We should like to see it obtain a fresh circulation, by a new edition, with a Life of the Author, and Notes, and Plates, as has been done for the Pilgrim's Progress.

Astronomical Occurrences

In MAY 1820.

THE Sun enters Gemini at 7 m. past 5 in the morning of the 21st of this month; and he rises and sets during the same period as stated in the following

TABLE

Of the Sun's Rising and Setting for every fifth Day. May 1st, Sun rises 37 m.after 4. Sets at 23 m. after 7

6th,

29

· 4
4

31

Equation of Time.

When it is required to regulate a clock by means of the time as exhibited by a good sun-dial, the following quantities must be subtracted from the time as shown by that instrument, and then the difference between the remainder and the time as shown by the clock at the same instant will be the error of the clock.

TABLE

Monday, May 1st, from the time by the dial subtract

Phases of the Moon.

Last Quarter 5th day, at 50 m. after 1 afternoon

Moon's Passage over the first Meridian.

The Moon will pass the meridian of the Royal Observatory at the following times, which will therefore afford convenient opportunities for observations, if other circumstances be favourable; viz.

May 3d, at 11 m. past 4 in the morning

Eclipses of Jupiter's Satellites.

There will be 29 eclipses of Jupiter's first and second satellites this month; but none of them will be visible at Greenwich, and therefore their insertion in this place is omitted.

Other Phenomena.

Mercury will attain his greatest elongation on the 10th, and Venus her's on the 19th of this month.' The Moon will be in conjunction with Saturn at 57 m. after 8 in the morning of the 9th; with ẞ in Taurus, at 49 m. past 11 in the morning of the 14th; with Venus at 18 m. past 1 in the morning of the 16th; with Pollux, at 23 m. after 9 in the evening of the same day; with a in Virgo, at 47 m. after 10 in the morning of the 24th; and also with -in Scorpio, at 18 m. after 11 at night of the 27th. The Moon

will likewise be in perigee on the 8th, and in apogee on the 20th of this month.

TIME of the SUN'S RISING.

The time of the Sun's rising is also a subject of astronomical calculation, and one of the familiar elements which we insert among our Occurrences under the head of each month; and this, as well as the time of his setting, is contained in the Ephemeris before referred to, for every day in the year. For the more readily calculating these times, astronomers have formed tables of the arcs which he describes during his continuance above the horizon; or rather of half these arcs, or those which he describes in passing from the horizon to the meridian, or from that circle to the horizon. These are called semi-diurnal arcs; and such a table occupies four pages; viz. from 40 to 43 inclusive, in White's Ephemeris. The calculation of these arcs depends upon the principles of spherical trigonometry, and is explained by most writers on practical astronomy. The tables which are inserted in this Ephemeris correspond to every degree of the Sun's de clination, both north and south; and to every degree of north latitude, from 39° to 60°, inclusive; and when either of these quantities contain parts of a degree, as minutes, &c., the corresponding parts of the semi-diurnal duration are easily found by proportion, and in most cases may be done mentally. These tables are thus limitted in latitude in order to abridge their extent; and these limits have been fixed upon, as including the united kingdom of Great Britain, certainly the most important part of the globe in the estimation of those for which a British almanac is designed. The use of these tables is extremely easy; and the following directions and examples will illustrate it.

The first, or left-hand, column of each page contains the Sun's declination; the degrees of latitude

are marked at the top of the other columns; and hence, when the Sun's declination and the latitude of the place is known, the semi-duration of the Sun above the horizon, corresponding to these given quantities, is found in the column answering to the latitude, and in the line with the declination, and is expressed in hours and minutes. This expresses the time of his setting, or that which elapses between his passing the meridian and the moment of his sinking beneath the western horizon; and, consequently, if this be taken from 12 hours, it will give the time of his rising on the same day. The declination which is to be used is that answering to noon of the given day. As an example, Let it be required to find at what time the Sun will rise and set on the 15th of April, 1820, in latitude 50°, the place being situated on the first meridian. The declination of the Sun answering to the time of his passing the meridian on that day, taken to the nearest minute, is 9° 50′ north; then looking in the first column for 9°, in the same line, and the column answering to the given latitude is 6h. 47 m. for the corresponding time. But as there is 5 m. difference between the time answering to 9° and 10° of declination, §ths of this must be added for the 50 m., which is 4 m. 10 s.; and, consequently, 6 h. 51 m. 10 s. will be the time of the Sun's setting on that day. Hence we also have 12 h. 6h. 51 m. 10 s. 5 h. 8 m. 50 s., or 8 minutes and 50 seconds past 5 in the morning, for the time of his rising.

Now it is evident, from the nature of these quantities, that double the time of his setting will be the length of his duration above the horizon, or the length of the day; and double the time of his rising will be the length of the night: in the present case the former is 13 h. 42 m. 20 s., and that of the latter 10 h. 17 m. 40 s.

Again, Let it be required to find the time of the Sun's rising and setting at York, supposing it to be

in latitude 53° 58′, on the 3d of August, 1820. In this case, neglecting the very slight variation in the Sun's declination between noon at the Royal Observatory and at York, the declination for that day will be 17° 30′ north; and with 17°, and latitude 53°, we have, in the table of semi-diurnal arcs, 7 h. 40 m., to which 3 m. must be added for the 30' of declination, and 4 m. for the 58' of latitude; and hence the time required is 7h. 50 m., which, taken from 12 h., gives 4 h. 10 m. for the time of his rising. These being doubled, also give 15 h. 40' for the length of the day, and 8h. 20 m. for that of the night.

If it were required to find the time of the Sun's rising and setting at Tobolsk, in Asiatic Russia, on the 1st of October, 1820, we should have the latitude of the place, taking the nearest minute, which is always sufficiently accurate in cases of this kind, 58° 12′ north, and the longitude 68° 6' east. Now the declination of the Sun, when he passes the first meridian of this country on the given day, is 3° 15′ south; and the change in the preceding 24 hours is 23′ 21′′; and therefore for the 4 hours, answering to the difference of longitude, 4' must be subtracted, since the longitude is east, and the declination increasing, which makes the declination of the Sun, when that luminary passes the meridian of Tobolsk, equal to 3° 10' south. Hence, by the table at page 43 of the Ephemeris, we have 5h. 45 m., corresponding to 3° of declination and 58° of latitude; to which 1' 13" must be added for the 10 of declination, and 12′′ subtracted for the additional minutes of the latitude; and therefore the true time of the Sun's setting at Tobolsk, on the day proposed, will be 46 m. 1 s. after 5; and the time of his rising 13 m. 59 s. after 6.

Here it may be observed, that when the Sun is approaching the zenith of the observer, that is, in these northern latitudes proceeding from the tropic of Capricorn to that of Cancer (or the contrary, on the south side of the equator), any change in his decli

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