of the nose fometimes happens, infomuch that they can tearce breathe, fuck, or fwallow; for the cure of which, after a fuitable purge, diffolve two or three grains of white vitriol in half an ounce of marjoram water; then filtre it, and apply it now and then to the noftrils with a linen-rag. Or you may apply oil of fweet almonds, impregnated with oil of marjoram, to the bottom and fides of the noftrils, which will refolve the filth. 11. Running of the eyes and ears is a very common complaint, which is cured by small dofes of the decoction of pimpernelroot, faffafras, and gentle laxatives, in which a grain or two of calomel is mixed. 12. Vomiting is rather accounted salutary than otherwife; but when too violent, it may be remedied by gentle clyfiers. 13. Suppreffion of urine is cured by giving half a scruple of fome neutral fait, as vitriolated tartar, arcanum duplicatum, and the like; but if these fail, a catheter must be introduced into the bladder, which is much easier in girls than boys. 14. Fevers of children, fee FE VER. 20. 15. Difficulty of teething, fee DENTITION. 16. Imperforations of the neceffary parts, fo that there is no paffage for the tools or urine; in which the afiflance of the furgeon must be ipeedily called in, or the infant is loft. 17. Jaundice, or a yellowness of the fkin, fee JAUNDICE. 18. Worms in children, tee WORMS. 19. Rickets feldom attack children before they are nine months old, fee RICKETS. Gripes another diforders of the bowels, are generally owing to corrupted milk; the cure of which confifts in the use of antiacids, mild cathartics, and clyfters of the fame intention, with gentle carmipatives. Sometimes, indeed, the gripes are fo violent as not to be cured without two drops of the thebaic tincture in a little fyrup of roles. Abforbents are allo deemed excellent in thefe diforders, as they cure the gripes, reftleffness, and watching in infants, as certainly as opium eafes pain in adults. Hare-Lip in INFANTS. See LIP. INFANT, in law, fignifies a perfon under the age of one and twenty. An infant may bind himself apprentice, and if he serve seven years, may have the benefit of his trade; but if he be guilty of misbehaviour, the mafter may give him gentle correction, or complain to a juftice of peace and have him punished. He may also bind himself for the pay ment of neceffaries, fuch as meat, fik, washing, apparel and learning, git not by bond with a penalty: 1 2 not obliged to pay for cloaths, wise be proved that they were for their on wearing, and convenient and tex for them to wear according to ther ingree and eftate; and though an may buy neceffaries, he cart borim money to do it; for the law will nored him with money, except at the pers the lender, who muft either fee in m laid out, or take care to lay it out hine: in fuch neceffaries. If an infant i defendant in an action, the plaintif fix years to commence his action in the infant comes of age; and an ist who is a plaintiff, has alfo fix years, he comes of age, to fue, by the of limitations. If an infant grants learn for a term of years, he may, at ba age, either confirm the leafe, or bung trefpafs against the leffee for the oce tion. Also a leafe granted to an may be avoided by waving the land bo fore the rent day expreffed therein, A infant may purchase lands, where purchafe is intended for his be tho' at his full age he may either a or confirm fuch purchase; and, in ca an infant fell lands by deeds indented as inrolled, he may avoid the fame. H ever, infants are bound by all acts of ce ceffity, as in prefentations to bene admittances and grants of copy). eftates, affenting to legacies, and cons tions annexed to lands, whether as clat comes by grant or by c'escent. INFANTE and INFANTA, all the font ar daughters of the kings of Spam an Portugal, except the eldeft; the princ being called infantes, and the princes infantas. INFANTRY, in military affairs, derot the whole body of foot-foldiers. See article SOLDIER. INFECTION, among physicians, the fam with contagion. Sze CONTAGION. INFERENCE, in matters of literature, corollary, conclufion, argument, or in duction drawn from fomething that wen before. See CONCLUSION, &c. INFERNAL STONE, lapis infernalis. So the article LAPIS. INFINITE, that which has neither beg ning nor end in which fenfe God act is infinite. See the article GOD. Infinite is also used to fignify that which has had a beginning, but will have ne end, as angels and human fouls. Th makri ces what the fchoolmen call infinitum arte poft; as, on the contrary, by intum a parte ante, they mean that which an end but had no beginning. NITE, or INFINITELY GREAT LINE, geometry, denotes only an indefinite ndeterminate line, to which no certain inds, or limits, are preferibed. NITE QUANTITIES. The very idea magnitudes infinitely great, or fuch as ceed any affignable quantities, does inide a negation of limits; yet if we arly examine this notion, we shall find at fuch magnitudes are not equal among emselves, but that there are really be les infinite length and infinite area, ree feveral forts of infinite folidity; all which are quantitates fui generis, and at thofe of each fpecies are in given roportions. nfinite length, or a line infinitely ong, is to be confidered either as begining at a point, and fo infinitely extended ne way, or elte both ways from the fame oint; in which cafe the one, which is a beginning infinity, is the one half of the whole, which is the fum of the beginning and ceafing infinity; or, as may be faid, of infinity a parte ante and a perte poft, which is analogous to eternity in time and duration, in which there is always as much to follow as is paft, from any point or moment of time: nor doth the addition or fubduction of finite length, or fpace of time, alter the cafe either in infinity or eternity, fince both the one or the other cannot be any part of the whole. As to infinite fur face, 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 faid line; but if from any point, in fuch a plane, two right lines be infinitely extended, so as to make an angle, the infi. nite area, intercepted between thofe infinite right lines, is to the whole infinite plane as the arch of a circle, on the point of concourfe of those lines as a center, intercepted between the laid lines, is to the circumference of the circle; cr, as the degrees of the angle to the 360 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 fuch a piane. But if two parallel infine lines be fup. pofed drawn on fuch an infinite plane, the area intercepted between them will be likewife infinite; but at the fame time will be infinitely lefs than that space, which is intercepted between two infinite lines that are inclined, though with never fo fmall an angle; for that, in the one cale, the given finite diffance of the parallel lines diminishes the infinity in one degree of dimenfion; whereas, in a fector there is infinity in both dimensions: and confequently the quantities are the one infinitely greater than the other, and there is no proportion between them. From the fame confideration arife the three feveral fpecies of infinite space or folidity for a parallelopiped, or a cylinder, infinitely long, is greater than any finite magnitude, how great foever; and all fuch folids, fuppofed to be formed on given bafes, are as thofe bafes in proportion to one another. But if two of thefe three dimenfions are wanting, as in the space intercepted between two parallel planes infinitely extended, and at a finite diftance, or with infinite length and breadth, with a finite thickness, all fuch folids fhall be as the given finite distances one to another; but these quantities, though infinitely greater than the other, are yet infinitely lefs than any of those wherein all the three dimenfions are infinite. Such are the fpaces intercepted between two inclined planes infinitely extended; the space intercepted by the furface of a cone, or the fides of a pyr:mid, likewife infinitely continued, &c. of all which notwithstanding, the proportions one to another, and to the To Ta, or vaft abyfs of infinite ipace (wherein is the locus of all things that are or can be; or to the folid of infinite length, breadth and thickness taken all manner of ways) are easily affignable; for the fpace between two planes is to the whole as the angle of thofe planes to the 360 degrees of the circle. As for cones and pyramids, they are as the spherical furface intercepted by them is to the furface of the fphere, and therefore cones are as the verfed fines of half their angles to the diameter of the circle: thefe three forts of infinite quantity are analogous to a line, furface, and folid; and, after the fame manner, cannot be compared, or have no proportion the one to the other.. INFINITESIMALS, among mathematicians, are defined to be infinitely fmall quantities. In the method of infinitefimals, the element, by which any quantity increases or decreafes, is fuppofed to be infinitely fmall, and is generally expreffed by two 10 Q2 or more terms, fome of which are infi. nitely less than the reft, which being neglected as of no importance, the remaining terms form what is called the difference of the propofed quantity. The terms that are neglected in this manner, as infinitely lefs than the other terms of the element, are the very fame which arife in confequence of the acceleration, or retardation, of the generating motion, during the infinitely small time in which the element is generated; fo that the remaining terms exprefs the elements that would have been produced in that time, if the generating motion had continued uniform: therefore thofe differences are accurately in the fame ratio to each other as the generating motions or fluxions. And hence, though in this method infinit.fimal parts of the elements are neglected, the conclufions are accurately true without even an infinitely fimall etror, and agree precifely with those that are deduced by the methed by fluxions. For example, (pl. CXLVI. fig. 1. no 1.) when DG, the increment of the bafe AD, of the triangle ADE, is fuppofed to become infinitely httle, the trapezium DGHE (the fimultaneous increment of the triangle) confits of two parts, the parallelogram E G, and the triangle EIH; the latter of which is infinitely lets than the former, their ratio being that of one half DG to AD: therefore, according to this method in fluxions, the part EIII is neglected, and the remaining part, viz. the parallelogram EG is the difference of the triangle ADE. Now it was fhewn, (fee the article FLUXIONS,) that EG is precifely that part of the increment of the triangle ADE which is generated by the motion with which this triangle flows, and that EI H is the part of the fame increment which is generated in confequence of the acceleration of this motion, while the bafe, by flowing uniformly, acquires the augment DG, whether DG be fuppofed finite or infi. nitely little. Example 2. The increment DELM HG (ibid, n° 2.) of the rectangle A E, confifts of the parallelograms E G, EM, and Ib; the last of which, Ib, becomes infinitely less than E G or EM, when DG and LM, the increments of the fides, are fuppofed infinitely fmall; becaufe Ib is fuppofed to E G as LM to AL, and to EM as DG to AD; therefore, Ib being neglected, the fum of the parallelograms EG and EM is the difference of the recargle AL. zd the fum of E G and EM that would have been generate is ne motion with which the refting 17 flows continued uniformly, but al is the part of the increment of angle which is generated in crepa of the acceleration of this cotion, a z time that AD and A L, by flowingne formly, acquire the augments DG. LM. The fame may be obima propofitions wherein the fluzions ci e... tities are determined; and thus the man ner of investigating the differences, fluxions of quantities, in the med infinitefimals, may be deduced from f principles of the method of th For inttead of neglecting EIH terse it is infinitely lefs than E G, no 1. (acording to the ufval manner of reeling in that method) we may us because we may thence conclude, th is not produced in confequente c generating motion DG, but of the fequent variations of this motion. A it appears why the conclufions in method of infinitefimals are not to Teprefented as if they were only new ze truth, but are to be held as accurate s true. In order to render the application o this method eafy, fome analogous pr ciples are admitted, as that the infinites fmall elements of a curve are right line or that a curve is a polygon of an infinite number of fides, which being product, give the tangents of the curve; and by their inclination to each other mealme the curvature. This is as if we fand fuppofe, when the bale flows uniforms, the ordinate flows with a motion which is uniform for every infinitely fmall part of time, and increases or decreases by infinitely fmall differences at the end of every fuch time. But however convenient this principle may be, it must be applied with caution and art on various occafions. It is uf! therefore, in many cafes, to relolve the element of the curve into two or more infinitely fmall right lines; and fometimes it is neceffary, if we would avoid error, to refolve it into an infinite number of fuch right lines, which are infinitefinals of the itcond order. In general, it is a poftulatum in this method, that we may defcend to the infinitefimals of any order whatever, as we find it neceffary ; Ov which means, any error that might arie in the application of it may be discovered and |