No one can fail to notice the beautiful set of phases through which the moon passes every month. A little after the almanac has announced 'new moon,' she begins to appear as a thin crescent low down in the West, and setting shortly after the sun. Night by night we can watch her moving eastward among the stars, and showing more and more of her illuminated surface, until at first quarter half of her disc is bright. The reader must distinguish this real eastward movement from the apparent east to west movement due to the daily rotation of the earth. Its reality can readily be seen by noting the position of the moon relatively to any bright star. It will be observed that if she is a little west of the star on one night, she will have moved to a position a little east of it by the next. Still moving farther East, she reaches full, and is opposite to the sun, rising when he sets, and setting when he rises. After full, her light begins to wane, till at third quarter the opposite half of her disc is bright, and she is seen high in the heavens in the early morning, a pale ghost of her evening glories. Gradually she draws nearer to the sun, thinning down to the crescent shape again until she is lost once more in his radiance, only to re-emerge and begin again the same cycle of change. The time which the moon actually takes to complete her journey round the earth is twenty-seven days, seven hours, and forty-three minutes; and if the earth were fixed in space, this period, which is called the _sidereal month_, would be the actual time from new moon to new moon. While the moon has been making her revolution, however, the earth has also been moving onwards in its journey round the sun, so that the moon has a little further to travel in order to reach the 'new moon' position again, and the time between two new moons amounts to twenty-nine days, twelve hours, forty-four minutes. This period is called a _lunar month_, and is also the _synodic period_ of our satellite, a term which signifies generally the period occupied by any planet or satellite in getting back to the same position with respect to the sun, as observed from the earth.