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in the same time. For several years, therefore, it would be nextto impossible to distinguish between an ellipse so varied and onethat had not varied at all ; and in a single revolution, the differ-ence between the original ellipse and the curve really representedby the varying one, is so excessively minute, that, if accuratelydrawn on a table, six feet in diameter, the nicest examination withmicroscopes, continued along the whole outlines of the two curves,would hardly detect any perceptible interval between them. Notto call a motion so minutely conforming itself to an elliptic curve,elliptic, would be affectation, even granting the existence of trivialdepartures alternately on one side or on the other ; though, on theother hand, to neglect a variation, which continues to accumulatefrom age to age, till it forces itself on our notice, would be wilfulblindness.
(654.) Geometers, then, have agreed in each single revolution,or for any moderate interval of time, to regard the motion of eachplanet as elliptic, and performed according to Kepler’s laws, witha reserve in favour of those very small and transient fluctuationswhich take place within that time, but at the same time to regardall the elements of each ellipse as in a continual, though extremelyslow, state of change; and, in tracing the effects of perturbationon the system, they take account principally, or entirely, of thischange of the elements, as that upon which any material changein the great features of the system will ultimately depend.
(655.) And here we encounter the distinction between what aretermed secular variations, and such as are rapidly periodic, andare compensated in short intervals. In our exposition of thevariation of the inclination of a disturbed orbit (art. 636), for in-stance, we showed that, in each single revolution of the disturbedbody, the plane of its motion underwent fluctuations to and fro inits inclination to that of the disturbing body, which nearly com-pensated each other; leaving, however, a portion outstanding,which again is nearly compensated by the revolution of the dis-turbing body, yet still leaving outstanding and uncompensated aminute portion of the change which requires a whole revolution ofthe node to compensate and bring it back to an average or meanvalue. Now, the two first compensations which are operated bythe planets going through the succession of configurations witheach other, and therefore in comparatively short periods, are