ALL 



A L L 



Tlve rule for tliii kiiul of alligalioii may be otiicnv'fc cx- 

 prcflVd and applied to nil the calciaboVc i iiii:;i<.iatcd, thus: 

 Haviiiir coupled tlie rates as before, then i\>r any pair of dif- 

 ferences, taLe their eiiuirmiltiples, or multiply tliein by any 

 number at plealm-e ; proceed in the fume maimer witli any 

 other pair ; and you will thus have a new fct of difierenccs 

 with which to woi 



lod. 

 ^li. fo that the mixture may 

 be fold at yf/. ; how mucli mult he take ? 



Exam/i/f I. A grocer would mix 12II1. of fugar at u 

 with two other forts at SJ. ami Ci/. fo that the mixture m 



Common IvTeth'iJ^ 

 10, 



Central Method. 



45 



I-.; 



The pair of dilferences atraiiid lo and 5, being 2 and i, 

 are mulLiplied by 2, and they bceome 4 and 2 : thofe 

 againll 8 and 5, being 2 and 5, are multiplied by 3, and 

 they become 6 and y ; fo that 4, 6, 11, will be the new fet 

 of dideienceG. 



rp, f 6 : 8//;. at %d. 



Ihen, 4 : 12 -{ ,, , 



t" = 33'''- at 5^/. 

 Example 2. A farmer would mix wheat at 4J. with rye at 

 3/. and bailey at 2s. and oats at u. per buflicl, in order to 

 obtain a quantity of 120 burticls, to be fold at 2j. 4^. per 

 bulhel ; how miieh of each mull be taken ? 



28 



i68 



TiS : 345- bufliels of wheat, 

 J 20 : 14^ rye, 



> 40 : 28^ barley, 



(60 : 42^ oats. 



But all quedions of this kind are moft eafily and accu- 

 rately folved by common algebra, which will enable us to 

 determine their limits ; as they form a fort of indeterminate 

 problems, and admit of many, or an indefinite number of 

 aivfwers. For a further explanation of this ride and exam- 

 ples, we refer to Ward, Wallis, Malcolm, Emerfon, and 

 other writers on arithmetic and algebra. 



We fhall add an example, wherein both the kinds of alli- 

 gation have place. Suppofe a mixture of wine of 119 

 quarts, required to be made of wines of the following 

 prices, 7</. 8(/. 14//. and \^d. per quart ; and fo aji that 

 the whole may be afforded at ild. per quart. 



Having linked 8 to 14, and 7 to 15, and counterchanged 

 their differences from the common price, 1 2;/. the fum of 

 their difference is found to be 14 ; by which dividing 119, 

 the quotient is S-^-'y, or 8i, or for convenience in opera- 

 tien y. 



Quarts. 

 yX2 = V = i7 



Tlien 168 : 120 : 

 Or, 7:5: 



8 ("2 

 7 Si 



X4= 

 X3^ 



= 25* 



yxj=V=_4i| 

 •'9 



ALLIGATOR, in Ztmh^^y, a name given to the Ame- 

 rican crocodile, a fpccics of Lackrta, under which article 

 it is dcfcribed. 



Alligator Pear, in Botany. See Latirus. 



ALLIONIA, in Botany, fo called in honour of Charles 

 AUioni, profefibr of botany at Turin, a genus of the tt- 



fra.rdrla minogynia clafs and order, of thi; natitral ord<ir of 

 c<^^rc^a!(t and dipfacce: of JuITku; the tharaderii of wl^ich arc, 

 lh.it the cid)'x is a perianthium common to three flower;,, 

 fnr.ple, oblong, fi.e-partcd, the parts ovate, acute, pc- 

 uianent ; and the pcriitvtl.'.iim proper is obfolete, fiperior ; 

 the coroil.< proper, o;it-peta!led, fminel-fliaptd, edjjc quin- 

 queSd, and creel ; the fiimna have fitaceous filaments, 

 longer thau the coioUa, bendi.ig to one fide, anlliers ixjuiid- 

 ifli ; the /i;'/7;('.'h)/. '.IS a germ inferior, olilong, Hylt lltaceous, 

 longer than the flamens, flignia mullifid and linear ; nopcn- 

 carphim ; feeds folitary, oblong, live-eonieiLd and naked : 

 tlie receptacle naked. Martyn enumerates two, and Cfiiielin 

 three fpccics, v':~. I. A. liolic-a, with leaves hcart-fhaped 

 and calyces quinquelid, a native of Cumnna, in South Ame- 

 rica. 2. A. incaniala, with leaves obliquely ovate, and ca- 

 lyces triphyllous, a native of Peru, in rocks and (xvAy 

 foils, introduced into the Pans garden from feeds fent by 

 Dombey, flourifliing there and perfecting its feeds in the 

 middle of fummer. 3. A. allidti of Gmeliri, with leaves 

 lanceolate, oppollte and roughiili, and calyces pcdidllatcd 

 and folitai-)-. 



ALLIOTH, in Aftronomy, a flar in the tail of the Great 

 Bear, whofe obfervation is much uled at lea. 



It is alfo written all'iol, and al'wt, and literally denotes » 

 horfe. The Arabs give this name to each of the three ihtra 

 in the tail of the Great Bear, on account of their appear- 

 ing like three horfes, ranged for the drawing of the wag- 

 gon, reprefentcd by four ftars, called Charles's wain. 



ALLIOTICUM, from aW.oi., to -jary, a Galenical 

 medicine, which alters and purifies the blood, confifting 

 chiefly of the roots of dandelion, fnccory, fennel, and rai- 

 fins ; with the herbs endive, common ox-eye, lettuce, for- 

 rel, fumitory, &.c. See AltkrativK. 



ALLITERATION, in Rkioric, is a figure or decora- 

 tion of language, chiefly ufed in poetry, and confiiling in 

 the repetition of the fame letter or letters at certain inter*- 

 vals,- whence its name is derived. This figure has been go 

 nerally regarded either as tiivial in itfelf, or as an iiillance 

 of falfe refinement ; but for the ufe of it we might refer to 

 the beft authority, and it unqucftionably facilitates the reci- 

 tation of vcrfe, contributes to both its fwcctnefs and energy, 

 fervcs to enforce the fentimcnt which it exprclTes, and aids 

 the memory in retaining it. Pontanus, one of thofe inge» 

 nious Itahans wlu) (louriflicd upon the revival of literaturt 

 in Europe, has particularly defcribed this figure, and fur- 

 nifhed inilanecs of it both from poetical and profe writers. 

 It occurs in the repetition of the fame letters, fyllables, or 

 words ; and when it takes place in the firft and laft fyllables, 

 and even in the middle ones, it is, he fays, wonderfully 

 pleafing. The inilanecs which he produces from Virgil are 

 fuch as follow : " S:Eva fedeus fuper arma." — " Tales cafus 

 Caffandra cancbat." — " Infontem infando indieio." — 

 " Longe falc faxa fonabant." — " Magno mifceri murmurc 

 pontiim." — " Quxcjuc lacus late liquidos." — In the follow- 

 ing inllance, cited from Lucretius, it is continued from qne 

 verfe to another : — 



«« Advcrfo flabra feruntur 



Flumine." 



Cicero (in Brut.) ufes this figure : — " Nulh res msgis- 

 pcnetrat in animos, cofque fmgit, format, flectit :"' and 

 alfo (De Orat.l : " Quodque ine follicitave fumme folct." 

 For the ufe of this figure we may add to that of Virgil the 

 fuperior authority of Homer. 11. ^. 201. 



"Hroi xccTXMicv TO .\XrI*''y oVo^ 'AXctTo, 

 ■'0» 9;uM xa'lf^wv, a-alw 'A>9{wT»n' 'A^li(>»l». 



Hermogene* 



