burn's Justice, vol. i. Art. Apprentices.

3d Modern Reports, p. 317. Judge Dolben, in delivering his opinion, said, that "No encouragement was ever given to prosecutions upon the statute 5 Eliz., and that it would be for the common good if it were repealed; for no greater punishment can be to the seller, than to expose to sale goods ill-wrought, for by such means he will never sell more."

- 2 Salk. 613. The Queen v. Maddox.-It was held by the court," that upon indictments upon the statute of 3 Eliz. the following of a trade for seven years to be suffici ent without any holding; this being a hard law." And so held in Lord Raymond, 738.

Burn's Justice." So detrimental was this statute thought, that by 15 Car. II. all persons spinning or making cloth of hemp or flax, or nets for fishing, or storin or cordage, might exercise those trades without serving apprenticeships. And so little did the legislature, at subsequent periods, think that any benefit was to be derived from the statute of 5 Eliz. or that manufactures were made better, or improved by this restraint; and the minds of men being more liberal, that trade should, as much as possible, be flung open; it is enacted, by 6 and 7 William III. that any apprentice discovering two persons guilty of coining, so as they are convicted, shall be deemed a freeman, and may exercise his trade as if he had served out his time."

And, in order still stronger to shew how little the legislature esteemed the seven years binding ameliorated manufactures, it is enacted, by 3 George III. cap. 8, that "All officers, marines, and soldiers, who have been employed in his Majesty's service, and not deserted, may exercise such trades as they are apt for, in any town or place.”

So dangerous and fatal has been the evil of combinations and conspiracies among journeymen, that in particular instances, as in trades where many hands are required and very little skill, as dyeing, and such like,

the legislature have made express laws to give relief to masters. See 17 Geo. III. cap. 33.; which enables dyers, in Middlesex, Essex, Surrey, and Kent, to employ journeymen who have not served apprenticeships. And to such a pitch has this mischief in the West Riding of Yorkshire increased, by the conspiracies facilitated by the act of 5 Eliz. that it goes to the total annihilation of our staple manufactures, and every other trade which hopes for success not only by the home, but from foreign consumption. See the report from the committee of the House of Commons, on the woollen trade and manufacture of these kingdoms, made in the last session of parliament, 4th July 1806.

After stating the above, let us quote the words of the immortal Lord Chief Justice Coke on this point.-"That, at the common law, no man could be prohibited from working in any lawful trade; for the law abhors idleness, the mother of all evilOtium omnium vitiorum mater-and espe-cially in young men, who ought in their youth (which is their seed time) to learn lawful sciences and trades, which are profitable to the commonwealth, whereof they might reap the benefit in their old age: for ' idle in youth, poor in age'.”

And therefore the common law abhors all monopolies, which prohibit any from working in any lawful trade. Aud that appears in 2 Hen. V. 5 b. A dyer was bound not to use the dyer's craft for two years: and there Judge Hall held, "that the bond was against the common law; and by G-d if the plaintiff was here, he should go to prison till he paid a fine to the king." And vide 7 Edw. III. 65 b.' “And, if he who takes upon himself to work is unskilful, his ignorance is a sufficient punishment to him, for imperitia est maxima mecanicorum pana; et quilibet quærit in quâlibet arte peritos-which is, that want of skill is the greatest punishment of mechanics; for every body will employ those that are the best skilled in their business.' And, if any one takes upon himself to work, and spoils it, an action on the case lies against him.”

Having observed thus much, and stated the opinions of two such great men as Lord Coke and Lord Mansfield, we can only add one dixit of Lord Coke's, that, "acts of parliament which are made against the freedom of trade, merchandizing, handicrafts, and mysteries, never live long." 4th Inst. 31.

It is to be observed, that this very great check upon trade, by not being able to em

ploy any hands that are able to perform the work required, and especially in those trades which are so easily learnt in a very short space of time, greatly enhances the prices of all articles, and that a time when population is daily increasing, and the demand proportionably increasing. And this statute is not only a restraining statute, but also an enabling statute, as it empowers the workmen to enter into combinations against their masters, and to dictate their own terms, encouraging vice, idleness, and drunkenness; demands being made on the masters for an increase of wages; those demands supported by dangerous combinations and conspiracies, and extorted by threats. And such increase, when obtained, not applied for the wholesome purpose of supporting themselves and their families, but to that very destructive purpose, ruinous to their families, and highly detrimental to the public at large, the enabling of the parties to spend more days of the week in idleness, drunkenness, vice, and immorality. In many manufactures, so much money is extorted by the journeymen, by means of these combinations, from their employers, that the journeymen will work but three days in the week; so that 600 are necessarily required to do the work that 300 might do.

Until these laws, restricting the binding of apprentices, are repealed, all laws made for the prevention of combinations among workmen can be of no avail, and will remain a dead letter in the law books: as in this free country, (however that freedom' may be limited as to the checking of masters binding apprentices), no law on this point can be so worded, that the art, wickedness, and ingenuity of men, will not con. trive to defeat. A bad and absurd law is made, viz. the "Apprentice Act," which, by the extension of trade, is found detrimental to trade; and then, to do away the mischiefs of that law, another absurd law is made, viz. the law to prevent combination, --so that mischief is heaped upon mischief, and absurdity upon absurdity. Trade should be as free as the air we breathe. This is an axiom, the truth of which every day convinces us.

APPROACHES, in fortification, the works thrown up by the besiegers, in order to get nearer a fortress, without being exposed to the enemy's cannon: such, in a more particular manner, are the trenches, which should be connected by parallels, or lines of communication,

This is the most difficult part of a siege, and where most lives are lost. The ground is disputed inch by inch, and it is of the utmost importance to make the approaches with great caution, and to secure them as much as possible.

The besieged frequently make counterapproaches, to interrupt and defeat the enemy's approaches,

APPROPRIATION, the annexing a benefice to the proper and perpetual use of a religious house, bishopric, college, &c. Where the king is patron, he may make appropriations himself; but in other cases, after obtaining his licence in chancery, the consent of the ordinary, patron, and incumbent is requisite. Appropriations cannot be assigned over, but those to whom they are granted may make leases of the profits. There are in England 2845 impropriations.

APPROVER, in law, a person, who being indicted of treason or felony, for which he is not in prison, confesses the indictment; and being sworn to reveal all the treasons and felonies he knows, enters before the coroner his appeal against all his partners in the crime. All persons may be approvers, except peers of the realm, persons attainted of treason or felony, or, out-lawed, infants, women, persons non compos, or in holy orders.

APPROXIMATION, in arithmetic and algebra, the coming nearer and nearer to a root, or other quantity sought, without expecting to be ever able to find it exactly. There are several methods for doing this, to be found in mathematical books, being nothing but infinitely converging series, some approaching quicker, others slower towards the truth.

By such an approximation the value of a quantity may be found, though not to the utmost degree of exactness, yet sufficiently so for practice. Thus / 21.41421356, &c. the approximating series 1+ +100+ 1000+ Toooo +, &c. or supposing

There is a general method of investigating the value of such series, for which see SE

RIES.

APPULSE, in astronomy, the approach of a planet towards a conjunction with the sun, or any of the fixed stars. The appulses of the planets to the fixed stars have always been of great use to astronomers in order to fix the places of the former. The ancients wanting an easy method of comparing the planets with the ecliptic, which is not visible, had scarce any other way of fixing their situations, but by observing their tract among the fixed stars, and remarking their appulses to some of those visible points. Dr. Halley has published a method of determining the places of the planets, by observing their near appulses to the fixed stars.

APPURTENANCES, in common law, signify things corporeal and incorporeal, that appertain to another thing as principal; as hamlets to a manor, and common of pasture and fishery. Things must agree in nature and quality to be appurtenant, as a turbary, or a seat in a church, to a house.

APRICOT, in botany, a species of prunus, with rosaceous flowers, and a delicious fleshy fruit, of a roundish figure. See PRUNUS.

APRON, in gunnery, the piece of lead which covers the touch hole of a cannon.

The dimensions of aprons are as follow; viz. for 42, 32, and 24 pounders, 15 inches by 13; for 18, 12, and 9 pounders, 12 inches by 10; and for cannon of less calibre, 10 inches by 8. They are tied by two strings of white marline.

APSIS, in astronomy, a term used indifferently for either of the two points of a planet's orbit, where it is at the greatest or least distance from the sun or earth. Hence the line connecting these points, is called the line of the apsides.

109

+ 11+,&c=1+4x2+

2x+, &c.

4 1

+

4

mated, shackled; wings fin-shaped, and without quill-feathers; feet fettered, fourtoed. This genus resembles the alca in colour, food, stupidity, eggs, nest, position of legs behind the equilibrium, and consequent erect posture. They are totally unfit for flight, but swim dextrously; nostrils linear, hid in the groove of the bill, palate as well as the tongue beset with a few rows of conic, retroflected, stiff papillæ; wings covered with a strong broad membrane; tail