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By the custom of London, an infant unmarried, and above die age of fourteen, if under twenty-one, may bind himself apprentice to a freeman of London, by indenture, with proper covenants, which covenants, by the custom of London, will be as binding as if of age.

If an infant draw a bill of exchange, yet he shall not he liable on the custom of merchants, but he may plead infancy in the same manner as he may to any other contract.

An action on an account stated, will not lie against an infant, though it be for necessaries.

INFANTRY, in military affairs, denotes the whole body of foot-soldiers.

INFINITE, that which has neither beginning nor end: in which sense God alone is infinite. See God.

Infinite, or Infinitely great line in geometry, denotes only an indefinite or indeterminate line, to which no certain bounds, or limits, are prescribed.

Infinite quantities. The very idea of Biagnitudes infinitely great, or such as exceed any assignable quantities, does include a negation of limits: yet if we nearly examine this notion, we shall find that such magnitudes are not equal among themselves, but that there are really besides infinite length and infinite area, three several torts of infinite solidity; all of which are fuanlitates sut generis, and that those of each species are in given proportions.

Infinite length, or a line infinitely long, is to be considered either as beginning at a point, and so infinitely extended one way, or else both ways from the same point; in which case the one, which is a beginning infinity, is the one half of the whole, which is the sum of the beginning and ceasing infinity; or, as may be said, of infinity a parte ante and a parte post, which is analogous to eternity in time and duration, in which there is always as much to follow as is past, from any point or moment of time: nor doth the addition or . subduction of finite length, or space of time, alter the case either in infinity or eternity, since both the one or the other cannot be any part of the whole. As to infinite surface, or area, any right line, infinitely extended both ways on an infinite plane, does divide that infinite plane into equal parts, the one to the right, and the other to the left of the said line; but if from any point, in such a plane, two right lines be infinitely extended, to as to make

an angle, the infinite area, intercepted between those infinite right lines, is to the whole infinite plane as the arch of a circle, on the point of concourse of those lines at a centre, intercepted between the said lines, is to the circumference of the circle; or, at the degrees of the angle to the three hundred and sixty degrees of a circle: for example, right lines meeting at a* right angle do include, on an infinite plane, a quarter part of the whole infinite area of such a plane.

But if two parallel infinite lines be sopposed drawn on such an infinite plane, the area intercepted between them will be likewise infinite; but at the same time will be infinitely less than that space, which is intercepted between two infinite lines that are inclined, though with never so small an angle; for that, in the one case, the given finite distance of the parallel lines diminishes the infinity in one degree of dimension; whereas, in a sector there is infinity in both dimensions: and consequently the quantities are the one infinitely greater than the other, and there is no proportion between them.

From the same consideration arise the three several species of infinite space or solidity; for a parallelopiped, or a cylinder, infinitely long, is greater than any finite magnitude, how great soever; and all such solids, supposed to be formed on given bases, are as those bases in proportion to one another. But if two of these three dimensions are wanting, as in the space intercepted between two parallel planes infinitely extended, and at a finite distance, or with infinite length and breadth, with a finite thickness, all such solids shall be as the given finite distances one to another; but these quantities, though infinitely great! er than the other, are yet infinitely lest than any of those wherein all the three dimensions are infinite. Such are the spaces intercepted between two inclined planet infinitely extended; the space intercepted by the surface of a cone, or the sides of a pyramid, likewise infinitely continued, &c. of all which notwithstanding, the proportions one to another, and to the n ■n'a.i, or vast abyss of infinite space (wherein is the locus of all things that are or can be; or to the solid of infinite length, breadth and thickness taken all manner of ways) are easily assignable; for the space between two planes is to the whole as the angle of those planes to the three hundred and sixty degrees of the circle. As for cones and pyramids, they are as the spherical surface intercepted by them is to the surface of the sphere, and therefore cones are as the versed sines of half their angles to the diameter of the circle: these three sorts of infinite quantity are analogous to a line, surface, and solid ; and, alter the same manner, cannot be compared, or have no proportion the one to the other.

INFINITESIMALS, anions mathematicians, are defined to be infinitely small quantities. In the method of infinitesimals, the element, by which any quantity increases or decreases, is supposed to be infinitely small, and is generally expressed by two or more terms, some of which are infinitely less than the rest, which being neglected as of no importance, the remaining terms form what is called the difference of the proposed quantity. The terms that are 'neglected in this manner, as infinitely less than the other terms of the element, are the very same which arise in consequence of the acceleration, or retardation, of the generating motion, during the infinitely small time in which the element is generated; so that the remaining terms express the elements that would have been produced in that time, if the generating motion had continued uniform: therefore those differences are accurately in the same ratio to each other as the generating motions or fluxions. And hence, though in this method infinitesimal parts of the elements are neglected, the conclusions are accurately true without even an infinitely small error, and agree precisely with those that are deduced by the method by fluxions.

In order to render the application of this method easy, some analogous principles are admitted, as that the infinitely small elements of a curve are right lines, or that a curve is a polygon of an infinite number of sides, which being produced, give the tangents of the curve , and by their inclination to each other measure the curvature. This is as if we shculd suppose, when the base flows uniformly, the ordinate flows with a motion which is uniform for every infinitely small part of time, and increases or decreases by infinitely small differences at the end of every such time.

But however convenient this principle may be, it must be applied with caution and art on various occasions. It is usual therefore, in many cases, to resolve the element of the curve into two or more infinitely small right lines; and sometimes, it is necessary, if we would avoid error, to

resolve it into an infinite number of: right lines, which are infinitesimals of the second order. In general, it is a postxaLatnxn in this method, that we may descend to the infinitesimals of any order whatever, as we find it necessary; by which means, any error that might arise in the application of it may be discovered and corrected by a proper use of this method itself. See Maclaw :n's Fluxions.

INFLAMMATION. See Medicijt* and Surgery.

Inflammation, in chemistry, is combustion attended with flame: under the article Combustion, we have referred to the spontaneous inflammation of certain bodies, in peculiar circumstances, and likewise to the combustion of living individuals in the human species. We shall in this place mention some of the causes of •ix>ntaneous inflammation. The heat produced by friction; the slacking of lime when ia> contact with combustible matter, the fermentation of hay, dunghills, ice. are well known. Many vegetable substances, LUhly dryed and heaped together will beat, scorch, and at last burst in a flame. A mixture of linseed, or rape oil, with almost any dry vegetable fibre, as hemp, cotton, matting, &c. and still more if united to certain carbonaceous matters, will in time, if in a warm place, burst out into a flame. To this circumstance many alarming and destructive fires are to be imputed, which at the time were supposed to have been occasioned by wilful crime. In 1781 a large magazine of hemp was destroyed in this way, at Cronstadt: and in the summer of 1794 an accident of this sort happened at Gainsborough, with a bale of yarn accidentally soaked in rape oil, which after remaining in the warehouse for several days began to smoke, and finally to burst out in a most violent flame. A similar accident happened at Bombay. A bottle of linseed oil had been thrown down in the night, the oil had penetrated into a chest of coarse cotton cloth, and in the morning the cloth was found reduced nearly to a cinder, and the wood of the chest completely charred in the inside. An experiment was immediately made to ascertain the true cause: a piece of the same cloth was dipped in the same sort of oil, and shut up in a box, and in three hours it was found scorching hot, and on opening the box it burst into a flame. Hence the spontaneous combustion of wool, or woollen yarn, which has sometimes happened when large quta

lilii's have been kept in heaps without the access of fresh air. The oil with which it is dressed seems to be the chief cause of combustion. Wheaten flour and charcoal reduced to powder, and heated in large quantities have been known to take fire spontaneously.

The cases of the spontaneous human combustion have never been satisfactorily accounted for; the facts themselves seem to be well authenticated, two are recorded in the Philosophical Transactions, and referred to under Combustion. They ought however to hold out a lesson of warning to those habitually given to excess with regard to spirituous liquors; for in every case, the subjects of this terrible calamity were drunkards, whose favourite liquor was alcohol, in the shape of brandy, gin, &c.

INFLECTION, or point of inflection, in the higher geometry, is the point where a curve begins to bend a contrary way. See Flexure.

There are various ways of finding the point of inflection ; but the following seems to be the most simple. From the nature of curvature it is evident, that while a curve is concave towards an axis, the fluxion of the ordina'e decreases, or is in a decreasing ratio, with regard to the fluxion of the absciss; but, on the contrary, that the said fluxion increases, or is in an increasing ratio to the fluxion of the absciss, where the curve is convex towards the axis; and hence it follows that those two fluxions are in a constant ratio at the point of inflection, where the curve is neither concave nor convex. That is, if x = the absciss, and y = the ordinate, then x is to y in a con

xy. .'

stant ratio, or - or 4 is a constant quantity.

But constant quantities have no fluxion, or their fluxion is equal to nothing; so that in

this case the fluxion of - or of- is equal to y x

nothing. And hence we have this general

rule: cir. put the given equation of the

curve into Anxious; from which equation of

x y the fluxions find either - or'f: ; then take

y x

the fluxion of this ratio or fraction, and put it equal to 0 or nothing; and from this last

equation find also the value of the same -.•

or • -I then put this latter value equal to the

former, which will be an equation from whence, and the tint given equation of the

curve, x and ;/ will be determined, being the absciss or ordinate answering to the point of inflection in the curve. Or, putting

the fluxion of? equal to 0,that isx?~~xy

J 9*

= 0, or xy —xy = 0, or xy= xy, or x: y::x:y, that is, the second fluxions have the same ratio as the first fluxions, which is a constant ratio; and therefore if x be constant, or x = 0, then shall y be = 0 also; which gives another rule, rtz. take both the first and second fluxions of the given equation of the curve, in which make both x and y = 0, and the resulting equations will determine the values of x and y, or abscissa and ordinate answering to the point of inflection.

To determine the point of inflection in curves, whose semi-ord mates CM,Cm (Plate Miscel.VII. fig. 13and 14.) are drawn from the fixed point C; suppose C M to be infinitely near C m, and make m H = M in; let T m touch the curve in M. Now the angles Ci»T,CM m, are equal; and so the angle CaH, while the semi-ordinates increase, does decrease, if the curve is concave towards the centre C, and increases if the convexity turns towards it. Whence this angle, or, which is the same, its measure will be a minimum or maxium, if the curve has a point of inflection or retrogression; and so may be found, if the arch TH, or fluxion of it, be made equal to 0, or infinity. And in order to find the arch T H, draw m L, so that the angle TisL be equal to mCL; then if C m = y, mr = x, m T = /, we

shall have y : x tit: —. Again draw the

arch H O to the radius C H; then the small right lines m r, O H, are parallel; and so the triangles O L H, m L r, are similar; but because H I is also perpendicular to m L, the triangles LHI, m r, are also similar :

whence t :x :: y : — ; that is, the quantities nT, ro L, are equal. But H L is the fluxion of H r, which is the distance of Ca = y; and H L is a negative quantity, because while the ordinate C M increases, their difference r H decreases; whence x x -f- y y y y = 0, which is a general equation for finding the point of inflection, or retrogracJarion.

Inflection, in grammar, the variation of nouns and verbs, by declension and conjugation. See Grammar.

INFLORESCENCE, in botany, a term used to denote the mode of flowering; the manner in which flowers are supported on their footstalks. The various modes in which flowers are joined to the plant by the peduncles or foot-salk are expressed by different terms. See Botany.

The various modes of flowering are applicable to those flowers which proceed from the angle formed by the leaves and branches, as is the case in most instances, and to such also as terminate the stem and branches. In the first case, flowers are termed "axillares," that is proceeding from the arm-pit of the leaf: in the latter " terminates," that is, the terminating the branches. Inflorescence affords a characteristic mark,, by which to distinguish the species of plants, but is not used as a generic difference.

INFLUENZA, in medicine, a species of contagious catarrh, so named because it was supposed to be produced by a peculiar influence of the stars. The phenomena of contagious catarrhs have been much the same with those of the simple kind, but the disease has always been particularly remarkable for this, that it has been the most widely and generally spreading epidemic known. It has seldom appeared in any one country of Europe, without appearing successively in most of the others.

IN FORMA PAUPERIS. When any man who has a just cause of suit, either in Chancery or any of the courts of common law, will come before the Lord Keeper, Master of the Rolls, either of the Chief Justices, or Chief Baron, and make oath, that he is not worth five pounds, his debts paid; either of the said judges will, in his own proper court, admit him to sue in forma pauperis, or as a poor man, and he shall have counsel, clerk, or attorney assigned him, to do his business, without paying any fees.

INFORMATION, in law, may be defined an accusation or complaint exhibited against a person for some criminal offence. It differs principally from an indictment in this, that an indictment is an accusation found by the oath of twelve men, but an information is only the allegation of the officer who exhibits it. Informations are of two kinds; first, those which are partly at the suit of the king, and partly at the suit of a subject, and secondly, such as are only in the name of the king: the former are usually brought upon penal statutes, which inflict a penalty on conviction of the offcn- der, one part to the use of the king, and another to the use of the informer, and are a sort of qui tarn or popular actions, only carried on

by a criminal instead of a civil pr Informations that are exhibited in the nan< of the king alone are also of two ki—dhi. first, those which are truly and properly his own suits, and filed ex officio by bis own immediate officer, the Attorney-Ge»eral; secondly, those in which, though tbe King is the nominal prosecutor, yet it it at the relation of some private person, or common informer, and they are tiled by the Master of the Crown-office, under the express direction of the court. And wbea an information is filed in either of these ways, it must be tried by a petit jury o* the county where the offence arises; after which, if the defendant be found gnilty, be must resort to the Court of King's Bench for his punishment. Common informers, by 18 Elizabeth, c. 5, are to pay costs ia case of failure of suit upon informations, unless the judge certifies tliat there was a reasonable cause for prosecuting.

INFUSION, in chemistry, is the maceration of any substance in water, or any other liquid, hot or cold, in order to extract its soluble parts. The liquid thus impregnated is called an infusion. Infnsioa differs from maceration, in being continued for a longer time, and it can only be employed for substances which do not easily ferment or spoil. See Pharmacy.

INFUSORIA, in natural history, the tilth order of the class Vermes, in the Linna?an system. They are simple microscopic animalcules. There are three divisions:

A, with external organs, of which there are five genera, viz.

Branchionus, Trichoda,
Cercaria, Vorticella,

Leucopera.

B, without external organs, flattened, four genera:

Colpoda, (ionium,

Cyclidium, Paramecium.

C, without external organs, round; six genera:

Bacillaria, Monas,

Bursaria, Vibria,

Euchelis, Volvox.

This order, Infusoria, is scarcely distinguished from the Intestina and Molluscs, by any other character than tbe minuteness of the individuals belonging to it, and their spontaneous appearance in animal and vegetable infusions, where we can discover n» traces of the manner in which they are produced. The process, by which their numbers are sometimes increased, is no less astonishing than their first production. Several of the genera often seem to divide spontaneously into two or more parts, which become new and distinct animals. The vcilvux, and some of the vorticella?, are remarkable for their continual rotatory motion, supposed to be intended for the purpose of straining their food out of the water: while other species of the vorticella resemble fungi or corallines in miniature.

INGOT, in the arts, is a small bar of metal made of a certain form and size, by casting it in hollowed iron or brass plates, called ingot moulds. The term is chiefly applied to the small bars of gold and silver, intended either for coining or exportation to foreign countries.

INHALER, a machine used for steaming the lungs with the vapour of hot water, for the cure of a cough, cold, inflamed throat, Ac.

INHERITANCE, in law, is a perpetuity in lands or tenements to a man and his, heirs; and the word inheritance is not only intended where a man has lands or tenements by descent, but also every fee-simple, or fee tail, which a person has by purchase, may be said to be an inheritance, because his heirs may inherit it. Inheritances are corporeal or incorporeal. Corporeal inheritances relate to houses and lands, which may be touched or handled; and incorporeal hereditaments are rights issuing out of, annexed to, or exercised with corporeal inheritances, as advowsons, tithes, annuities, offices, commons, franchises, privileges, and services. There are several rules of inheritance of lands, according to which estates are transmitted from ancestor to heir; viz. 1. That inheritances shall lineally descend to the issue of the person last actually seized, in infinitum, but shall never lineally ascend. 3. Where there are two or more males in equal degree, the eldest only shall inherit; but the females altogether. 4. The lineal descendants, in infinitum, of any person deceased shall represent their ancestor; that is, shall stand in the same place as the person himself would have done had he been living: thus the child, grandchild, or great grandchild, (either male or female) of the eldest son succeeds before the younger son, and so in infinitum. 5. On failure of issue of the person last seized, the inheritance shall descend to the blood of the first purchaser.

VOL. III.

6. The collateral heir of the person last seized must be his next collateral kinsman of the whole blood. 7. In collateral inheritances the male stocks shall be preferred to the female, unless where lands are descended from a female : thus the relations on the father's side are admitted in infinitum before these on the mother's side are admitted at all, and the relations of the father's father before those of the father's mother, and so on.

INJECTION, in surgery, the forcibly throwing certain liquid medicines into the body, by means of a syringe, tube, clysterpipe, or the like.

Injection, anatomical, the filling the vessels with some coloured substance, in order to make their figures and ramifications visible.

INJUNCTION, in law, is a prohibitory writ, restraining a person from committing or doing a thing which appears to be against equity and conscience. An injunction is usually granted for the purpose of preserving property in dispute pending a suit; as to restrain the defendant from proceedings at the common law against the plaintiff, or from committing waste, or doing any injurious act. Injunctions issue out of the courts of equity in several instances: the most usual injunction is to stay proceedings at law, as if one bring an action at law against another, and a bill be brought to be relieved either against a penalty or to stay proceedings at law, on some equitable Circumstance?, of which the party cannot have the benefit at law. In such case the plaintiff in equity may move for an injunction either upon an attachment, or praying a dedimus, or praying a farther time to answer; for it being suggested in the bill that the suit is against conscience, if the defendant be in contempt for not answering, or pray time to answer, it is contrary to conscience to proceed at law in the mean time, and therefore an injunction is granted of course; but this injunction only stays execution touching the matter in question, and there is always a clause giving liberty to call for a plea to proceed to trial, and for want of it to obtain judgment; but execution is stayed till answer, or farther order. The methods of dissolving injunctions are various.

INK, common writing. The preparation of common writing ink is a subject of great importance in technical chemistry. A good ink is of a proper consistence to flow freely from the pen, of a full deep black, so permanent as to remain for a number of years

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