_D_ = 103 days. 69/70 × _D_ × 4 = 406m. = 6h. 46m. _W_ = 4h. 0m. _S_ = 10h. 46m. The daily gain of sidereal upon mean solar time is 69/70 of 4 minutes, and March 23d is the date on which sidereal and mean solar time are together, taking the average of one year with another, but it varies a little from year to year on account of the extra day introduced in leap years. RULE II. When the stars in the northern sky can be seen. Find β Cassiopeiæ, and imagine a line drawn from it to Polaris, and another line from Polaris to the zenith. The sidereal time is equal to the angle between these lines, provided that that angle must be measured from the zenith toward the west. Turn the angle from degrees into hours by dividing by 15. 55. THE EARTH'S ROTATION.--We are familiar with the fact that a watch may run faster at one time than at another, and it is worth while to inquire if the same is not true of our chief timepiece--the earth. It is assumed in the sections upon the measurement of time that the earth turns about its axis with absolute uniformity, so that mean solar time never gains or loses even the smallest fraction of a second. Whether this be absolutely true or not, no one has ever succeeded in finding convincing proof of a variation large enough to be measured, although it has recently been shown that the axis about which it rotates is not perfectly fixed within the body of the earth. The solid body of the earth wriggles about this axis like a fish upon a hook, so that the position of the north pole upon the earth's surface changes within a year to the extent of 40 or 50 feet (15 meters) without ever getting more than this distance away from its average position. This is probably caused by the periodical shifting of masses of air and water from one part of the earth to another as the seasons change, and it seems probable that these changes will produce some small effect upon the rotation of the earth. But in spite of these, for any such moderate interval of time as a year or a century, so far as present knowledge goes, we may regard the earth's rotation as uniform and undisturbed. For longer intervals--e. g., 1,000,000 or 10,000,000 years--the question is a very different one, and we shall have to meet it again in another connection.