The moon circuits the heavens in a path but slightly inclined to that of the sun, called the ecliptic, and for our present purpose we may speak of the moon as travelling in the ecliptic. Now we know that during the winter half of the year the sun is south of the equator, the circle of the heavenly sphere which passes through the east and west points of the horizon, and has its plane square to the polar axis of the heavens. During the other or summer half of the year he is north of the equator. In the former case the sun is above the horizon less than half the twenty-four hours, day being so much shorter as the sun is farther south of the equator; whereas in the latter case the sun is above the horizon more than twelve hours, day being so much the longer as the sun is farther north of the equator. Precisely similar changes affect the moon, only, instead of taking place in a year (the time in which the sun circuits the stellar heavens), they occur in what is called a sidereal month, the time in which the moon completes her circuit of the stellar heavens. For about a fortnight the moon is above the horizon longer than she is below the horizon, while during the next fortnight she is below the horizon longer than she is above the horizon. Now clearly when the length of what we may call the moon's diurnal path (meaning her path above the horizon) is lengthening most, the time of her rising on successive nights must change least. She comes to the south later and later each successive night by about 50½ minutes, because she is always travelling towards the east at such a rate as to complete one circuit in about four weeks; and losing thus one day in 28, she losses about 50½ minutes per day. If the interval between her rising and her arriving to the south were always the same, she would rise 50½ minutes later night after night. But if the interval is lengthening, say by 10 minutes per night, she would of course rise only 40½ minutes later: if the interval _is_ lengthening 20 minutes per night, she would rise only 30½ minutes later, and so forth. But the lunar diurnal arc is lengthening all the time she is passing from her position farthest south of the equator to her position farthest north, just in the same way as the solar day is lengthening from mid-winter to midsummer, only to a much greater degree. And as the solar day lengthens fastest at spring when the sun crosses the equator from south to north, so the time the moon is above the horizon lengthens most, day by day, when the moon is crossing the equator from south to north. It lengthens, _then_, from an hour to an hour and 20 minutes in one day, that is, the interval between moon-rise and moon-setting increases from 30 to 40 minutes. At this time, then, whenever it happens in each lunar month, the moon's time of rising changes least: instead of the moon rising night after night 50½ minutes later, the actual difference varies only from 10 to 20 minutes.