BRITISH ENCYCLOPEDIA, OR DICTIONARY OF ARTS AND SCIENCES; COMPRISING AN ACCURATE AND POPULAR VIEW OF THE PRESENT IMPROVED STATE OF HUMAN KNOWLEDGE. BY WILLIAM NICHOLSON, Author and Proprietor of the Philosophical Journal, and various other Chemical, Philosophical, and Mathematical Works, ILLUSTRATED WITH UPWARDS OF 150 ELEGANT ENGRAVINGS, BY MESSRS. LOWRY AND SCOTT. VOL. III. E....I. LONDON: PRINTED BY C. WHITTINGHAM, Goswell Street ; FOR LONGMAN, HURST, REES, AND ORME, PATERNOSTER-ROW; J. JOHNSON ; R. BALDWIN ; F. AND C. RIVINGTON; A. STRAHAN ; T. PAYNE; J. STOCKDALE; SCATCHERD AND LETTER MAN; CUTHELL AND MARTIN; R. LEA; LACKINGTON AND CO., VERNOR, HO AND SHARPE ; J. BUTTERWOKTH ; J. AND A. ARCH; CADELL AND DAVIES; S. BAGSTER ; BLACK, PARKY, AND KINGSBURY; J. HARDING ; J. MAWMAN ; P. AND W. WYNNE ; SHERWOOD, NEELY, AND JONES ; B, C. COLLINS; AND T. WILSON AND SON. IN VOL. III. The Binder is requested to place the Plates in the following order, taking care to make all the Plates face an even Page, unless otherwise directed. GALVANISM, opposite the article GAMBOGE. XI. at the end of Sheet D. XIV. at the end of Sheet L. VI. at the middle of Sheet D d. VII. at the middle of Sheet M m. Pisces IV. opposite the article GYMNOTUS. Rowntree's Fire Engine double barrelled Pump Engine 1 opposite the article Trevithick’s Pressure Engine ENGINEER. THE BRITISH ENCYCLOPEDIA. ELLIPSIS. , or turning into itself, and produced from to that diameter; and a third proportional the section of a cone by a plane cutting both to two conjugate diameters, is called the laits sides, but not parallel to the base. See tus rectum, or parameter of that diameter Conic SECTIONS. which is the first of the three proporThe easiest way of describing this curve, tionals, in plano, when the transverse and conju- The reason of the name is this : let B A, axes AB, ED, (Plate V. Miscell, fig. 1.) ED, be any two conjugate diameters of an are given, is this : first take the points F,f, ellipsis (fig. 2, where they are the two in the transverse axis A B, so that the dis- axes) at the end A, of the diameter AB, tances CF, Cf, from the centre C, be each raise the perpendicular AF, equal to the equal to AC-CD; or, that the lines latus rectum, or parameter, being a third FD, FD, be each equal to AC; then, hav. proportional to AB, ED, and draw the ing fixed two pins in the points F,f, which right line BF; then if any point P be are called the foci of the ellipsis, take a taken in BA, and an ordinate PM be thread equal in length to the transverse drawn, cutting BF in N, the rectangle uniaxis A B; and fastening its two ends, one der the absciss A P, and the line PN will to the pin F, and the other to f, with ano- be equal to the square of the ordinate PM, ther pin M stretch the thread tight; then Hence drawing N O parallel to AB, it apif this pin M be moved round till it returns pears that this rectangle, or the square of to the place from whence it first set out, the ordinate, is less than that under the abkeeping the thread always extended so as sciss AP, and the parameter AF, by the to form the triangle FMf, it will describe rectangle under AP and O F, or NO and an ellipsis, whose axes are A B, D E. OF; on account of which deficiency, Apol The greater axis, AB, passing through ' lonius first gave this curve the name of an the two foci Ff, is called the transverse ellipsis, from smaal 819, to be deficient. axis; and the lesser one DE, is called the In every ellipsis, as A E B D, (fig. 2), the conjugate, or second axis : these two always squares of the senii-ordinates MP, mp, are bisect each other at right angles, and the as the rectangles under the segments of the eentre of the ellipsis is the point C, where transverse axis A P X PB, Ap X PB, made they intersect. Any right line passing by these ordinates respectively; which holds through the centre, and terminated by the equally true of the circle, where the squares carve of the ellipsis on each side, is called of the ordinates are equal to such rectana diameter ; and two dianieters, which na- gles, as being mean proportionals between turally bisect all the parallels to each other, the segments of the diameter. In the same bounded by the ellipsis, are called conju- manner, the ordinates to any diameter gate diaineters. Any right line, not pass- whatever, are as the rectangles under the ing through the centre, but terminated by segments of that diameter. the ellipsis, and bisected by a diameter, is As to the other principal properties of VOL. III. B |