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way between the positions favourable for advance orregression, or as in fig. 36 : but instead of this wefind y> 2 much nearer to the line joining S and e 2 . Andso with the positions e 4 , e 6 , and e 8 .
We have seen that the eccentricity of the lunarorbit, though affected during any given revolution, aswell by the radial as by the tangential disturbingforces, is yet not subject to permanent alteration.The range within which the eccentricity varies is,however, one of the most important of all the featuresof the lunar theory. I do not propose here to enteron the consideration of the circumstances producingthese oscillations in the value of the eccentricity,though the materials for the inquiry are containedin the considerations illustrated by the four figures30, 31, 32, 33, and those of Plate IX. The studentwill find no difficulty whatever in satisfying himselfthat when the axis is placed as in fig. 34 or 35,—orm either of these positions, but with perigee andapogee interchanged,—the eccentricity is not appre-ciably affected in a complete lunation. When theaxis is placed as in fig. 36 (or exactly reversed), theeccentricity is on the whole diminished in a completelunation; and when the axis is placed as in fig. 37(or exactly reversed), the eccentricity is on the wholeincreased in a complete lunation. Thus it is easilyseen that as the earth passes from the position e x tothe position e 3 (fig. 42), the eccentricity passes froma maximum to a minimum value; at e 5 it is again ata maximum; at e 7 again at a minimum; and, lastly,