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LET. XIII. OF THE EQUATION OF TIME.

this cause alone, cannot be equal to eachother.

If two bodies, therefore, were to move in theplane of the ecliptic, so as to go exactly roundit in a year; the one describing an equal arc everytwenty-four hours, and the other describingsometimes a less arc in twenty-four hours, andsometimes a greater, gaining at one time of theyear what it lost at another; it is evident, thatone of those bodies would come sooner or laterto the meridian than the other, according totheir situations: and when they were both inconjunction, they would come to the meridianat the same instant. But as this may not bereadily understood, it will, perhaps, appear moreevident by means of a figure. pl g

For this purpose, let A B C D be the ecliptic,or the elliptical orbit which the sun, by an irre-gular motion, describes in the space of a year;and the dotted circle abed the orbit of animaginary star, coincident with the plane of theecliptic, and in which it moves through equalarcs in equal times. Let Id IK, also, be theearth, which revolves round its axis, everytwenty-four hours, from west to east; and sup-pose the sun and star to set out togetherfrom A and a, in a right line with the plane ofthe meridian E H ; the sun at A, being at hisgreatest distance from the earth, at which timehis motion is slowest ; and the star at a, whoseP 4 motion