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Mercurms dulcis, or calomel, is an extremely fafe and va- luable purge for children, provided that they have no fever ; it is to-be given from one grain, to three or four. In cafes of diforders from the retropullion of cutaneous humors, this does more good than could well be expected from any medi- cine. Junker's Confp. Med. p. 751.
Manna, infufions of fena, and fmall dofes of fyrup of buck- thorn, may alfo be given as purges to children, where there is no fever joined with their complaints ; but where there is a feverifh dilpolition, rhubarb is to be preferred to all other things. In violent gripingsj and pains attended with crying out, terrors and tremblings, and acrid ftools, mucilaginous medicines often prove of more fervice than the common ab- forbents. Worms in Infants, when alive in the bowels, of- ten bring on atrophies and convulfions ; and when dead and putritied, they occafion many malignant effects, with con- vulfions, and often unaccountable fymptoms. When alexi- pharmic or diuretic medicines arc round neceffary, it is al- ways much better to give them to the nurfe than to the child ; but antimony-diaphoretic, when faithfully prepared, is a me- dicine of great power, and yet lb fafe that it may be given to the Infant. Narcotic medicines are to be given with the utmoft caution ; a fingle grain of theriaca feems as proper as any thing for this purpofe. Cinnabar in fmall dofes is found to be an excellent remedy in convulfions ; but if it be given too*ireely, it generally loads the ftomach. Infant, in law, if it appear that an Infant, under the age of difcretion could diftinguifh between good and evil, as if one of nine or ten years of age fhould kill another, and hide the body, or himfelf, cfc. by the law of England he may be con- victed, and condemned, iffc. But the judge in prudence will refbite the execution. Hawk, P. C. b. 1. c. x. XNFERIvE, in antiquity, facrifices offered to the Dii manes, or the fouls of decealed heroes and illuftrious perfons ; or even any relation or perfon whole memory was held in vene- ration- Pitlfc. Lex. Ant. in voc. INFERIOR (Cycl.)— Inferior Courts of Record, in Englifh law-writers, is ufed as a general name for corporation-courts, courts-leet, and fhcriffs-torns. Hale, Analyf. p. 36. 2 Inft. 143. 4lnft. 263. See the article Inferior Courts. Moft courts are fubordinate to fome other j but for diftinc- tion fake the term Inferior-court is by Sir Matthew Hale, and others, applied in the manner here mentioned. Hate, ibid. Inferior Penis, in anatomy, a name given by Spigelius to one of the mufcles of the penis, generally called the Acce- lerator hythz moderns i and by Vefalius, and others of his time, Primus penis. See the article Accelerator, Cycl. INFER NAL-Sa/r, a name given by Hoffman, and fome other of the chemical writers, to nitre ; they have alfo called it cerberus cbemicus. INFERTILITY. See the article Fertility. INFIBULATION, Infibidatio, in medicine. See the article
Ancteriasmus. INFINITESIMALS. In the method of Infinitcftmals, or of infinitely fmall quantites, the element by which any quantity increafes or decreafes is fuppofed to be infinitely fmali, and is generally expreft by two or more terms ; fome of which are infinitely Iefs 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 arc neglected in this manner, as infinitely left than the other terms of the element, are the very fame which arife in con- fequence of the acceleration, or retardation, of the generat- ing motion, during the infinitely fmall time in which the element is generated ; fo that the remaining terms exprefs the element that would have been produced in that time, if the generating motion had continued uniform, as is farther ex- plained in the article Fluxion.
Therefore thofe differences are accurately in the fame ratio to each other, as the generating motions or fluxions. And hence, though infinitejimal parts of the elements are neg- lected, the conclufions are accurately true, without even an infinitely fmall error, and agree precifely with thofe that are deduced by the method of fluxions.
In order to render the application of this method eafy, fome analogous principles are admitted, as that the infinitely fmall -elements of a curve are right lines, or that a curve is a poly- gon of an infinite number of fides, which being produced give the tangents of the curve, and by their inclination to each other meafure the curvature. This is as if we fhould fuppofe that when the bafe flows uniformly, the ordinate flows with a motion which is uniform for every infinitely fmall part of time ; and increafes or decreafes, by infinitely fmall differences at the end of every fuch time. But however convenient this principle may be, it muff, be applied with caution and art, on various occafions. It is fcfaal therefore, in many cafes, to refolve 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 In- ■ fimtefunah of the fecoriS order. In general, it is a pojlula- turn in this method, that, we may defcend to Infiniujimals
of any order whatever, as we find it neceffary ; by which . means any error that might arife in the application of it, may be diicovered and corrected by a proper ufe of this me- thod itfelf. See Maclaurin's Fluxions, Art. 40,5 — 502. It is alfo to be obferved, that when the value of a quantity that is required in a philofophical problem becomes in cer- tain particular cafes infinitely great, or infinitely little, the folution would not be always juft, tho" fuch magnitudes were admitted. As when it is required, to find by what centripetal force a curve could be defcribed about a fixed point that is either in the curve, or is fo fituated that a tan- gent may be drawn from it to the curve. The value of the force is found infinite at the center of the forces in the for- mer cafe, and at the point of contact in the latter ; yet it is obvious, that an infinite force could not inflect the line de- fcribed by a body that fhould proceed from either of theie points, into a curve ; becaufe the direction of its motion ia either cafe palles through the center of the forces, and no force how great foever that tends towards the center could caufe it to change that direction. But it is to be obferved, that the geometrical magnitude by which the force is mea- lured is no more imaginary in this than in other cafes, where it becomes infinite ; and philofophical problems have limita- tions that enter not always into the general iblution given by geometry.
But altho' by proper care errors may be avoided in the me- thod of Inpnitejimals, yet it mult be owned that to fuch who have been accuftomed to a more ftrict and rigid kind of demonftration in the elementary parts of geometry, it may not feem to be coniiftent with perfect accuracy, that, in de- termining die firft differences, any part of the element of the variable quantity mould be rejected, merely becaulc it is infinitely lefs than the reft ; and that the fame part ihould be afterwards employed for determining the fecond and hio-her differences, and refolving fome of the moft important pro- blems. Nor can we fuppofe, that their fcruples will be removed, but rather confirmed, when they come to confidcr what has been advanced by fome of the moft celebrated wri- ters on this method, who have expreffed their fentimentS concerning infinitely fmall quantities in the precifeft terms ; while fome of them deny their reality, and confidcr them only as incomparably lefs than finite quantities, in the lame manner as a grain of fund is incomparably lefs than the whole earth ; and others reprcfent them, in all their orders', as no lefs real than finite quantities. And altho* it appears ■ from what has been faid in this article, that a fatistactoiy account may be given for the brief way of reafoning that 1*3 ufed in the method of Infinitefiwals ; while nothing is neg- lected without accounting for it ; and that the harmony be- tween the method of fluxions and that of Infinitejhnah, thus appears more perfect.
And however fafe and convenient this method may be, vet fome will always fcruple to admit infinitely little quantities, and infinite orders of Inf.Jiitcfimals, into a fciencc that boafts of the moft evident and accurate principles, as well as of the moft rigid demonftrations. It is therefore proper, that this extenfive and ufeful doctrine fhould be efiablifhed on unexceptionable principles. See the articles Fluxion, and Limit. See alio Mr. Mac la win's Treat, of Fluxions in the Introduction, pag. 39, 4c, oc. and Book 1. Art. 405, to 502.
INF1NITO, in the Italian mufic, is ufed for fuch canons or fugues, as may be begun again and again : Whence they are alfo called perpetual fugues. See the article Fugue, Cycl. & SuppL
IFFLAMMAfJILITY of Oils with Acids. Among the many furprifing phenomena which the world owes to the late improvements in chemiftry, there is none which has more attracted the admiration of the generality of mankind than that remarkable one of the producing actual flame, by mixing; two liquors both cold to the touch ; the acid (pints of mi- nerals, and the chemical oil of vegetables. Beehcr is the firft author who has publifhed an account of ■ this phenomenon. He obferves, in his phyfica fubterranea, that oil of vitriol which is a very ftrong acid liquor, with oil of turpentine which is a very fulphureous one, produces a violent heat, and actual fire or flame. Beehcr giving no farther account of the procefs than this, feveral oi the fuc- ceeding chemifts tried the experiment, but all without fuc- cefs. At length Borrichius explained it, with all the necef- fary particulars, and the effect according to his directions has been fometimes produced ; tho' the great uncertainty of a thoufand little accidents, all of which muft necellarily concur to the producing the flame, has made it often mifs even in the moft careful hands. The method of Borri-- chius is this, mix in a glafs veflel four ounces of frefh drawn and highly rectified oil of turpentine, with fix ounces of aqua fortis newly made and carefully prepared ; cover the veflel, and fhake the two liquors well together. After they have ftood together half an hour, open the veflel, and. there will proceed out of the mouth of it large quantities of flame mixed with great clouds of fmoke. The experiment will not fucceed however unlefs the liquors are frefh made, and the veflel be expofed to the heat of the fun. And many who
have
