12 Surge-Siddhihita point and the apsi, or to be mean normaly, when the latter is reckoned, in the usual manner, from the apsis forward to the planet. Thus, in the figure, suppose A to be the place of the apsis (adocca, the apogee of the sun and snoon, the aphelion of the other planets), and P that of the opposite point (perigee, or perihelion; it has in this treatise no distinct. ive name; and let My and M be bwo mean positions of the planet, or actual positions of the centre of the epicycle ; the lesser circles drawn about these four points epresent the epicycle: this is made, in the figura, o£ $wice the size of bhat assumed for the moon, or a little Emaller than that of Mang Then, when bhe centre of bhe epicycle is at A, te planet's place in the epicycle is at a ; ns the centre advances to M, M', and P, the planet moves in the opposite direction, to 7, , and p, bhe are g' w boing equal to AM, ' to AM’, and t" p to AP. It is as if, while the axis Eg revolves about IE, ths. part of it A relzair1€d (m. stant in direction, parallel to A, RESuming the positions 3, M and Pp, successively. The efect of this combination of motions is to make the plane virtually traverse the orbt indicated in the figure by the broken line, which is a circle of equal ¥ndius with the brue orbit, but having the centre vermoved from E, towara A, by a distance equal to big. B. Ad, the radius of the epicycle. This identity of the virtual orbit with an eccentric circle, of which the eccentricity is equal to the radius of the epicycle , was doubtless known to whe Hindus, as to Ptolemy: bhe lather, in the third book of his Syntaxie, demonstrates the equivalence of whe suppositions of an epicycle and an eceenbrie, and chooses the latter to zepresent the first inequality: the Hindus have preferred the other supposition, as better suited to their methods of calculation, and as ad mitting a general similarity in the processes for the apsis and the con junction. The Hindu bheory, however, as remarked above (under yर . 1-5 of bhis chapter), rejects bhe ide of the actual motion of the plane
