EQUATION, annual, of the mean mo tion of the sun and moon's apogee and nodes. The annual equation of the sun's mean motion depends upon the excen tricity of the earth's orbit round him, and is 1611 such parts, of which the mean distance between the sun and the earth is 1000 ; whence some have called it the equation of the centre, which, when great est, is 1° 56' 20".
The equation of the moon's mean mo tion is 11' 40"; of the apogee, 20'; and of its node, 9' 30".
These four annual equations are always mutually proportionable to each other ; so that when any of them is at the great est, the three others will also be greatest; and when one diminishes, the rest di minish in the same ratio. Wherefore the annual equation of the centre of the sun being given, the other three correspond ing equations will be given, so that one table of the central equations will serve for all.
EquATIoN of a curve, is an equation shewing the nature of a curve by express ing the relation between any absciss and its corresponding ordinate, or else the re lation of their fluxions, &c. Thus, the
equation to the circle is a x — x. = where a is its diameter, x any absciss or part of that diameter, and y the ordinate at that point of the diameter; the mean ing being, that whatever absciss is de noted by x, then the square of its cor responding ordinate will be a x — In like manner the equation of the ellipse is pa a x—x' = y., of the hyperbola is -L. a x-{-x' = a of the parobola is p x = y.
Where a is an axis, and p the parameter. And in like manner for any other curves.
This _method of expressing the nature of curves by algebraical equations was first introduced by Des Cartes, who, by thus connecting together the two sciences of algebra and geometry, made them mu tually assisting to each other, and so laid the foundation of the greatest improve. meats that have been made in every branch of them since that time.