ELA
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ELC
confidering them as confiding of a greater or left dumber of fine Fibres of the fame Thicknds ; the Number where- of muft be taken in the Ratio of the Solidity of thofe Fibres i. e. as the Squares of the Diameters, or as the Weight ot the Fibres, when their Lengths are equal. Such Fibres, ot Confequence, will be equally ftretch'd by Forces that are in the fame Ratio of the Squares of the Diameters ; which fame Ratio, is likewife required between the Forces whereby the Chords are inflected, that the Sagitte may be equal in the given Fibres. . .
5 The Motion of a ftretch'd Fibre agrees with the Mo- tion of a Body vibrating in a Cycloid; and how unequal Sever the Vibrations are, they are all perform d in the fame Time. See Cycloid. _„-,,, ,
6. In two equal Chords, unequally ftretch d, Unequal Forces are required to inflect them equally. Their Mo- tions may be compared to thofe of two Pendulums, defcribing fimiiar Cycloids, by different Forces. Confequently, the Squares of the Times of the Vibrations of the Fibres are to each other inverfely, as the Forces whereby they are equally inflefted, which are as the Weights by which the Chords are ftretch'd.
f. The Motions of fimilar Chords, equally ftfetch d, but of different Lengths, muft be compared with that of Pen- dulums after another Manner ; for as the Times of the Vibrations are to be confider'd, the Celerities alfo, where- with the Chords are moved, muft be confider'd. Now thefe Celerities are to one another direflly as the Weights whereby the Chords are inflected, and inverfely as the Quantities of Matter in the Chords ; that is, inverfely as their Lengths. The Celerities, therefore, are in an inverfe duplicate Ratio of thofe Lengths ; that is, inverfely as the Squares of the Lengths : And the Squares of the Times of the Vibrations, are likewife in the inverfe Ratio. Con- fequently, the Lengths of the Chords will be as the Times of the Vibrations.
Elaftic Laminm, or Plates, may be confider d as Con- geries's, or Bundles of Elaftic Chords. When the Plate is inflected, fome Fibres are lengthen'd ; and there are unequal Lengthenings in feveral Points of the Plate.
The Curve form'd by the inflefted Plate, is eafily deter- mined from what has been /hewn concerning Chords. In Effect, in the Vibrations of fuch Plate, or Spring, the Motion thereof is accelerated, after the fame Manner as the Motion of a Chord, and of a Pendulum in a Cycloid, are accelerated. And the Vibrations of fuch Springs are all perform'd in the fame Time.
Elaftic Sails, Spheres, &c. may be confider'd as confift- ing of feveral Elaftic Plates, or Springs ; and the Introceffions, or' Yieldings inward uf any Point thereof, are proportionable to the Forces wherewith the Body is comprefs'd.
The Elasticity of Fluids is accounted for, from their Particles being all endowed with a Centrifugal Force ; whence Sir Ijdac Newton, Prop. 23. Book 2. demonftrates, that Particles, which mutually avoid, or fly off from one another by fuch Forces as are reciprocally proportional to the pittances of their Centre, will compofe an Elaftic Fluid, whofe Denfity fhall be proportional to its Compreffion ; and vice verfta, if any Fluid be compofed of Particles, that fly off and avoid one another, and hath its Denfity proportional to its Compreffion; then the Centrifugal Forces of thofe Particles will be reciprocally, as the Diltances of their Centres. , . ,.
Elasticity of the Mr, is the Force wherewith it di- lates it felf, upon Removing the Force whereby it was comprefs'd. See Air.
The Elafticity or Spring of the Air, was firft difcover d by the great Galileo. Its Exiftence is proved by this Experiment of that Philofopher : That an extraordinary Quantity of Air, being intruded by Means of a Syringe into a Glafs or Metal Ball, rill fuch Time as the Ball, with this Acceffion of Air, weigh confiderably more in the Ba- lance than it did before ; upon opening the Mouth thereof, the Air rufties out, till the Ball have funk to its former Weight.
For hence we argue, that there is juft fo much Air gone out, as comprefs'd Air had been crouded in. Air, therefore, returns to its former Degree of Expanfion, upon removing the Force that comprefs'd, or refifted its Expanfion 5 confe- quently it is endued with an Elaftic Force.
It muft be added, that as the Air is found to rufh out, in very Situation, or Direction of the Orifice ; the Elaftic Force of the Air afts every Way, or in every Direction.
The Elafticity of the Air making a considerable Article in the new Pneumaticks 5 we lhall here give the principal Laws thereof.
1. The Elafticity of the lower Air, is equal to the Weight of all the upper incumbent Air. For the upper Air is eafily proved to prefs on the lower. See Pres- sure.
And the Elafticity of the Air, has already been fliewn
equal to the comprefling Power : Whence it follows, that the Elafticity of the Air is equal to the Weight of th» whole incumbent Atmofphere.
Hence, as the Weight of the upper Air, incumbent on the lower, is equal to the Weight of a Column of Water of the fame Diameter with the Column of Air, and the Altitude of 5 1 Feet ; or to a Column of Mercury 28 Inches high : The Spring of the lower Air is equal ro the fame Column of Water, or Mercury.
Hence, again, the Spring of the Air, included in a Veffel, iSc. is likewife equal to the Weight of the whole incum- bent Atmofphere. Confequently the Air, included in a Veflel, prefles with the fame Force, as the Weight of the Atmofphere. And, therefore, the Elafticity of the included Air, is able to fuftain Mercury to the Height of 28 Inches, and Water, to the Height of 3 1 Feet, in an empty Tube. See Air-Pump.
2. The Elaftic Force of Air comprefs'd, is to that of the fame Air dilated reciprocally, as the Bulk of the di- lated Air to that of the comprefs'd Air.
For the Elafticity of Air more comprefs'd, is to that of Air lefs comprefs'd ; as the Weight incumbent on that, to the Weight incumbent on this. "But the Bulks of more, and lefs comprefs'd Air, are in the fame reciprocal Ratio of thefe Weights. Therefore the Elaftic Force, &c.
Hence the Elafticity of Air more comprefs'd, is ftronger than that of Air lefs comprefs'd.
3. The Elafticity of more comprefs'd Air, is to that of Air lefs comprefs'd, Ceteris paribus, as Mafs, or Quantity of more comprefs'd Air is to the Mafs of Air lels com- prefs'd, under the fame Bulk.
4. The Ratio of the Space fill'd by Air prefs'd only by the Weight of the Atmofphere, to the Space it is redue'd into byturther Compreflion, being given; to determine the Elaftic Force of the comprefs'd Air.
Since the Spring of the "Air, prefs'd only by the Weight of the Atmofphere, is equal to the Weight of a Column of Mercury of the fame Bafe with the Column of Air, and of the Height of 28 Inches ; to the Bulk of the comprefs'd Air, that of the Air not comprefs'd, and the Weight of the Column of Mercury ; feck a fourth proportional : This will exprefs the Quantity of the Elaftic Force in the comprefs'd Air.
Hence, fubftraaing the Weight of the Column of Mercury from the Quantity of the Elaftic Force, thus determined, the Remainder is the Force of Elafticity, whereby it ex- ceeds the Refiftance of the Weight of the Atmofphere.
5. Heat increafes the Elafticity of the Air 3 and Cold diminifhes it. See Heat and Cold.
6. The Elaftic Force of the Air, whereby it is expanded, in Rarefaction, is to the Elafticity of the Air condenfed j as the Bulk of the rarified Air, to the Bulk of the con- denfed Air.
ELATERIUM, in Pharmacy, a purgative Medicine, prepared from the wild Cucumber.
'Tis made of the Juice of the Plant, by ftraining it thro* a Cloth, aud evaporating the Moifture thereof till it come to the Confiiience of an Extract, or a Mafs for Pills.
Elaterium is a vigorous Purge, and is ufed in Lethar- gies, Palfics, and Hypochondriacal Melancholies.
The Word is form'd from the Greek, sAat/ro, / repel.
ELBOW, the outer Angle made by the Flexure, or Bend of the Arm : Or the Point to which the two Bones that form the Arm incline. See Arm.
That Eminence, whereon the Arm refts, called by us Elbow, is by the Latins call'd Cubitum, and the Greeks Ayyjuv, and by others oAeitearss.
Elbow, is alfo ufed by Architects, Mafons, &c. for an obtufe Angle of a Wall, Building, Road, (Sc. which diverts it from its right Line. See Cubit.
ELCESAITES, or ELCESAIANS, as Theodoret calls them, antient Hereticks thus call'd from the great Prophet Elcefai, or Elxai.
This Elxai, who lived in the Time of Trajan, gave into the Sentiments of the Ebionites, touching Jeftis thrift ; tho' he alter'd and reform'd them in fome Things, to de- nominate himfelf the Author of a Sect.
His Fundamental Doctrines were, that Jeftis Chrift, who was born from the Beginning of the World, had appear'd from Time to Time under divers Bodies ; that he was a celeftial Power, or Virtue, call'd the Chrift, whereof the Holy Spirit was Sifter ; (Note, the Hebrew Word for Spirir, is Feminine') and that both of them had defcended into Jeftis the Son of Mary.
The Elcefaites, according to St. Epiihanius, were alfo called Samfeans, from the Hebrew Word Sanies, Sun.
Scaliger was notorioufly miftaken, in holding that Elxai was no more than EjJ'ai, or Effean ; on which Suppofi- tion the Elcefaites were the Tame with the Sect of Efjians, which is contrary to all Antiquity,
Origen
