At the present time the position of the equinoctial points shows a recession of the whole, 30° 1´ 40´´.2. At this rate of motion the constellations called the Signs of the Zodiac are some distance from the divisions of the ecliptic that bear their names. At the rate of 50´´.1 the whole revolution of the equinoctial points will be accomplished in 25,868 years; but this is again modified because the precession must vary in different centuries for the following reasons: the sun’s motion is direct, the precession retrograde; therefore, the sun arrives at the equator sooner than he does at the same star of observation. Now, the tropical year is 365d. 5h. 48´ 49´´.7; and as the precession is exactly 50´´.1, we must suppose it takes some time for the sun to move through that arc. By direct observation it is found that the time required for such translation is 20´ 19´´.6. By adding this amount to the tropical year we have the sidereal year of 365d. 6h. 9´ 9´´.6 in mean solar days. This amount of precession has been on the increase since the days of its first recorder, Hipparchus, as the augmentation amounts to no less than 0.´´455. By adding that to the known precession we find that the civil year is shorter now by 4´´.21 than in his time; but, as a great division of time, the year can be changed by this cause not more than 43.´´ The action of the moon on the accumulation of matter at the earth’s equator is a source of disturbance that in very accurate observations for time should be eliminated. Thus the moon, with the conjoint action of the sun, depending on relative position, causes the pole of the equator to describe a small ellipse in the heavens with axes of 18´´.5 for the major, and 13´´.674 for the minor; the longer axis being directed to the pole of the ecliptic. This inequality has a period of 19 years,--it being equal to the revolution of the nodes of the lunar orbit. The combination of these disturbances changes, by a small quantity, the position of the polar axis of the earth in regard to the stars, but not in regard to its own surface. With so many disturbing causes, we must add that of Jupiter, whose attraction is diminishing the obliquity of the ecliptic by 0´´.457 according to M. Bessel.