The second kind of year is called the tropical year, and it is measured by the period taken by the sun to pass round the sky from one conjunction with the vernal equinox to the next. This period differs slightly from the first, because, owing to the precession of the equinoxes, the vernal equinox is slowly shifting westward, as if to meet the sun in its annual course, from which it results that the sun overtakes the equinox a little before it has completed a sidereal year. The tropical year is about twenty minutes shorter than the sidereal year. It is, however, more convenient for ordinary purposes, because we naturally refer the progress of the year to that of the seasons, and, as we have seen, the seasons depend upon the equinoxes. But yet the tropical year is not entirely satisfactory as a measure of time, because the number of days contained in it is not an even one. Its length is 366 days, 5 hours, 48 minutes, 46 seconds. Accordingly, as the irregularities of apparent solar time were avoided by the invention of mean solar time, so the difficulty presented by the tropical year is gotten rid of, as far as possible, by means of what is called the civil year, or the calendar year, the average length of which is almost exactly equal to that of the tropical year. This brings us to the consideration of the calendar, which is as full of compromises as a political treaty—but there is no help for it since nature did not see fit to make the day an exact fraction of the year, or, in other words, to make the day and the year commensurable quantities of time. Without going into a history of the reforms that the calendar has undergone, which would demand a great deal of space, we may simply say that the basis of the calendar we use to-day was established by Julius Cæsar, with the aid of the Greek astronomer Sosigenes. This is the Julian calendar, and the reformed shape in which it exists at present is called the Gregorian calendar. Cæsar assumed 365¼ days as the true length of the year, and, in order to get rid of the quarter day, ordered that it should be left out of account for three years out of every four. In the fourth year the four quarter days were added together to make one additional day, which was added to that particular year. Thus the ordinary years were each 365 days long and every fourth year was 366 days long. This fourth year was called the bissextile year. It was identical with our leap year. The days of both the ordinary and the leap years were distributed among the twelve months very much as we distribute them now.