moment of F1 around the same axis; for the moment of F2 around this axis is zero.) In a perfectly similar manner the resultant of two parallel forces in opposite directions may be found.

One of the most important illustrations of parallel forces is given by the gravitational action of the earth on a body. Experiments show that the accelerations of all bodies-all materials and all quantities-when falling freely toward the earth at any point on its surface are the same, 'g.'

Therefore each particle of matter of mass m near the surface of the earth is being acted upon by a force mg, whose direction is toward the centre of the earth. Any large rigid body is, then, under the action of a great number of parallel forces. Their resultant is a vertical force Mg, if M is the total mass of the body. Its centre, i.e. the point through which its line of action always passes, however the body is turned, is called its 'centre of gravity' (q.v.). It may be shown analytically and by experiment that this point coincides with the centre of inertia of the body. This is further evident from the fact that, if a body falls, however it revolves in so doing, its centre of gravity must have the acceleration g; and this property has been shown to be peculiar to the centre of inertia.

It is evident that if a rigid body is under the action of three co-planar parallel forces, one of which is equal and opposite to the resultant of the other two, the body is in equilibrium. The conditions then are (1) that the algebraic sum of the three forces equals zero; (2) that the algebraic sum of the moments of the three forces

If,

around any axis equals zero. If any number of co-planar forces, parallel or non-parallel, act on a rigid body their resultant may be found by compounding them in pairs, as described. however, the final pair of forces is a couple, that is, consists of two equal and opposite forces, there is no resultant. The moment of a couple around any axis perpendicular to their plane is the product of either of the forces by their distance apart; this product is called the 'strength' of the couple. The action of a couple is to make a body rotate about an axis perpendicular to its plane and passing through the centre of inertia of the body; and this can be balanced, not by a single force, but by another couple of equal strength, and opposite in direction. A couple is then a rotor.

The action on a rigid body of any number of forces in all directions can be reduced in the end to a single force through the centre of inertia and a couple; for each force can be replaced by a parallel force through the centre of inertia and a couple lying in their plane, and so all the forces reduce to the sum of a number of forces all passing through the centre of inertia and to the sum of an equal number of couples each tending to produce rotation around its own axis passing through the centre of inertia.

The dynamics of fluid bodies are considered in HYDRODYNAMICS and PNEUMATICS (qq.v.). WORK AND ENERGY. Two general formulæ were developed in the discussion of translation and rotation,

Fx = {ms2 — { ms2 2

Lo= } I w2 — 1 w2

Thus a

The first formula may be expressed in words as follows: if a particle whose mass is m is moving with a speed s。 in any direction, this will be changed to s in that same direction under the action of a constant force F in that direction, provided the distance traversed in that time is x as given by the relation Fx 11⁄2 ms2- 1⁄2ms2. An illustration is afforded by an arrow shot from a bow: 8。 = 0, then Fx = 1⁄2ms. 1/2ms. Fx is called the 'work' done by the bow, and the quantity 11⁄2ms2 is called the kinetic energy of translation. Any body, not itself in motion, which has the power of producing kinetic energy in another body is said to have potential energy. bent bow, a compressed spring, a stretched elastic cord, etc., have potential energy. To bend the bow, compress the spring, stretch the cord, etc., a force must be overcome; that is, motion is produced in a direction contrary to the elastic force of the body. The numerical value of the potential energy is defined as equal to the product of the force overcome and the distance through which this has been done, i.e. to the 'work done on' the bow, spring, or string. If the spring is compressed by a body falling upon it, the spring gains potential energy since work is done on it and the body loses kinetic energy. (The spring and body together would naturally continue to vibrate up and down, but it may be supposed here that the spring is caught and held when it is compressed to its greatest extent.) If F is the force of opposition due to the spring; x, the distance required to change the speed of the body of mass m from s to so; the gain of potential energy of the spring in that distance is Fx, and the loss of kinetic energy is ms2-ms,2, where Fx = {ms2 — {ms。2.

2

Sim

ilarly, if the spring expels the body, the spring does work on the body and loses potential energy, and the body gains kinetic energy; the loss in potential energy being Fx and the gain in kinetic energy being Ims2—1ms2 if in the distance x the speed is increased from s, to s; and as before Fx = {ms2 — {ms, 2. The kinetic energy of the spring itself is neglected.

In words, this formula means that the loss of potential energy of the system producing the acceleration equals the gain of kinetic energy of the particle accelerated; or, the gain of potential energy of a system producing retardation equals the loss of kinetic energy of the retarded particle. Kinetic energy may also be produced by the impact of another body; and all experiments are in accord with the idea that the kinetic energy gained by a body in this case equals that lost by the impinging particle provided no other effects are produced. This is illustrated by the impact of perfectly elastic bodies. (In general, when there is impact, heateffects such as rise of temperature are produced, in which case the kinetic energy gained by the particle does not equal that lost.) In general, then, in mechanics, whenever one body loses energy another body gains an equal amount, work being simply the transfer of the energy. Work is done in two ways: producing a change in speed and in overcoming some opposing elastic force. Unless there is motion in the direction of the force, no work is done.

It is evident that the kinetic energy of a moving body involves the idea of speed, not velocity, because the amount of work it can do is independent of the direction of the motion. (Also if there is no change in the speed of a body, the force is at right angles to the motion and so no work is done, whatever the change in direction may be.) Illustrations of the second formula, Lo = 1 Iw2 — {Iw2, are given by the turning of a grindstone, and by a fly-wheel being set in motion or stopped.

There are other ways of doing work than in overcoming elastic forces and producing speed, e.g. raising a body up from the earth, separating a piece of iron from a magnet, separating two bodies electrified oppositely, overcoming the force of friction, etc. In all these cases, the body doing the work loses energy and the system on which work is done gains energy. The 'principle of the conservation of energy' is that in every case the energy lost by the former equals that gained by the latter; so that on the whole there is no change. Every phenomenon in nature is in accord with this principle so far as is

known.

When a body is raised from the earth, work is done equal to the product of the weight of the body and the vertical height it is raised, mgh. This amount of energy is gained by the system consisting of the earth and the body whose mass is m; but until gravitation is understood it will be impossible to locate the energy in any definite place or places. If a body falls through a height h, it and the earth lose potential energy, mgh, which is gained in the form of kinetic energy by the falling body and the earth, principally by the former, since the change in the speed of the earth occasioned by the body as it falls toward it is so infinitesimal. If, after the body falls a distance, h, its speed is s, its kinetic energy is 1⁄2ms2, and therefore mgh = 1⁄2 ms2 or s2 = 2gh.

This formula shows that the speed of a falling body depends upon the vertical height traversed, not on the slope or length of the path itself; it may fall vertically, or down an inclined plane, or down a spiral, etc.

The cases of work being done against electrical and magnetic forces are discussed under ELECTRICITY and MAGNETISM (qq.v.). Whenever work is done in overcoming friction, it is observed that heat-effects are produced, which can be traced to the fact that the minute portions of the body on which the work is done gain energy. This question is fully discussed under HEAT (q.v.). Since, when any inelastic body is deformed in any way, there is internal friction, part of the energy gained by such a body when it strikes another body goes into producing heateffects.

It is a general property of motion, which follows at once from the definition of potential energy, that all motions take place of themselves in such a manner as to make the potential energy of the system decrease, and that equilibrium is not reached until the potential energy has reached a value such that it is a minimum-that is, is as small as is possible under existing conditions.

The unit of work or energy is that corresponding to a unit force acting through a distance of a unit length. On the C. G. S. system this unit is, then, that corresponding to a force of 1 dyne acting through 1 cm.; it is called an 'erg.' An erg is, however, such a small unit that 10 ergsa 'joule,' as it is called-is ordinarily used as the practical unit. The amount of work done in a unit interval of time by any agency is called its 'activity' or 'power' (q.v.). On the C. G. S. system the unit is, then, 1 erg per second. practical unit is, however, I joule per second; this is called a 'watt.'

The

MACHINES are mechanical appliances by means of which a force applied at one point and in a definite direction is made to produce a different force at another point and generally in a different direction; the work done by means of the latter force can never be greater than that done by the former—it is in practice always less, owing to friction and other causes. The 'mechanical advantage' of the machine is the ratio of the two forces described above. There are many forms of machines: levers, pulleys, inclined plane, wedge, screw, windlass, etc. (See the separate articles.) The problem in any one case is to determine the theoretical mechanical advantage of a machine; that is, on the assumption that there is no friction when the forces are working. There are two general methods of solving this: one is to imagine a certain force acting on the machine and to determine by the ordinary principles of equilibrium what second force will just balance the action of the first; the second is to consider the machine in equilibrium under the action of these two forces, then to imagine a small displacement, and to express the fact that the work done by one force equals that done against the other. For the application of these principles to the various machines reference should be made to the separate articles in which they are described.

BIBLIOGRAPHY. A brief useful treatise for the general reader, which gives a clear conception of the elementary principles of mechanics, is Maxwell, Matter and Motion (New York, 1892). The

following works, all of which are standard, can be recommended to the student of mechanics: Mach, Science of Mechanics (Eng. trans., Chicago, 1893), a critical and historical discussion of the principles; Ziwet, Theoretical Mechanics (New York, 1894), an elementary text-book of the best type; Love, Theoretical Mechanics (Cambridge, 1897), a most critical treatment of the fundamental principles; Routh, Elementary Rigid Dynamics (London, 1882); id., Advanced Rigid Dynamics (London, 1884); id., Statics (2 vols., Cambridge, 1892); id., Dynamics of a Particle (Cambridge, 1898).

MECHANICSBURG, mê-kăniks-burg. A borough in Cumberland County, Pa., 8 miles west of Harrisburg; on the Cumberland Valley Railroad (Map: Pennsylvania, D 3). It is the seat of Irving College (Lutheran), and has a public library. The city is surrounded by an agricultural and iron-mining country, is an important shipping point for iron ore and a depot for supplies for the iron region, and manufactures spokes, wheels, carriages, and foundry and machine-shop products. The government is vested in a mayor, elected every three years, and a council. Mechanicsburg was settled in 1806, and was incorporated as a borough in 1828. Population, in 1890, 3691; in 1900, 3841.

MECHANICS' LIEN. A statutory lien or charge upon real estate to secure payment for work and labor performed on, or materials furnished for, buildings or other improvements thereon, at the request or with the consent, express or implied, of the owner. Under the early English law no liens on real estate were recognized, as it was against the policy of the feudal system to permit a tenant thus to charge land which he held of his feudal lord, who in turn held of the King. After the feudal system was abolished, lands might be charged with liens by express agreement of the owner, and this became common in the form of mortgages. Courts of equity also recognized certain agreements in the nature of mortgages. Therefore, there are no common-law liens on real estate. By statutes, however, several liens were created, such as judgment liens, and liens for taxes and assessments. With the development of business customs much work which was formerly done by persons acting as servants for a master came to be performed by independent contractors who stood on an equal footing with those who engaged them. For the protection of such contractors and of material men whose wares are used in buildings and other improvements on real estate, the statutes known as 'mechanics' lien laws' have been enacted in all the United States and in Canada, but not in England. There was a precedent by analogy for such laws in the common-law liens of artisans on personal property for labor bestowed on it, such as the repair of a wagon or a pair of shoes. Somewhat similar liens on real estate were also recognized and protected by the civil law. The theory on which mechanics' liens are given by statute is that the value of the real estate has been increased by the addition of the improvements on which the work was performed or materials furnished, and that the property should accordingly be held subject to such claims. This creates a preference of these claims over those of unsecured creditors of the owner, but a mechanics' lien is subject to valid prior liens on the real estate, such as

mortgages, judgments, taxes, etc. The term mechanics' lien is used in a general sense to cover all liens for labor, whether skilled or unskilled, and to describe liens for materials furnished. These liens give a right to look to the property for compensation, but do not create a personal claim against the owner. As a general rule, the lien attaches both to the building or improvement and to the land on which it is erected; but if the improvement is placed on the land without the owner's consent the lien will not extend to the land, but will cover the improvement to the extent of the interest of the person who ordered the work and materials. The lien only attaches to the very property on which the work was done, and will not affect the other real estate of the owner. A mechanics' lien may be filed against any title or interest in real estate, even though it is quite limited, as a lease for a year, provided it is such an interest as may be sold on execution.

The statutes in the different States vary in their provisions as to the character of the improvements which will serve to raise a lien. In general, however, such liens will attach to the real estate where any structure in the nature of a building is constructed, altered, or repaired. In some States the right is extended to cover the erection of fences, laying pipes, building sewers, grading, terracing, or sodding the land, and all other improvements which may be said to benefit the land.

The idea of benefit is usually consistently followed, in that the lien does not attach where buildings are torn down or moved from the land. In most States only a person who does work or furnishes materials at the request of the owner is entitled to protect himself by a mechanics' lien. However, in a number of States, subcontractors, that is, those who work or furnish materials for the one who contracts directly with the owner, are allowed to file direct or subordinate liens against the property.

As a general rule the work to which the owner is entitled under a contract must be entirely performed before the contractor can file a lien, but where an owner defaults in his payments or otherwise breaks his part of the contract, the right to file a lien usually attaches at once. In order to perfect a mechanics' lien the statutes of most jurisdictions provide that a notice setting forth the names of the owner and the party claiming the lien, the character of the work done, a description of the premises, the total contract price, the amount paid thereon, the amount still due, and the date when the last item of work was performed, shall be filed in the county clerk's office and a copy thereof served on the owner of the property affected. In a number of the States this lien attaches and relates back to the time of the commencement of the work

upon its being filed, and is prior to all liens subsequent to that time, but it is hardly the general rule, as they usually attach and take precedence according to the order of their being filed. The statutes of the States vary in their details as to procedure, time of filing, etc., and must be consulted to ascertain those particulars. See GARNISHMENT; LIEN; MORTGAGE.

MECHANICS OF DEVELOPMENT. This term, or 'Entwicklungsmechanik' of the German embryologists and cytologists, is in frequent use, suggested by the changes undergone during cell-division (see MITOSIS) and also in the

egg of all animals previous to and following fertilization. These changes are so orderly and complex as to suggest mechanical causes for them. As early as the first quarter of the last century Pander (1817) inquired into the mechanics of development, and Lotze followed him with some luminous suggestions. The subject The subject was continued by His and by Rauber, Van Beneden, and more recently through observation and experiments in artificial fertilization and in animal grafting carried on by O. Hertwig, Boveri, Fol, Bütschli, Pflüger, Born, Roux, Driesch, Schultze, Gerlach, Wilson, Loew, and others. Thus Bütschli by his researches on 'foam' has shown that the forms of the amoeba and other Protozoa may be due to mechanical causes of the environment. His studies may be called 'protoplasmic mechanics.' Here also come in the suggestions of Herbert Spencer and of Ryder as to the mechanics and mathematics of the initial steps taken during the growth of organisms. See GROWTH.

MECHANICSVILLE, mê-kănʼiks-vil. A village in Saratoga County, N. Y., 19 miles north of Albany; on the Hudson River and the Champlain Canal, and on the Delaware and Hudson and the Boston and Maine railroads (Map: New York, G 3). It has a public school library of

over 4200 volumes. The industrial interests are favored by abundant water power, and include extensive manufactures of pulp and paper, knit goods, sash and blinds, and other establishments. The water-works are owned and operated by the municipality. Population, in 1890, 2679; in 1900, 4695.

MECHANICSVILLE, BATTLE OF. A battle fought at Mechanicsville, on the Chickahominy River, seven miles from Richmond, Va., June 26, 1862, between a Federal force of about 5000 under the immediate command of General Fitz John Porter and a Confederate force of about 10,000 under the command of General Robert E. Lee. The Confederates in three corps, commanded by A. P. Hill, Longstreet, and D. H. Hill, made two attacks on the strong Federal position, but made little impression, and, after suffering great loss, were finally driven back. Early on the morning of the 27th, however, General Jackson with a strong Confederate reënforcement having arrived in the vicinity, General Porter abandoned his position for a stronger one several miles to his rear, where later in the day he was again attacked. (See GAINES's MILL.) In the engagement at Mechanicsville the Federals lost about 360; the Confederates about 2000. The engagement was the first of the so-called 'Seven Days' Battle' of the Peninsular campaign, and is sometimes known as the battle of Beaver Dam Creek.

MECHANISM (Lat. mechanisma, contrivance, from Gk. unxavý, mechanē, device). In philosophy properly employed to designate any view which seeks to explain the universe in terms of motion; in this sense it is practically equivalent to materialism (q.v.). It is, however, often used more loosely as a synonym for naturalism (q.v.); in this latter sense its antonym is teleology (q.v.).

MECHERINO, mảki-rēnổ, IL. A name sometimes applied to the Italian painter Domenico Beccafumi (q.v.).

MECHLIN, měк'lin, or MALINES. One of the chief cities of the Belgian Province of Antwerp, situated 13 miles south-southeast of the city of Antwerp, on the navigable River Dyle, which flows through the city in a number of arms (Map: Belgium, C 3). The city is circular in shape, surrounded by a canal and a wide boulevard. As the See of the Cardinal Primate of Belgium, it retains a considerable ecclesiastical importance; of its numerous churches, the most noteworthy is the Cathedral of Saint Rombaud, a vast Gothic structure, adorned in the interior with many fine paintings and choice carvings, the altarpiece by Van Dyck being one of that master's finest works. It was built between the twelfth and fifteenth centuries, and one tower, 320 feet in height, remains unfinished. The other buildings most worthy of notice are the churches of Saint John and of Our Lady, which contain works by Rubens; the town hall, dating from the fifteenth century, and known as the Beyard; the market hall, erected in 1340; and the splendid modern archiepiscopal palace. Mechlin has two seminaries, an academy of painting, a gymnasium, and a botanical garden. It was formerly the seat of important lace manufactures, but its chief manufactures now are caps and woolen goods, 'gobelin' tapestry, tobacco, starch, and beer. There are also extensive workshops at the railroad station outside the city, which is the centre of several important railroad lines. Population, in 1890, 51,014; in 1900, 56,013.

MECHLIN LACE. A lace so named from being originally manufactured at Mechlin, in Belgium. It is a hexagon mesh of three threads in which the pattern is worked. The mesh consists of four plaited and two twisted sides. See LACE.

MECK'EL'S GANGLION, or THE SPHENOPALATINE GANGLION. The largest of the four sympathetic ganglia connected with the fifth cranial nerve, the others being the ophthalmic (q.v.), the otic (q.v.), and the submaxillary (q.v.). It lies deep in the spheno-maxillary fossa (a small triangular space just beneath the apex of the orbit), close to the spheno-palatine foramen. The ganglion is a small triangular or heart-shaped body, of a reddish-gray color, and was first described by Meckel. Like the other ganglia of the fifth nerve, it possesses a motor, a sensory, and a sympathetic root. Its sensory root is derived from the superior maxillary branch of the fifth nerve, through its two spheno-palatine branches; its motor root from the facial nerve, through the large superficial petrosal nerve; and its sympathetic root from the carotid plexus, through the large deep petrosal nerve. The ganglion gives off branches of distribution in four groups: an ascending group, which passes to the orbit; a descending, to the palate; an internal, to the nose; and posterior branches to the pharynx and nasal fossæ. See NERVOUS SYSTEM AND BRAIN.

probable that only one meeting was held, although this has always been a debatable question and has given rise to a detailed and prolonged controversy. The copy of the resolutions made by the secretary of the meeting is said to have been destroyed by fire, but on April 30, 1819, what purported to be a copy, made probably from recollection, was published in the Raleigh (N. C.) Register. The use of phrases in the published copy similar to certain passages in the real Declaration of Independence of July 4, 1776, caused doubt to arise as to the authenticity of the Mecklenburg Declaration. The Legislature of North Carolina in 1831, after an investigation of the subject, declared May 20th a legal holiday. The weight of authority at present is overwhelmingly against the authenticity of the Declaration, and favors the opinion that only one meeting was held the one of May 31st-and that the resolutions there adopted, bearing no resemblance to Jefferson's Declaration, constitute the nearest approach there was to a Mecklenburg Declaration of Independence. The resolutions, as published in the Raleigh Register in 1819, are five in number. They declare: (1) that whoever aids or abets the invasion of American rights is "an enemy to this country-to America-and to the inherent and inalienable rights of man;" (2) that all political bands between those passing the resolutions and the mother country are dissolved, the allegiance of the citizens of Mecklenburg County to the British Crown being absolved and all political connection with that nation broken off; (3) that "we do hereby declare ourselves a free and independent people; are, and of a right ought to be, a selfgoverning association, under the control of no power other than that of our God and the general government of the Congress; to the maintenance of which independence we solemnly pledge to each other our mutual coöperation, our lives, our fortunes, and our most sacred honor;" (4) that those passing the resolutions acknowledge the existence of no law or public officer, but readopt their former laws in so far as these laws do not recognize the authority of the Crown, thus vacating all civil and military commissions granted by the Crown; and (5) that all military officers in the county are retained in their former command and that every member of the convention be henceforth a civil officer with power to issue process, hear and determine all matters of controversy, preserve peace and harmony, and endeavor to spread the love of country until a more general organized government be established in the province.

The best discussion of the authenticity of the Declaration is that by Lyman C. Draper, The Mecklenburg Declaration: Its Origin, History, and Actors, with a Bibliography of its Literature and Explanatory Documents, a work which was never published and forms part of the manuscript collections of the Wisconsin Historical Society. After an elaborate consideration of the evidence, Draper decided against the authenticity of the Declaration. In the library of the Wisconsin Historical Society are also many documents bearing on the subject. For briefer discussions consult articles in the North American Review for 1874, and in vol. xxi. of the Magazine of American History, and the note (p. 423) in Frothingham, Rise of the Republic of the United States (Boston. 1881)

-all opposing the authenticity of the Declara

tion; and a chapter by Hawks in Cooke, Revolutionary History of North Carolina (Raleigh, 1853), and Graham, Address on the Mecklenburg Declaration of Independence of May 20, 1775 (New York, 1875)-defending its authenticity. měk❜lĕn

MECKLENBURG-SCHWERIN,

bōōrk shvȧ-rēn'. A grand duchy and constituent State of the German Empire, bounded by the Baltic Sea on the north, the Prussian Province of Pomerania and the Grand Duchy of MecklenburgStrelitz on the east, the Prussian provinces of Brandenburg and Hanover on the south, and Schleswig-Holstein, the Principality of Ratzeburg (belonging to Mecklenburg-Strelitz), and the Territory of Lübeck on the west (Map: Germany, D 2). Area, including the three enclaves in Brandenburg and Mecklenburg-Strelitz, 5135 square miles.

The country is generally flat with the exception of the central part, which is traversed from southeast to northwest by a chain of low hills, forming the watershed between the Elbe and the Baltic Sea. The flat coast-line is 100 miles long and is broken by a number of deep indentations, including the Bay of Wismar. Numerous rivers traverse the country from north to south. The Recknitz, the Warnow, and the Stepenitz flow toward the Baltic, and the New Elde and the Sude are tributaries of the Elbe, which for a few miles forms the southern boundary of the grand duchy. The country abounds in lakes, the largest of which are the Müritz See (51 square miles), the Schweriner See (23 square miles), the Kölpiner, and the Plauer See.

The climate is mild and healthful, although somewhat raw. The average annual temperature is 46° and the annual precipitation 21 inches. There are chalybeate springs at Doberan and Goldberg and saline springs at Sülze. According to the industrial census of 1895 nearly one-half of the population depended for their livelihood on agriculture. The land is divided between the Crown, the aristocracy, the clergy, and the towns, the peasantry forming an hereditary tenantry class. About 90 per cent. of the area is under cultivation in pastures and in forests. The crops exceed the local demand and are partly exported. Rye, wheat, oats, barley, and potatoes are the staples. Tobacco is cultivated to some extent. Stock-raising is carried on extensively, and dairying is an important adjunct to agriculture.

The manufacturing industries are far inferior to the agricultural interests. There are a number of foundries, machine works, sugar refineries, breweries, distilleries, paper mills, tanneries, tobacco factories, brick yards, etc.; but many manufactures are imported for local consumption, and the native exports contain no manufactured product of importance. The trade is very extensive and favored by the situation of the country. The imports pass chiefly through the seaports of Warnemünde and Wismar. The chief exports are agricultural, dairy, and animal products, live animals, etc., and are transported mostly by rail. The annual outward and inward shipping exceeds 900,000 tons. The transportation facilities are excellent, consisting of a system of navigable rivers and canals, and a number of State railway lines with a total length of 740 miles in 1901.

The constitution of the two duchies of Mecklenburg-Schwerin and Mecklenburg-Strelitz is based