on which was a meridian line. When the shadow cast on this line was the shortest, it indicated the summer solstice; and when it was the longest, the winter solstice. The number of days required for the sun to pass from one solstice back to it again determined the length of the year. This they found to be 365 days. As that is nearly six hours less than the true solar year, dates were soon thrown into confusion. If, at a certain date, the summer solstice occurred on June 20th, in four years it would fall on the 21st; and thus it would gain one day every four years, until in time the summer solstice would happen in the winter months.

Julian Calendar.-Julius Cæsar first attempted to make the calendar year coincide with the motions of the sun. By the aid of Sosigenes, an Egyptian astronomer, he devised a plan of introducing every fourth year a leap-year, which should contain an extra day. This was termed a bissextile year, since the sixth (sextilis) day before the kalends (first day) of March was then counted twice.

Gregorian Calendar.-Though the Julian calendar was nearly perfect, it was yet somewhat defective. It considered the year to consist of 3651 days, which is 11 minutes in excess. This accumulated year by year, until in 1582 the difference amounted to ten days. In that year, the vernal equinox occurred on the 11th of March, instead of the 21st. Pope Gregory undertook to reform the anomaly, by dropping ten days from the calendar and ordering that thereafter only centennial years which are divisible by 400 should be leap-years. The Gregorian

calendar was generally adopted in Catholic countries. Protestant England did not accept the change until 1752. The difference had then amounted to 11 days. These were suppressed and the 3rd of September was styled the 14th.* Dates reckoned according to the Julian calendar are termed Old Style (O.S.); and those according to the Gregorian calendar, New Style (N.S.).

Commencement of the Year.-The Jews began their civil year with the autumnal equinox; but their ecclesiastical year, with the vernal equinox. When Cæsar revised the calendar, the Romans commenced the year with the winter solstice (Dec. 22), and it is probable he did not intend to change it materially. He ordered it to date from January 1, in order that the first year of his new calendar should begin with the day of the new moon immediately succeding the winter solstice.

The Earth our Timepiece.-The measure of time is, as we have just seen, the length of the mean day. This is estimated from the length of the sidereal day. Hence, the standard for time is the rotation of the earth on its axis. All weights and measures are based on time. An ounce is the weight of a given bulk of distilled water. This is measured

Prof

*This sweeping change was received in England with great dissatisfaction. De Morgan narrates the following: "A worthy couple in a country town, scandalized by the change of the calendar, continued for many years to attempt the observance of Good Friday on the old day. To this end they walked seriously and in full dress to the church door, on which the gentleman rapped with his stick. On finding no admittance, they walked as seriously back again and read the service at home. There was a widespread superstition that, when Christmas day began, the cattle fell on their knees in their stables. It was asserted that, refusing to change, they continued their prostrations according to the Old Style. In England, the members of the Government were mobbed in the streets by the crowd, which demanded the eleven days of which they had been illegally deprived."

by cubic inches. The inch is a definite part of the length of a pendulum which vibrates seconds in the latitude of London. Arago remarks, a man would be considered a maniac who should speak of the influence of Jupiter's moons on the cotton trade. Yet there is a connection between these incongruous ideas. The navigator, travelling the waste of waters where there are no paths and no guide-boards, may reckon his longitude by the eclipses of Jupiter's moons, and so decide the fate of his voyage. We can easily see how the rotation of the earth on its axis influences the cost of a cup of tea.

VI. CELESTIAL MEASURE

MENTS.

Many persons read the enormous figures which indicate the distances and dimensions of the heavenly bodies with a questioning, indefinite idea, entirely unlike the feeling of certainty with which they read of the distance between two cities, or the number of square miles in a certain State. Many, too, imagine that celestial measurements are so mysterious in themselves that no common mind can hope to grasp the methods. Let us attempt the solution of a few of these problems.

1st. To Find the Distances of the Planets from the Sun.-In Fig. 108, E represents the earth; ES, the earth's distance from the sun; V, the planet Venus; and VES, the angle of elongation (a rightangled triangle). It is clear that, as Venus swings

apparently east and west of the sun, this angle may be easily measured; also, that it will be the greatest when Venus is in aphelion and the earth in perihelion at the same time, for then VS will be the longest and ES the shortest. Now in every right

S

Fig. 108.

E

angled triangle the proportion between the hypothenuse, ES, and the side opposite, VS, changes as the angle at E varies, but with the same angle remains the same whatever may be the length of the lines themselves. This proportion between the hypothenuse and

Comparative Distance of Venus and the the side opposite any angle is termed the sine of that

Earth.

angle. Tables are published containing the sines for all angles. In this way, the mean distance of Venus is found to be 7 that of the earth; Mars, times; Jupiter, 5 times, etc.*

2nd. To Measure the Moon's Distance from the Earth. (1.) THE ANCIENT METHOD.-As the moon's distance is so much less than that of the other heavenly bodies, it is measured by the earth's semidiameter. The method, an extremely rough one, which was in use among the ancients, was something

* If the pupil has studied Trigonometry, he may apply here the simple proportion— ES VS Radius: Sine of 47° 15" greatest elongation of Venus The same result would be obtained by the use of Kepler's third law; and on page 19, we saw how the distances of the planets themselves could be determined by the periodic times, if the distance of the earth from the sun is first known. So that when we have accurately determined the sun's distance from us, we can then decide by either of the methods named the distance of all the planets. Indeed the sun's distance is, as already remarked, the "foot-rule" for measuring all celestial distances.

like the following: In an eclipse of the moon, that body passes through the earth's shadow in about four hours. If, then, in four hours, the moon travels along its orbit a distance equal to the diameter of the earth, in twenty-four hours it would pass over six times, and in a lunar month (about thirty days) one hundred and eighty times, that distance. The circumference of the lunar orbit, then, must be one hundred and eighty times the diameter of the earth. The ancients supposed the heavenly orbits to be circles, and, as the diameter of a circle is about § of the circumference, they deduced the diameter of the moon's orbit as 120 times, and the distance of the moon from the earth as 60 times, the semi-diameter of the earth.

(2.) MODERN METHOD BY THE LUNAR PARALLAX.Under the head of parallax, we saw how, in common life, we obtain a correct idea of the distance of an object by means of our two eyes. We proved that one eye alone gives no notion of distance. Just, then, as we use two eyes to find how far from us an object is, so the astronomer uses two astronomical eyes, or observatories, located as far apart as possible, to find the parallax of a heavenly body. In Fig. 109, M represents the moon; G, an observatory at Greenwich; and C, another at the Cape of Good Hope. At the former, the distance from the north pole to the center of the moon, measured on a meridian of the celestial sphere, is found to be 108°. At the latter station, the distance from the south pole to the moon's center is measured in the same way, and found to be 73. The sum of these angles