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The anomalistic year is the interval between two successive passages of the earth through its perihelion. It is 4min., 40 sec. longer than the sidereal year.

The Ancient Year.—The ancients ascertained the length of the year by means of the gnomon. This was a perpendicular rod standing on a smooth plane 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 the 20th June, 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 Caesar 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 ixtra day. This was termed a bissextile year, since 'he sixth (sextilis) day before the kalends (first day) if 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 365£ days, which is 11 min. 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 all Catholic countries. Protestant England did not accept the change until 1752. The difference had then amounted to 11 days. These were suppressed and the 3d 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.) This sweeping change was received in England with great dissatisfaction. Prof. 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 wide-spread 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."

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

The Earth Our Timepiece.—The measure of time is, as we have just seen, the length of the mean day. That is estimated from the length of the sidereal day. Hence the standard for time is the revolution 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 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 revolution of the earth on its axis influences the cost of a cup of tea.

CELESTIAL MEASUREMENTS.

Many persons read the enormous figures which indicate the distances and dimensions of the heavenly bodies with an indefinite idea, which conveys no such feeling of certainty as is experienced when 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 FKOM

The Sun.—In the figure, E represents the earth, ES the earth's distance from the sun, V the planet Venus, and VES the angle of elongation (a right-angled 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

COaiPAKATIVB D1STANOK OP VEMU9

is in aphelion and the earth AND TBK

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in perihelion at the same time, for then VS will be the longest and VE the shortest. Now in every right-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 the side opposite any angle is termed the sine of that angle. Tables are published which contain the sines for all angles. In this way, the mean distance of Venus is found to be ^nr* that of the earth, Mars \ times, Jupiter h\ times, etc.

The same result would be obtained by the use of Kepler's third law; and on page 29, 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 that is, as already remarked, the "foot-rule" for measuring all celestial distances.

2d. 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 semi-diameter.

* If the pupil has studied Trigonometry, he may apply here the simple proportion—

B8 : VS :: Radius : Sine of 47* 15" = greatest elongation of Venus.

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