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, FOR LONGMAN, HURST, REES, AND ORME, PATERNOSTER-ROW; J. JOHNSON; R. BALDWIN; F. AND C. RIVINGTON; A. STRAHAN; T. PAYNE; J. STOCKDALE; SCATCHERD AND LETTERMAN; CUTHELL AND MARTIN; R. LEA; LACKINGTON AND CO., VERNOR, HOOD, AND SHARPE; J. BUTTERWORTH; 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. 1809. 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. AVES VI. middle of Sheet Q. VII. middle of Sheet E e. FORTIFICATION, at the end of Sheet O. GALVANISM, Opposite the article GAMBOGE. HERALDRY I. and II. middle of Sheet G g. HOROLOGY, middle of Sheet Ii. HYDRAULICS, at the end of Sheet K k. IRON FOUNDRY, at the end of Vol. III. MAMMALIA X. to face the first article, ELLIPSIS. XII. at the end of Sheet G. XIII. at the end of Sheet I. XIV. at the end of Sheet L. MISCELLANIES V. at the end of Sheet M. 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 opposite the article Trevithick's Pressure Engine ENGINEER. THE BRITISH ENCYCLOPEDIA. ELLIPSIS. ELLIPSIS, in geometry, a curve line re- called the ordinate, or ordinate-applicate turning into itself, and produced from the section of a cone by a plane cutting both its sides, but not parallel to the base. See CONIC SECTIONS. The easiest way of describing this curve, in plano, when the transverse and conjuaxes AB, ED, (Plate V. Miscell. fig. 1.) are given, is this: first take the points F,f, in the transverse axis A B, so that the distances CF, Cf, from the centre C, be each equal to /ACCD; or, that the lines FD,ƒD, be each equal to A C; then, having fixed two pins in the points F, f, which are called the foci of the ellipsis, take a thread equal in length to the transverse axis A B; and fastening its two ends, one to the pin F, and the other to f, with another pin M stretch the thread tight; then if this pin M be moved round till it returns to the place from whence it first set out, keeping the thread always extended so as to form the triangle FMf, it will describe an ellipsis, whose axes are A B, D E. The greater axis, A B, passing through the two foci Ff, is called the transverse axis; and the lesser one D E, is called the conjugate, or second axis: these two always bisect each other at right angles, and the eentre of the ellipsis is the point C, where they intersect. Any right line passing through the centre, and terminated by the curve of the ellipsis on each side, is called a diameter; and two diameters, which naturally bisect all the parallels to each other, bounded by the ellipsis, are called conjugate diameters. Any right line, not pass ing through the centre, but terminated by the ellipsis, and bisected by a diameter, is VOL. III. to that diameter; and a third to two conjugate diameters, is called the latus rectum, or parameter of that diameter which is the first of the three proportionals. The reason of the hame is this: let BA, ED, be any two conjugate diameters of an ellipsis (fig. 2, where they are the two axes) at the end A, of the diameter A B, raise the perpendicular A F, equal to the latus rectum, or parameter, being a third proportional to AB, ED, and draw the right line BF; then if any point P be taken in BA, and an ordinate PM be drawn, cutting BF in N, the rectangle under the absciss A P, and the line PN will be equal to the square of the ordinate PM. Hence drawing NO parallel to A B, it appears that this rectangle, or the square of the ordinate, is less than that under the absciss A P, and the parameter AF, by the rectangle under AP and OF, or NO and OF; on account of which deficiency, Apollonius first gave this curve the name of an ellipsis, from λy, to be deficient. In every ellipsis, as A E B D, (fig. 2), the squares of the semi-ordinates MP, mp, are as the rectangles under the segments of the transverse axis A P × PB, Ap × p B, made by these ordinates respectively; which holds equally true of the circle, where the squares of the ordinates are equal to such rectangles, as being mean proportionals between the segments of the diameter. In the same manner, the ordinates to any diameter whatever, are as the rectangles under the segments of that diameter. As to the other principal properties of B |