The rotation of the earth is a basis for time-measurement and as regards Universal Time (U.T.) this rate of rotation is assumed to be uniform. Recently, first crystal and then atomic clocks-now accurate to 1 part in 1013-have shown that the earth's rotation is at times irregular, the deviations from uniformity being minute—of the order of 1 or 2 milliseconds per day—and unpredictable. In the gravitational theories of the bodies of the solar system, the passage of time is postulated to be uniform', this time is defined as Ephemeris Time (E.T.) and it is in terms of E.T. that astronomical quantities are now tabulated in the almanacs. The epoch from which E.T. is measured is

1900 January 0.5 [E.T.],

more elaborately defined in 1958 as “the instant near the beginning of the calendar year A.D. 1900 when the mean longitude of the sun was 279° 41' 48".04, at which instant the measure of E.T. was 1900 January 0, 12 h. precisely.” The epoch for U.T. is 1900 January 0, 12 h. [U.T.]. Although the two epochs are apparently denoted by the same expression, they do not correspond to the same instant of time, the epoch of E.T. being 4 s. later than that of U.T.

The E.T. for any instant is then defined by the following formula for the geometric mean longitude of the sun:

L = 279° 41' 48".04+129602768".13T+ 1".089T2.

Here T is the ephemeris time measured in Julian centuries of 36525 ephemeris days from the fundamental epoch. The R.A. of the fictitious mean sun is given by the same expression with the effect of aberration added. The R.A. of the fiducial point for U.T., which we are calling simply the mean sun, has the same expression as that of the fictitious mean sun with universal time replacing ephemeris time as the argument.

It may be added that the fundamental unit of time is 1 second (E.T.) derived as 1/31556925.9747 of the length of the tropical year for 1900.0.

Occultations of stars by the moon.

As the moon's sidereal period of orbital revolution around the earth is about 27⅓ days, it moves eastwards with reference to the stars at an average rate of rather more than half a degree per hour. In its passage over the stellar background it is continually interposing its disc between us and the stars, and the sudden disappearance of a star in this way is called the occultation of the star by the moon. After an interval, which depends on a variety of factors, the star reappears. The disappearance and reappearance of the star are generally referred to as immersion and emersion respectively. The disappearance of the star and its reappearance are instantaneous phenomena and, if the time of one or the other is noted accurately, there is obtained at that instant a definite relation between the moon's position in the sky and the position of the observer, it being assumed that the star's position is known accurately. Formerly, occultations were utilised for the determination of longitude, but the introduction of radio time-signals has rendered the occultation method obsolete.

If the moon's position is known accurately, the particulars of the occultation of a star at any place can be predicted and, under these circumstances, it is to be expected that prediction and observation would agree. Now the moon's position is predicted in the almanacs for any instant of Ephemeris Time, while the recorded time of the observation of an occultation will be in Universal Time. The study of suchoccultations, therefore, provides a ready means of determining the relationship between Universal and Ephemeris Time, and, in particular, of deriving the correction ΔT. The occultations of radio sources are also important, as precise radio positions are difficult to measure. The first positive optical identification of a quasar was made by timing the cessation of its radio signals in the course of a lunar occultation.

The geometrical conditions for an occultation.

Consider Fig. 134, in which the earth (regarded as a spheroid) and the moon (regarded as a sphere) are shown with their centres at E and M respectively.