table of southing would not serve, because the Moon moves a good way eastward, in the interval of her southing at London, and southing at New York, &c.

The rising and setting of the Moon are also frequently given. These differ greatly day by day in the same Almanac,-their rate of variation is not the same as for southing; and tables arranged for different places show very dissimilar results. The causes for all this are much too complicated to be explained here; but we may mention one or two:-the Moon is constantly moving eastward in the heavens: the rapidity of her motion is continually varying: and she is not moving in the same path as the Sun moves. The latitude and longitude of the observer's position, the place of the Moon in her orbit, the rapidity of her motion, and other particulars, are therefore to be taken into account in computing the rising and setting of the Moon; and this forms altogether a tedious and difficult part of the Almanac-maker's duties.

The Moon's phases are given in all Almanacs; that is, as before explained, the times when she is a full Moon, a half Moon, (twice in the month,) and a new or invisible Moon. All these terms relate, not to the actual quantity of light which falls on the Moon from the Sun, but to the portion of the illuminated half of the Moon which happens to be turned towards the Earth; and therefore, in every case, what we call the age of the Moon, depends on the position of the Earth with respect to the Sun and Moon.

We may here remark, that the Moon's influence on parts of the human body, as given in some old-fashioned Almanacs, is an entire fallacy: it is most untrue and absurd, often indecent, and is a discredit to the age we live in.

Equation of time, as given in Almanacs, is the difference between the time as indicated by a sun-dial, and that indicated by a correct clock. It is occasioned by the circumstance that the Sun, which is the chief agent in forming measures of time, does not appear to move equally fast on all days of the year; so that an hour by a sun-dial, which correctly indicates the Sun's motion, is sometimes longer, and at other times shorter, than an hour indicated by a good clock:-a clock's hours are all equal, but the Sun's hours are not all equal. The equation of time shows how many minutes are to be added to or subtracted from sun-dial time, in order to obtain clock time, or vice versa. The same table of equation of time will serve all over the world.

II. The NOTES usually given at the commencement of an Almanac, were the elements employed in the correction of the Calendar. They are the following; which we proceed briefly to explain :

1. Golden Number.

2. Epact.

3. Solar Cycle.

4. Sunday Letter.

5. Roman Indiction.

6. Number of Direction.

7. Julian Period.

1. The GOLDEN NUMBER is the number which any given year holds in the Lunar Cycle, which is a period of nineteen years, at the lapse of which the new Moons take place on the same days of the same months respectively, as at the commencement of the Cycle. Therefore, while the Sun performs its annual course nineteen times, those of the Moon amount to two hundred and thirty-five. The importance of this dis

covery in the regulation of time was held to be so great, that the rule for ascertaining the number of the year in the Lunar Cycle was engraved on a golden tablet, and set up in the market-place of Athens. Hence the term GOLDEN Number. The rule is given in the Calendar, which prefaces the Church-Service.

2. The EPACT is the number of days over and above all the complete courses of the Moon, for any number of years, in any part of the Lunar Cycle. Hence, it is the Moon's age at the beginning of any year; that is, the number of days which have elapsed since the last new Moon in the preceding year.

3. The SOLAR CYCLE is a period of twenty-eight years, which, owing to Leap-year, must necessarily pass round, before the days of the month can return respectively to the same days of the week, as at the commencement of the Cycle.

4. The Dominical or SUNDAY LETTER is one of the first seven letters of the Alphabet; which letters are used to denote respectively the days of the week, and one of which letters must of course fall to the Sunday throughout the year. But, owing to Leap-year, their order is every fourth year disturbed; so that the Solar Cycle must pass round, before the letters can fall respectively to the same days of the week. The year 1840 being Leap-year, there are two Sunday Letters ; the left hand letter is used till the end of February, and the other till the end of the year.

5. ROMAN INDICTION was a period of fifteen years, appointed by the Emperor Constantine, A. D. 312, for the payment of certain taxes from the subjects of the empire.

6. The NUMBER OF DIRECTION. It having been

decided by an assembly of Christian bishops, at the Council of Nice, in Italy, A. D. 325, that EASTERDAY is always "the first Sunday after the Full Moon, which happens upon, or next after, the 21st of March;" it follows that Easter-day cannot take place earlier than the 22nd of March, nor later than the 25th of April; so that from one date to the other (both inclusive) are thirty-five days. The Number of Direction is that day of the thirty-five, on which Easter Sunday falls.

7. The JULIAN PERIOD consists of 7980 years; which is produced by the multiplication into each other of the Solar Cycle, the Lunar Cycle, and the Roman Indiction; (28×19×15-7980.) This period is reckoned from 709 years before the Creation of the world, when the three cycles are supposed to commence together, which circumstance cannot take place again until the lapse of the entire period, A. D. 3267.

The Roman Indiction and the Julian Period are not now of practical use in the Calendar; but the other observations may assist those who wish to understand the Calendar, which is prefixed to the ChurchService in the Prayer-Book.

HAPTER XV.

ASTRONOMICAL INSTRUMENTS, COMMONLY USED IN THE MEASUREMENT OF TIME. EARLY DIVISIONS OF TIME.

SUN-DIAL-HORIZONTAL

LINE.

AND VERTICAL.

MERIDIANMOON-DIAL. ASTROLABE. HADLEY'S QUADRANT.

ARTIFICIAL HORIZON.

WE come now to consider the elementary instruments used to ascertain, with accuracy, the divisions of time, and to estimate the motions, real or apparent, of such heavenly bodies as gave effect to the instruments in question. We may confine ourselves, therefore, to an examination into the nature and uses of the SUN-DIAL and the QUADRANT; having first taken a cursory view of the early and well-established divisions of time.

In the dawn of society, when man had not yet entered upon that career of activity which the developement of mind, the ties of social life, and the gradual growth of his wants and wishes, rendered necessary, the progress of time was not an occurrence of paramount importance to him. The day was quite long enough to enable him to cultivate and gather the produce of the ground, or to hunt and appropriate for purposes of food the animals around him. From these he obtained food and clothing; and thus his wants, limited in extent, were easily supplied.

But when increase of population rendered necessary the search for new regions, and when the mental tastes of men began to multiply the number and variety of their employments, it was found necessary to mark the course of TIME; to distinguish those periods of the