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though infinitely greater than the other, are yet infinitely less than any of those wherein all the three dimensions are infinite. Such are the spaces intercepted between two inclined planes 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 re roy, or vast abyss of infinite space (wherein is the loeus 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, after the same manner, cannot be compared, or have no proportion the one to the other. ... INFINITESIMALS, among 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 should 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 infinitc number of . such right lines, which are infinitesimals of the second order. In general, it is a postulatum 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 Maclaurin's Fluxions. INFLAMMATION. See Medicine and SURGERY. INFLAMMAtion, in chemistry, is combustion attended with flame: under the article CoM Bust 1o N, 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 spontaneous inflammation. The heat produced by friction; the slacking of lime when in contact with combustible matter; the fermentation of hay, dunghills, &c. are well known. Many vegetable substances, highly dried and heaped together, will heat, 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 ...' crime. In 1781 a large magazine of hemp was destroyed, in this way, at Constradt; 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 sunoke, and finally to burst out into 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 quantities 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 CoMhustion. 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 Flexuhe.
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 ordinate 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 r = the absciss, and y = the ordinate then it is to $ in a constant, ratio, or #or; 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&isequal
to nothing, And hence we have this general rule : viz. put the given equation of the curve into fluxions; from
which make both r and y = 0, and the resulting equations will determine the values of x and y, or absciss and ordinate, answering to the point of inflection. To determine the point of inflection in curves, whose semi-ordinates C. M., C m (Plate Miscel. VII. fig. 13 and 14.) are drawn from the fixed point C; suppose C M to be infinitely near C m, and make m H = M m; let T m touch the curve in M. Now the angles C m T, C M m, are equal; and so the angle C'm H, 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 maxmium, if the curve has a point of inflection, or retrogression ; and so may be found, if the arch T H, 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 Tm L be equal to m C. L.; then if C m = y, m r = r, m T =t, we shall have y : * : : ... “. 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 L H I. m r, are also similar: whence t : * : : y :
#. that is, the quantities m T. m. L, are
equal. But H L is the fluxion of Hr, which is the distance of C m = y; and
modes in which flowers are joined to the plant by the peduncles or foot-stalk 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 “axillaries,” that is, proceeding from the arm-pit of the leaf. in the latter “terminales,” 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 ... of the stars. The pheno- mena of contagious catarrhs have been it much the same with those of the simple to kind, but the disease has always been particularly remarkable for this, that it ... has been the most widely and generally o spreading epidemic known. It has seidom appeared in any one country of Euo rope, without appearing successively in most of the others. IN FORMA PAUPERIS., when any to 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 1 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. , INFOit MATION, in law, may be dei fined an accusation or complaint exhibited against a person for some criminal of. fence. It differs principally from an ino dictment in this, that an indictment is an ... accusation found by the oath of twelve WOL. VI.
men, but an information is only the alletion of the officer who exhibits it. Inormations 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 offender, one part to the use of the king, and another to the use of the informer, and are a sort of qui tam, or popular actions, only carried on by a criminal instead of a civil process. Informations that are exhibited in the name of the king alone are also of two kinds; first, those which are truly and properly his own suits, and filed ex officio by his own immediate officer, the Attorney General; secondly, those in which, though the King is the nominal prosecutor, yet it is at the relation of some private person, or common informer, and they are filed by the Master of the Crown-office, under the express direction of the court. And when an information is filed in either of these ways, it must be tried by a petit jury of the county where the offence arises; after which, if the defendant be found guilty, he must resort to the Court of King's Bench for his punishment.— Common informers, by 18 Elizabeth, c. 5, are to pay costs in case of failure of suit upon informations, unless the judge certifies that 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. Infusion 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 PHARM Acy. INFUSORIA, in natural history, the fifth order of the class Vermes, in the Linnaean system. They are simple microscopic animalcules. There are three divisions:
C, without external organs round: six genera:
Bacillaria, Monas, Bursaria, Vibrio, Enchelis, Volvox.
This order, Infusoria, is scarcely distinished from the Intestina and Mollusca §: other character, than the minuteness of the individuals belonging to it, and their appearance in animal and vegetable infusions, where we can discover no 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 volvox, and some of the vorticellae, 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. In some individuals of this order, the very singular property is exhibited of retaining the vital principle when perfectly dried; after being kept for years in a cabinet, they may be resuscitated at pleasure, by restoring them to their proper fluid. 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. IN HALER, a machine used for steaming the lungs with the vapour of hot water, for the cure of a cough, cold, inflamed throat, &c. 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 feesimple, 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 inheritances 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 lineal. ly ascend. 2. Where there are two or more males in equal degree, the eldest only shall inherit; but the females altogether. 3. The lineal descendants, in inJinitum, 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, grand-child, or great grand. child, (either male or female) of the eldest son succeeds before the younger son, and so in infinitum. 4. On failure of issue of the person last seized, the inheritance shall descend to the blood of the first purchaser. 5. The collateral heir of the |. last seized must be his next colateral kinsman of the whole blood. 6. 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 those 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, clyster pipe, 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 commit. ing or doing a thing which appears to be against equity and conscience. An injunction is usually granted for the pur. pose 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 circumstances, 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 variotis. 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 without materially fading or becoming illegible, dries very soon after writing with it, and does not considerably corrode or soften the pen. The basis of all the common writing inks is the fine black, or dark blue precipitate, formed by the addition of vegetable astringents, and particularly the soluble part of the gall-nut, to a solution of iron, generally the sulphate. But as this, if diffused in water alone, would subside in a short time, and leave the supernatant liquor nearly without colour, the precipitate is kept suspended, by thickening the water with gum arabic, or any other gum mucilage, which also gives the ink the due consistence, and enables it to trace a fine stroke on the paper, without running. These materials, therefore, that is, gall-nuts, green vitriol, (sulphate of iron) gum arabic, and water, are all that are necessary for the composition of ink; and if they are of good quality, and properly proportioned to each other, every other addition usually made adds very little to its perfection. It is not well ascertained how soon the present kind of writing ink came into use. It has certainly been employed for many centuries in most European countries ; but the ancient Roman inks were, for the most part, of a totally different composition, being made of some vegetable carbonaceous matter like lamp-black diffused in a liquor. The Chinese, and many of the inks used by the Oriental nations, are still of this kind. - - On the subject of the common writing ink, Dr. Lewis (“Commerce of Arts”) has so full and so accurate an investigation, and his experiments are, so simple and well devised, that little else can be added to the subject in a technical point of View. For a fuller chemical inquiry into the nature of the atramentous precipitate, the reader is referred to the arti
Dr. Lewis first endeavoured to ascertain the best proportion between the galls and the sulphate of iron, to render the ink permanent; for it is to be observed, that with almost any proportions, if the entire quantity be sufficient, the ink will be fine and black at first; but many of these inks, if kept for some time, especially exposed to light and air, will grow brown and fade, and the letters made with it will become nearly illegible. By trying different proportions of galls and sulphate of iron, it was found, that when about in equal quantities (the galls being powdered, and boiled fully to extract their soluble parts) they appeared to be mutually saturated, so that the mixed liquors would receive no additional blackness from a further dose of one or the other. This, however, was only a rough approximation to accuracy, for the same ef. fect was produced when either substance was also in a small degree superior in quantity to the other. But Dr. Lewis found that an ink, with equal parts of the two, though very black at first, changed to a yellowish brown, upon exposure to the sun and air only for a few days. This was again blackened by washing with fresh gall infusion, and hence it appears in fair inference that the galls are a perishable substance, so that to insure durability, a much greater proportion must enter into the ink than is required for mere saturation in the first instance. Thus it was found that two parts of galls and one of vitriol make a much more durable ink than with equal parts, and three of galls with one of vitriol was still more durable. When the galls were increased beyond this point, the colour was indeed quite permanent, but it was not of so full a black. The proportion of water or other liquid to the solid ingredients will admit of great variation. One part of vitriol, three of galls, and fifty parts of water, gave an ink black enough for common use; but the finest and blackest was made when only ten of water were employed; nor was any deficiency in the gallic acid observed after fifteen years, though the water was scarcely more than sufficient to cover the galls, and therefore could hardly be supposed capable of extracting all the soluble part of them; and though the vitriol, from , its greater solubility, would probably be dissolved entirely, and thus be in greater proportion than usual. Other liquors besides water were tried. Of these, white wine and vinegar appeared to answer somewhat better;