LIN
acute diftempers, yet he has found it fafe in feverifh colds ; and by the cafes he there mentions, it feems probable that Lime-water, by its diluent, and diuretic qualities, may prove more ufeful in fevers, than is at prefent believed. However, this may prove on farther trials, it may be faid, in general, that Lime-water is diluent, detergent, antifcep- tic, anthelmintic, diuretic, and vulnerary ; ufeful in all dif- eafes proceeding from, or accompanied with obftrudfions in the bowels or glands, vifcid phlegm, calculous concretions, or putrefaaion 5 and commended for the fcuryy, fcrophube, gravel, confumption, empyema, afthma, arthritis vaga, cede- rnatous fwellings, diabetes, fluor albus, fluxes, &c. and out- wardly for difeafes of the fkin, ulcers, gangrenes, &c. It may be taken to the quantity of a pound, once, twice, or thrice a day ; or ufed for common drink. See Dr. Alllon's Differ- tation on quick-lime, and Lime water, Edinb. 1752. The ingenious and learned Dr. Whytt of Edinburgh, has greatly recommended Lime-water, in the ftone and gravel. See his efl'ay on the virtues of Lime-water, in the cure of the ftone. This gentleman prefers oyfter-fhell Lime-water to any other for thofe diftempers. Dr. Alfton feems to think this a matter of indifference, and was himfelf cured chiefly by the ftone quick-lime water before-mentioned.
LIMER, or hlME-Hcund, names fometimes ufed for the blood-hound. See the article Hound, Suppl.
LIMITED,' adjunfl. See the article Adjunct, Cycl.
LIMITS (Suppl.) — We may add to what is faid under this . head in the Supplement, that there being two cafes of vari- able quantities and ratio's tending to a Limit, it might have conduced to perfpicuity, and prevented difputes, to have dif- tinguifhed thefe different Limits by fome addition^ As in the full: cafe, to have called it a Limit or ultimate ratio inclufive ; becaufe the Limit is the laft of the quantities or ratio's limit- ed : And in the fecond, to have called it a Limit or ultimate ratio excluftve ; becaufe the quantities limited never attain to the Limit, tho' they approach to it indefinitely. This diftinaion may perhaps receive fome farther illuftration from the following example. It is known that the ofcula- tory circle is a circle that touches a curve fo clofely that no other circle can be drawn through the point of contafi between them, all other circles pafling within or without them both ; and hence the ofculatory circle is fuppofed to have an equal curvature with the curve at that point. See Mr. Mac Lau- riti's flux. art. 364. Now if we conceive the ofculatory circle at the end of the
- great axis of an ellipfis, it will fall entirely within the cllipfis ; and the curvatures of the ellipfis and ofculatory circle may both be faid to be limits of the curvatures of all the circles falling wholly within, and touching the ellipfis at the end of its great axis. But the term Limit will not in both cafes have precifcly the fame meaning ; for the ofculatory circle is a Li- mit inclufive, being the lafi of the circles limited ; and the ellipfis is a Limit exclufive, none of the circles limited ever coinciding with it. As to the circles which fall wholly with- out the ellipfis, and touch it at the end of its great axis, they have no Limit inclufive, no circle touching the ellipfis fo clofely, that no other can pafs between ; the only Limit here is exclufive, the ellipfis itfelf.
The contrary of this happens at the endo f the leer axis. At any other point of the ellipfis one half of every ofculatory circle is a Limit inclufive of the femicirclcs that fall within, and the other half is a Limit inclufive of thofe that fall without. May we not afk, if a curve is the Limit of its inferibed or circumfcribed polygons in any other fenfe, than the curvature of the illipfis is the Limit of the curvatures of the circles be- fore defcribed, which approach nearer and nearer to the curve, but never coincide with it ? It is true we hear it often faid, that the ofculatory circle is a^quicurval, and fo coincides with the ellipfis ; but this feems a confequence of the language of infinitefimals. It would be more accurate to fay, that the curvature of the ellipfis is the Limit exclufive of all the be- fore mentioned circles, and that the ofculatory circle is their Limit inclufive. That excellent geometer, Mr. Simfon, in his Conic Seaions, Lib. v. Prop. 36. Cor. fays only, after demonftrating the chief property of the ofculatory circle, that eandem habere cum feclione conica curvaturam dicitur, giving this only as an appellation, but not as a propofition.
LIMNOPEUCE,in botany, the name by which Vaillant calls the Hippuris of Linnaeus. See the article Hippunrs, Suppl.
LINE (Cycl) — Algebraic Lines are divided into different orders, according to the degree of their equations. Thefe degrees are eftimated, as in determined equations, by the de- gree of the higheft term of the equation. Thus a-\-by-\-cx~o\s?i general equation, expreffing the
• nature of Lines of the firft order, or of ftrait Lines.
The equation a -|- by -f- c X -J- dyy -f- e xy -f- f X X = o re- prefents the lines of the fecond order ; that is, the conic feaions, and the circle, which is one of them. And the equation a -- by -\- c x -f- dyy 4- e xy -f- fx x 4- g> 3 + i> x yy -- i # * y -f- /* 3 = 0, exprefles in general the lines of the third order. And the Lines of the fourth and higher orders may be expreffed in the like manner. See Cramer, Introd. a l'analyfe des lignes courbes. p. 52, feq. J.Mr. Cramer ufes the terms, Line of the fecond, third, fourth, 4
L I T
&c. order, and Curve of the fecond, third, fourth, &c. or- der, indifferently. Sir Ifaac Newton has made a diftinaion : according to him,
Line of the third order is the fame as Curve of the fecond kind\ becaufe a Line of the firft order, cannot, ftridtly (peaking, be called a Curve.
Lines of the third order may be cut by a right line in three points, and by a circle in fix points.
We have a fliort treatife by Sir Ifaac Newton upon the Lines of the third order, entitled, Enumeratio lincarum tertii ordinis y which was firft printed at the end of Dr. Clarke's latin tranf- lation of Sir Ifaac's Optics 5 and fince publifhed more cor- rectly by the late Mr. Jones in 171 r 9 with the treatife of quadratures, and other trails of its illuftrious author. This enumeration is fo concife, as to need a comment. Mr. Stirling gave one in 17 17 ; but this comment is too difficult for beginners. Mr. Cramer has lately explained this fubjecl: very fully, in his Introduction a l'analyfe des lig- nes courbes algebriques, printed at Geneva 1750, 4-to, to which the curious may have recourfe ; as alio to the Appendix to Mr. Mac Ljurin's Algebra, entitled, Delinearum geome- tricarum proprietatibus generalibus ; and to Mr. Euler's Ana- lyfis infinitorum, Vol. II.
An algebraic Line of the order m can cut another algebraic Line of the order n, in the number of points expreffed by m n, but not in more. Thus if m = 1 and n = 2, the lines of thofe orders can interfeel: each other in two points only ; and if m = 2 and n = 2, then may they, interfeel: each other in four points, as is well known ; fince a ftrait Line cannot interfeel: a conic fection in more than two points ; nor can one conic fe£tion interfeel another in more than four points. In like manner if m.=> 5 and n = 4, then may the titles of thefe orders interfeel: each other in 20 points ; but not in more. See Cramer, Anal des liynes courbes, p. 75, 76. The number of the fpecies of the Lines of the third order amount to 78. See Mr. Murdoch's Genefis Curvarum per Umbras. Sir Ifaac reckoned only 72 fpecies of the third or- der ; but Mr. Stirling and Mr. Stone have fhewn his enume- ration to be imperfeel j and Mr. Murdoch has fince found fome new fpecies.
LION. The Lion is comprehended among the fe lis, or cat- kind of animals. See the article Felis, Append.
Lion's leaf the Englifh name of a genus of plants, defcribed by Toumefort under that of Leontopetalon. See the article Leontopetalon, Suppl.
Lion's foot, the Englifh name of a diftirnEr. genus of plants, called by botanifts Catanancc. See the article Catanance, Suppl.
LIQUID Amber, in botany, the mme of a diftinft genus of plants, called by botanifts Anthofpermum, and Toumefortia. See the articles Anthospermum, Jppcnd. aad Tourn'e-
FORTIA, Suppl.
LIQUORICEf Suppl. J— JWj-Licojorice, the Englifh name of a genus of plants, called by botanifts Orobus. See the article Orobus, Suppl.
Wild Liquorice, the name of a diftincl: genus of plants, called by authors Ajlragalus. See the article Astragalus, Suppl.
LIQUORS, fermented. See the article Fermented liquors, Suppl. and Append.
LIST, in the fea-Ianguagc, the fame with lujr. See the article Lust, Suppl.
L1THONTRIPTIC (Suppl) — The reward which the par- liament of England gave to Mrs. Stephens, the inventrefs of fome medicines, which were faid to be a perfect and certain cure for the Stone, made the generality of the world believe, that they were really as efficacious as they were pretended to be ; but it appeared, on examination, that the opinion of a cure in the very inftances on the fuccefs of which the re- ward was given, was erroneous ; and that the Stones had, all the time remained in the bladders of the patients, tho' fup- pofed to have been voided, after being dilTolved and wafhed away by the medicines.
The principal inftance of a fuppofed cure was Mr. Gardiner. This man was in December 1748, examined by able fur- geons, and found to have a ftone in his bladder j after this he took Mrs. Stephens's medicines for eight months without intermiffion ; and at the end of that time he declared himfelf free from all his ufual complaints ; and on fearching him, there could no ftone be found in the bladder. Mr. Gar- diner died about three years afterwards, and his body was opened. When the bladder was examined, there were found in it fix preternatural apertures of different fizes ; but the biggeft capable of admitting the end of a finger. Each of thefe apertures led to a feparate bag form'd by an enlargement of the internal membrane of the bladder, protruded between the fibres of its mufcular coat. Thefe bags were eafily feen on the back part of the bladder a little above the veficulx feminales, and when viewed on the outfide, they feemed to be but two, tho' in reality equal in number to the open- ings within, and divided from one another by the duplica- ture of the internal membrane, which form'd a feptum be- tween each of them. Philof. Tranf. N° 462. p. 12. . As to Mrs. Stephens's medicine, it is a compofition of foap, and lime made of different fhelis, which every body
knows
