E Q^U
The old method of Vieta, for folving aufe£ed Equations, was extremely tedious. It was formed by analogy, from the 1 common method of extracting the roots of pure powers. See Vietse Opcr. Math. ap. Elzev. p. 173. or TVallh\ Al- gebra, Ougbtred's Clavis, De Lagny Elemens d'Arithm. ■
. &d'AIgebr. p. 515, tiV.
Equation of the Center* in aftronomy. — This Equation not] being conftant, there is a place in the planet's orbit where it is greateft:. Hence feveral queftions in aftronomy arife ; as, what is the greateft Equation for every planet ? To what mean anomaly does this Equation correfpond ? Alfo, as the greateft Equation is determined by the excentricity of the planets orbit, it may be reciprocally requifite to determine the excentricity by the greateft Equation.
The rigorous folutions of thefe queftions being no where ex- tant, Mr. Euler has enquired into them, in Mem. de TAcad. de Berlin. Tom. 2. p. 225. feq. Where he folves the fol- lowing problems.
i°. To find the true and mean anomaly, correfponding to the planet's mean diftance from the fun ; that is, when the planet is in the extremity of the conjugate axis of its orbit. 2°. The excentricity of a planet being given, to find the ex- centric anomaly correfponding to the greateft Equation. 3 . The excentricity being given, to find the mean anomaly correfponding to the greateft Equation. 4 . From the fame data to find the true anomaly correfpond- ing to this Equation,
5 . From the fame data to find the greateft Equation. 6°. The greateft Equation being given to find the excentri- city. Mr. Euler obferves, that this problem is very difficult, and that it can only be folved by approximation, and tenta- tively, in the manner he mentions. But, if the excentricity be not great, it may be then found directly from the greateft Equation. Thus, if the greateft Equation =zm, and the excentricity = ;;, then,
m = 2«+ ^*i + i92-n* +, &c
48 '5120
Whence by converfion
n = - m - — - m
768
«s _, &c.
Where the greateft Equation ?n, muft be cxprefted in parts of the radius, which may be done by converting the angle m, into feconds, and adding 4 . 6855749 t0 the l°g aritnm of " the refulting number ; for this will be the logarithm of the num- ber m. The mean anomaly to which this greateft Equation corref-
ponds, will be, x = go -J- | m -£- nfi — — — mi — ,
r ? ' v 8 29.3 29 . 5
£&.
Whence, if to go° we add ~ of the greateft Equation) we
{hall fufficiently approximate to this mean anomaly. Mr. Euler gives us a table, in which may be found the great- er! Equations, the excentric and mean anomalies, correfpond- ing to thefe greateft Equations, for every hundredth part of of unity, which he fuppofes equal to the greateft excentricity, or when the diftance of the foci and the tranfverfe axis be- come infinite. The laft column of his table alfo gives us the logarithm of that diftance of the planet from the fun, where its Equation is greateft. By the help of this table, any excen- tricity being given, we may find the greateft correfponding Equation, by interpolation. But the principal ufc of the table is, to determine the excentricity when the greateft Equation is known, and Mr. Euler thinks the queftion infa- llible without this help. See the Table, lib. cit. p. 245. feq. EQUESTRIA, among the Romans, a place in the theatre,
where the equites, or knights, fat. Hofm. Lex. in voc. EQUESTRIAN (Cyd.) — Equestrian Cohort, in antiquity.
See Cohors Equitata.
Equestrian Games, ludi Equeflres, among the Romans,
horfe-raccs ; of which there were five kinds, the prodromus,
or plain horfe race, the chariot race, the decurfory race about
funeral piles, the ludi fevir ales, and the ludi neptuna-les. Pi-
iifc. Lex. Ant. in voc.
EQUINUS Barbatus, a kind of comet. See Htppeus, Cyd.
EQUIRIA, in antiquity, a feftival inftituted by Romulus, in
honour of Mars, at which there were horfe races. P'ttifc. EQUISELL, in ichthyology, a name given, by Gaza, and fome other writers, to the dorado, or dolphin : The cory phasna with the forked tail of Artedi. See Coryphjena. EQUISELIS, in natural hiftory, the name of a large fly, of the fize of a hornet, but having only two wings and no fting. It otherwife much refembles the common hornet in fhape. This fly is found only in Macedonia. We have alfo, in Eng- land, flies which nearly refemble the hornet, wafp, and bee, but in their wanting ftings, and having only two' wings. EQUISELIS, in ichthyography, a name ufed, by fome authors, for the hippurus, a fea-fifli, caught on the Spanifh fhores, and fuppofed by many to be the fame with the dorado. IVillugbby's Hift. Pifc. p. 213. See the article Hippuris. EQU1SETUM, Horfetail, in botany, the name of a genus of plants, the characters of which are thefe : The flower is of
ERE
the apetalous kind, being compofed of a number of ftamina, each furni&ed with a mufhroom-like head, and , all difpofed in a fort of fpiked form. Thefe flowers are barren, and the feeds of the fame fpecies grow on plants of a very different figure, which have no flowers, and only produce black rough feeds. To this it is to be added, that the plant confifts of feveral joints, one received into another, in the manner of larger and fmaller tubes. See Tab. 1. of Botany, Clafs 15. The fpecies of Horfetail, enumerated by Mr. Toumafort, are thefe : 1. The marfh Horfetail, with long branches. 2. The marfh Horfetail, with ihorter branches. 3. The field Horfetail, with very long briftles. 4. The wood Horfetail, with very (lender briftles. 5. The rum- like naked, or not branched Horfetail. 6. The great marfh Horfetail. 7. The great naked, but branched Horfetail, 8. The fmall naked variegated Horfetail. Town. lnft. P- 532-
The common great marfh Hfirfetail is ufed in medicine as an aftringent and vulnerary. Schroder recommends it in all kinds of hemorrhages, and exukerations of the kidneys and bladder.
EQUITATA Cohors, in antiquity. See Cohors Equitata.
EQUUS, the Horfe, in the linnxan fvftem of zoology, this makes a difrinct genus of animals, of the jumenta kind, the cha- racters of which are, that the creatures have two paps, fituated in the groin, the dentes inciibrcs are fix in each jaw ; the canine, or dog-teeth, are placed at a diftance from the others, and are but little longer than they. According to thefe cha- racters, the author includes in this genus, the horfe, the afs, the wild afs, and mule, and the zebra, or, as lie calls it, the ftriped horfe. Linnai Syftem. Natur. p. 40.
Equus Marivus, in zoology, a name given, by fome, to an animal very different from the hippopotamus, or river horfe, and more ufually known by the name of the morfe. See Morse.
ERA, in chronology. See /Era, Cyd.
ERANDGAAS, in zoology, the mime of a fowl, ofthegoofe kind, defcribed by fome authors. It is faid to be fomewhat fmaller than the common wild goofe. Its head grey, and its neck adorned with a red ring. Its breaft, wings, and neck, are grey, and its feet red. Mr. Ray much fuipcefs the ac- count of this bird. Ray's Ornithol. p. 308.
ERANTHEMUM, in botany, a name given, by fome authors, to the flos Adonis, or red maithes. J. Bauhiu. vol. 3. p. 129.
EREBENNUS, e p jWc, a name given by Galen, and fome other of the Greek writers, as a diftincfive epithet for the black chamadeon thiflle, which was efteemed porfonous, and was by this word diftinguifhed from the fegleus, or aty?^;, or white chameleon, which was an efculent plant, and ufed by fome as an antidote. It has happened, however, that the white ehamaekon thiftle has been by fome called a poifon, as well as the black, but this is only owing to a miftakc of Pliny, in fuppofing the effects of birdlime to have been attri- buted to this plant, becaufe yielding a vifcous, but fafe gum, at its root. It was called, by fome, ixios chamselecn. Galen.
ERECT Leaf, Ere Rum folium, among botanifts. See Leaf.
EREGMOS, a word ufed, by the antients, to exprefs a bean decorticated, and broken into fmall pieces, in order to be boiled in ptyfans. This name was not, however, kept ftrictly to this fenfe, but they applied it indifferently to all the leguminous fruits, broken in the fame manner. Ecefius will have it to fignify bean meal, but others are againft this ; and Galen, in fome places, ufes it only to exprefs a bean divided into two parts.
ERETHISMOS, a word ufed by Galen and Hippocrates, to cxprefs any thing that irritates. Galen fays, that Hippocrates means by it alfo every thing that reduces the habit of body to an infirm ftate, among which are to be reckoned, before all other things, irritating, acrimonious, and pungent humours in the ftomach and bowels, particularly in the mouth of the ftomach, worms afcending from the inteftines into the fto- mach, nocturnal itchings of the whole fkin, or of fome part of it, which, by' their irritation, and prevention of flecp, greatly exhauft ftrength.
ERETRIA Terra, Eretriun Earth, in the materia medica, the name of a very peculiar kind of bole, dug in the Ncgro- pont, near the antient Eretria, and once in great ufe as an aftringent and a fudorific.
The antient writers in medicine all mention the eretrian earth j and Diofcorides and Galen defcribe two kinds of it, a grey and a white. The gfey is what is properly diftinguifhed by this name, being an earth of a different kind from alt the other boles. The white, though the antients fecm not to have obferved it, yet was plainly, from their own defcriptions, the fame with the white bole armenic, tho' found in a different place. i#/fs Hift. of Fof£ p. 5.
The grey, orgetiiii.ne' eretrian ea*pf, is a fine and puregrcyifh white earth, moderately heavy, naturally of a frnooth fur- face, of a friable texture, eafily crumbling to pieces between the fingers, but not ftaining the fkin in handling ; it flicks firmly to the tongue, but melts into a butter-like fubftance in the mouth ; it burns to a perfedt fnow white, and effcrvefces
violently
