190 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1949 
a convention, into the details of which I need not enter. The extreme 
differences between mean and true solar times range from 16 minutes 
about November 3, when true noon precedes mean moon, to 14% 
minutes about February 12, when true noon follows mean moon. 
Astronomers, however, find it more convenient to determine time 
by the observation of the stars. There are many stars but only one 
sun and, moreover, the time of transit of a star can be determined more 
accurately than the time of transit of the sun. The sidereal day is 
defined by the rotation of the earth relative to the stars. It is about 
4 minutes shorter than the solar day. If we imagine the sun and a 
star to be on the meridian of some particular place at the same instant, 
then after the lapse of one sidereal day the star will again be on the 
meridian; but, because of the orbital motion of the earth round the 
sun, the earth will have to turn a little more in order to bring the sun 
onto the meridian. In the course of a year the earth completes its 
orbit around the sun and there must consequently be exactly one more 
sidereal day in the year than mean solar days. 
If the relative positions of a number of stars in the equatorial region 
of the sky have been accurately determined, we can think of them as 
equivalent to the graduations on the face of a clock. As the earth 
rotates, a telescope, fixed so as to be able to move only in the meridian, 
will sweep across these stars in turn, each at a definite specific instant 
of sidereal time. By observing the transit of stars whose positions 
are known, the sidereal times at the instants of meridian transit are 
therefore determined. The beginning of the sidereal day or, in other 
words, Oh. of sidereal time, is defined by the transit of the point in 
the sky at which the ecliptic crosses the equator from south to north; 
this point is called the vernal equinox or the First Point of Aries. 
By defining the commencement of the sidereal day in this manner, 
we are provided with a means for converting from sidereal time to 
mean solar time, which is required for the purposes of everyday life. 
But it has one inconvenience. The First Point of Aries is not fixed 
relative to the stars. It has a slow retrograde motion, due to the 
precessional motion of the earth’s axis, and superposed on this uniform 
motion is a slow to-and-fro drift, caused by the nutational or nodding 
motion of the axis. The nutation depends upon the relative positions 
and distances of the sun and moon from the earth. The principal 
term in the nutation has a period of about 18 years and a semi- 
amplitude of about 1 second of time. There is also a 6-monthly term 
amounting to 0.08 second and a number of short-period terms 
amounting to 0.020 second, of which the principal term has a period 
of 2 weeks. The precision of modern clocks is such that these small 
terms cannot be neglected. The true sidereal day, measured relative 
to the true position of the First Point of Aries, is therefore not abso- 
lutely uniform in length, and it is necessary to introduce the con- 
