some coherent account of the subject, he made many observations of the places of these wandering stars.  How great were the advances which Hipparchus accomplished may be appreciated if we reflect that, as a preliminary task to his more purely astronomical labours, he had to invent that branch of mathematical science by which alone the problems he proposed could be solved.  It was for this purpose that he devised the indispensable method of calculation which we now know so well as trigonometry.  Without the aid rendered by this beautiful art it would have been impossible for any really important advance in astronomical calculation to have been effected.

But the discovery which shows, beyond all others, that Hipparchus possessed one of the master-minds of all time was the detection of that remarkable celestial movement known as the precession of the equinoxes.  The inquiry which conducted to this discovery involved a most profound investigation, especially when it is remembered that in the days of Hipparchus the means of observation of the heavenly bodies were only of the rudest description, and the available observations of earlier dates were extremely scanty.  We can but look with astonishment on the genius of the man who, in spite of such difficulties, was able to detect such a phenomenon as the precession, and to exhibit its actual magnitude.  I shall endeavour to explain the nature of this singular celestial movement, for it may be said to offer the first instance in the history of science in which we find that combination of accurate observation with skilful interpretation, of which, in the subsequent development of astronomy, we have so many splendid examples.

The word equinox implies the condition that the night is equal to the day.  To a resident on the equator the night is no doubt equal to the day at all times in the year, but to one who lives on any other part of the earth, in either hemisphere, the night and the day are not generally equal.  There is, however, one occasion in spring, and another in autumn, on which the day and the night are each twelve hours at all places on the earth.  When the night and day are equal in spring, the point which the sun occupies on the heavens is termed the vernal equinox.  There is similarly another point in which the sun is situated at the time of the autumnal equinox.  In any investigation of the celestial movements the positions of these two equinoxes on the heavens are of primary importance, and Hipparchus, with the instinct of genius, perceived their significance, and commenced to study them.  It will be understood that we can always define the position of a point on the sky with reference to the surrounding stars.  No doubt we do not see the stars near the sun when the sun is shining, but they are there nevertheless.  The ingenuity of Hipparchus enabled him to determine the positions of each of the two equinoxes relatively to the stars which lie in its immediate vicinity.