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grey winged grajliopper. This is diftinguifhed by having grey wings fpotted with black. 3. The fmali brown grajbopper with a long rhomboidal head. The antennse in this fpecies are very ihort. 4. The great green grajliopper. This is accurately defcribed by Joan, de Muralto in the German Ephemerrdes, and Mr. Kay has taken the whole into his hiftory. The antennae are long and fiender, the eyes black and prominent, and the breaft is remarkably high and narrow. 5. The great Spanifh locuji of a brownifh grey with fpotted wings. This is about three inches long, and is the fpecies lately found in England. 6. The great
' African locuji with filiated fhoulders. This differs from the former only in thefe ftreaks. 7. The great African hcuji. This is four inches long, and is of a green colour. Under the moulders there are only fniall rudiments of wings, and it has two ftrong yellow forceps's under the tail,which terminate in black points. Thofe fpecies of this genus commonly called crickets*, fee under the article Gryllus. Ephem. Germ. Anno 12. Obf. 16. Rcty's Hilt. Inf. p. 64. See alfo Cicada and Harvest^.
The country of the Coflacks or Ukrain is, in dry fummcrs, much inferred with fwarms of loeujh driven thither by an eaft or fouth eaft wind. The number of thefe infects is fo great, that they darken the air, and devour all the corn of the country, f hey lay their eggs in autumn and then die. It is faid that each of thefe creatures lays two, or three hun- dred eggs, which hatching the enfuing fpring-, produce fuch a number of locujls, that they do far more mifchief than be- fore, unlefs the rains fall, which kill both the eggs and the infeefs, or unlefs a ftrong north or north weft wind arifes, which drives all into the Euxine Sea. The hogs of the country arc fond of thefe eggs, and devour great quantities of them. In the night, when thefe infects reft on the ground, they cover it to the height of three or four inches. If a wheel pafs over them they emit an intolerable ftench. Phil. Tranf. N° 8. p. 137. where Monfieur Beauplan's defcription of Poland, and Thevenot's Voyages, Part I. are referred to.
Water Locust, kcufla aquatica, the name given by authors to a fpecies of water infecf , fomewhat refembling the locuji kind in Ihape. It is about three inches long, its tail an inch and quarter, and its legs are of different lengths ; the anterior pair being the fhorteil of all. Its body is fiender, and its fore-legs are always carried ftrait forward, fo as to reach beyond the head in the form of antenna;. Thefe, well as the other legs, end each in two claws. The eyes are fmall and not very prominent, and the upper wings are cruftaccous, the under ones membranaceous, thin, and tranfparent. The middle joint of the leg is fuch, that the creature can only move them upwards, not downwards and there runs an acute tongue or probofcis under the belly, as is the cafe in the Water fcorpion and notonccta. Jim's Hift. Inf. p. 59. "
Locusta puhx, a name given by Swammcrdam to a genus of infects, defcribed fince by Mr. Ray, under the name cicadula. See Cicadula.
LOCUSTELLA, in zoology, the name of a (mail bird of the lark kind. It is fmaller than the common wren, and of a brownifh yellow colour fpotted with black ; its tail is long and brown, and its belly and thighs are variegated with oblong ftreaks of a blackifh brown ; its legs are very long, fiender, and brown. It feeds on flies, and makes the fam' fort of noife that the grafhopper does, only much louder and ufually, as it fmgs, fits on the fummit of fome prickly fhrub, and vibrates its wings about very brifkly. Jolmfon de Avibus.
LOESELIA, in botany, the name of a genus of plants, called alfo royenia by Houfton. The charaflcrs are thefe : the perianthium is one leaved, and tubular 5 it is fhort, and divided into four fegments, and remains after the flower is fallen. The flower confifts of one irregular petal. It is formed into a tube of the length of the cup, and its verge is divided into five equal fegments, all bending toward "one fide, and of an oval figure. The ftamina are four filaments of the length of the flower. Two of thefe are fhorter than the others. The anthers arc fimple, and the germen of the piftil is oval. Theftyle is fimple, the ftigma thick, the capfulc is of an oval figure, divided into three cells and containing a number of feeds of an angular fioure. Limai Gen. PI. p. 306. Houjtmi A. A.
LOG (Cycl.)— Log, in the Jewifb antiquities, a meafure which held a quarter of a cab, and consequently five fixths of a pint. There is mention of a tog, 2 Kings vi. 2 s. un- der the name of a fourth part of a cab. But in Leviticus the word log is often met with, and fignifies that meafure of oil, which lepers were to offer at the temple after they were cured of their difeafe.r— Cablet. Difi. Bibl. Levit. xiv. 12, 24. — ]
Dr. Arbuthnot fays, that the log was a meafure of liquids, the72^ part of the Batb or Ephah, and 12" part of the Km, according to all the accounts of the Jewifh writers. Arbuth. Tables of antient coins, <5V.
Log-M, at fea, a book ruled and columned like the log- board. It is tiled by fome to enter the log-hard's account in SiipPL. Vol. I,
LOG
every day at noon* with the obfervations then made ; and. from' hence it is corrected and entered into the journals.
Loo-wood, the wood of a tree called by Ray arbor filiquofa floribus papiiionaceh. It is defcribed by Breynius under the name of crifla pavonis eorouillcs folio fecuxda, and erythroxyhun indicum fpmofijjimum colutea: foliii, foribus lutcis, filiquis maximis. It grows both in the Eaft and Weft-Indies, but no where fo plentifully as on the coaft of Campeche. Sec Campeche, Cycl.
Befide its ufe among dyers, it is found to be an excellent aftringent, and is given, with fuccefs, in form of cxtraS in diarrhoeas.
LOGARITHM {Cycl.)— Logarithm! are not only of great ufe for facilitating computations in arithmetic and trigonometry, but have been found of extenftve fervice in the higher geome- try, particularly in the method of fluxions. The nature and genefis of logarithms is explained in the Cyclopaedia, after the manner made ufe ot in moil elementary treatifes; but it may be proper to add fomething more on this fubjecf from Mr. Mac Laurin's Treatife of fluxions, who has explained the nature and genefis of logarithm!, agreeably to the notion of their firft inventor Lord Napier.
Logarithm!, and the quantities to which they correfpond, may be fuppofed to be generated by the motion of a point. If this point moves over equal fpaccs in equal times, the line defcribed by it increafes equally.
Again, a line decreafes proportionally when the point that moves over it defcribes fuch parts in equal times as are al- ways in the fame conftant ratio to the lines from which they are fubducted, or to the diftances of that point at the begin- ning of thofe times, from a given term in the line. Inlike manner, a line may increafe proportionally, if in equal times the moving point defcribes fpaces proportional to its durances from a cettain term, at the beginning of each time. Thus, in the firft cafe, let ac be to ao, cd to Co, de to do,
d
f
Q.R
c/"to eo, fg to fo, always in the fame ratio of Q_R to Q_S ; and fuppofe the point p fets out from a, defcribing ac, cd, ' le , 'f, fg, in equal parts of the time ; and let the (pace de- fcribed by p in any given time, be always in the fame ratio to the diftance of p from at the beginning of that time then will the right line ao decreafe proportionally. Inlikemannertheline oa, increafes proportionally, if the point p in equal times defcribes fpaces ac, cd, de, ef, fg, &c. fo that a c is to ao, cdtoco, de to do, &c. in a conftant ratio.
a c d e
If we now fuppofe a point P defcribing the line A B with an uniform motion, while the point p defcribes a line increafing or decreafing proportionally, the line AP de- fcribed by P with this uniform motion, in the fame time that oa by increafing 'or decreafing proportionally be- comes equal to op, is the logarithm of op. Thus A C, AD, AE, CSV. are the logarithm! of oc, od, oe, &c. re- fpeflively ; and a is the quantity whofe logarithm is fup- pofed equal to nothing.
We have here abftracfed from numbers, that the do&rine may be the more general ; but it is plain, that if A C, A D, A E, &c. be fuppofed 1, 2, 3, CSV. in arithmetic progreffion; oc, od, oe, &c. will be in geometric pro»ref- fion, and that the logarithm of a, which may be taken for unity, is nothing.
Lord Napier, in his fiifS fcheme of logarithm!, fupoofes, that whiles^ increafes or decreafes proportionally, the' uni- form motion of the point P, by which the logarithm of op is generated, is equal to the velocity of p at a ; that is, at the term of time, when the logarithms begin ro be generated. Hence logarithm formed after this model are called Napier's logarithms, and fometimes natural logarithm!. When a ratio is given, the point p, defcribes the difference of the terms of the ratio in the lame time. When a ratio is duplicate of another ratio, the point p defcribes the dif- ference of the terms in a double time. When a ratio is triplicate of another, it defcribes the difference of the terms in a triple time 5 and fo on. Alfo when a ratio is com- pounded of two or more ratio's, the point p defcribes the difference of the terms of that ratio, in a time equal to the (urn of the times, in which it defcribes the differences of the terms of the fimple ratios of which it is compounded. And J S S what
