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to itself, since the equation of time takes the same values after each revolution. It will not, however, be symmetrical, since the epochs at which the equation of time vanishes are not equal to each other. There is a meridian of this kind drawn by M. Bouvard, upon the Palace of Luxembourg, at Paris. The time which elapses between two consecutive passages of the Sun through the same equinoctial point, is very nearly equal to 365 d. 5 h. 48m. 51 s., and as in this time answers to one complete revolution of the sphere, or 360°, we have

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which is the arc daily described by the Sun in his orbit, supposing his motion to be uniform. His passage would therefore be daily retarded, with regard to sidereal time, by (59′ 8"33) = 3′ 36′′ 33′′"32 of sidereal time; and which is therefore the excess of the mean above the sidereal day. The duration of the mean hour is to the duration of the sidereal hour as 360° 59′ 8"33 is to 360°, or as 24h. 3m. 56.5554 is to 24 h.; and hence we have the equation the duration of the mean hour

the duration of the sidereal hour

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Thus, the duration of the mean hour is equal to 1.00273791 of the sidereal hour; and the duration of the sidereal hour is equal to

the duration of the mean hour

1-00273791

•99726967 of the mean hour.

If s be any duration whatever, expressed in side

real time, and m the same duration in mean time, we have

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it will therefore be expressed by a less number in mean time than in sidereal time.

From the equation, s = 1.00273791, we readily deduce s m = 1.00273791m m = 0·00273791m; so that when we know m, we have only to add 0.00273791m, in order to obtain s. Thus, if we suppose m 1 h., we shall find 98568 to be added to it, in order to have s = 1. Om. 9.8568.

Again, if we suppose m = 7. 30m., the quantity to be added to obtain s, will be 98568 × 7.5= 1. 13926; and, consequently, s7h. 30". + 1. 139267h. 31. 13926.

The same result may be obtained from the previous equation, in which s = 1.00273791m; for, multiplying m by this number, we shall have the value of s. Taking the last example, 1·00273791 × 7.5 =7.520534325 = 7h, 31m. 13-924.

When s is given and m required, it is evident from the above equation that, if the value of s be multiplied by the reciprocal of the preceding number, or -99727, we shall have the value of m. It is also obvious, that, if we subtract 00273 from the given time, we shall also obtain the value of m.

Thus, taking the above value of s, namely 7. 31TM. 13924, as an example, we have 7-521 x 99727 =7h. 30. Or, by the second method, we have 7h-521 ×·00273021 nearly; and 7·521-021 — 7h. 30m., as before.

One sidereal hour answers to 15° of motion of the celestial sphere. One mean hour answers to 15° + 2′ 27′′-8526 15° 2′ 27′′-8526: and it is upon this principle that astronomers have calculated tables for converting mean time into degrees; according to which, 1m. of mean time answers to 15′ 2′′-4642, and 13. of mean time corresponds to 15"-04107 of a

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degree. The table thus formed is necessary to those astronomers who regulate their clocks by mean solar time, in order to find the horary angles of the stars, or the differences of mean right ascensions, m = s(1 —·00273791) + (0·002738)—&c. = s―·0027344. Let s 1 sidereal hour, m = 1 h. 9"-8292. From this formula the table for reducing sidereal time to mean time is calculated at the rate of 95.8292 per hour, or 3m. 55901 for 24 hours.-This table is necessary for astronomers who regulate their clocks by sidereal time, for when they have observed the time of any phenomena, it is only in this species of time that it is known. And in order to have it expressed in mean time, they calculate the mean place of the Sun referred to the apparent equinox. This mean longitude, converted into time at the rate of 1 h. to 15°, is the Sun's mean right ascension, or the sidereal time of the passage of the Sun's mean place over the meridian, or, in other words, the sidereal time at mean noon. This time subtracted from the time of the observation, gives an interval of sidereal time, which is then to be converted into mean time. The following example will illustrate this process.

Suppose, then, any observation to be made at 17h. 9m. 235-5 of sidereal time; and that the mean longitude of the Sun at mean noon was

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This is the mean time elapsed since the passage of the mean Sun over the meridian, and is what is called the mean time of the observation. This time supposes the motion of the Sun on the equator to be uniform; and it is the passage of the point of the equator which corresponds to this uniform motion, which determines what is called mean noon, and the interval from this noon constitutes mean time, as the interval from apparent noon constitutes apparent time.

Apparent time is too unequal a measure for astronomers, though it may answer for civil purposes. Clocks can mark only mean or sidereal time as these alone are uniform; they can never indicate apparent time except by a particular construction, and then not with accuracy. Hence all astronomers regulate their clocks by sidereal time, when they have a fixed observatory, and by mean solar time in other cases. Apparent time therefore serves only to find mean or sidereal time. If the transit of the Sun over the meridian be observed by means of a clock regulated to sidereal time, and the rate of which is known, we shall have the Sun's right ascension; but if the rate be not known, the time of the observation is to be compared with the Sun's right ascension, either as calculated or taken from an Ephemeris, and the difference is the correction of the clock. By calculating at the same time the equation of time or the mean right ascension of the Sun, we have the difference between the clock and mean time for the instant of apparent noon.

If the observation of the Sun's passage over the meridian be ascertained by means of a clock regulated to mean time, the time is to be compared with the Sun's mean right ascension in time, and the difference is the error of the clock at the instant of apparent noon; and if this observation be repeated for several successive days, the rate of the clock will be

found, and we shall be able to assign the time of any observation whatever.

If the Sun's zenith distance were observed, with this distance, the height of the pole and his declination, the apparent horary angle is calculated, any this, corrected by the equation of time, gives the mean time of the observation, and consequently the actual error of the clock. Several comparisons of this kind give the progress of this error, and consequently the rate of the clock. Mean time multiplied by 15 gives the mean horary angle, which added to the Sun's right ascension calculated for the same time, gives the right ascension of mid-heaven, or sidereal time. Hence it is obvious, that apparent time, or that which is shown by the apparent motion of the Sun in the heavens, serves astronomers only for calculating mean and sidereal time.-See Delambre's Abrégé d'Astronomie, Leçon XII.

[To be continued.]

The Naturalist's Diary

For MAY 1819.

Call the vales, and bid them hither cast
Their bells, and flowrets of a thousand hues.
Ye valleys low, where the mild whispers use
Of shades, and wanton winds, and gushing brooks;
On whose fresh lap the swart star sparely looks,
Throw hither all your quaint enamelled eyes,
That on the green turf suck the honied showers,
And purple all the ground with vernal flowers.

MILTON.

THIS is often the most delightful month of the whole year, and is remarkable for the profusion of verdure which it exhibits: nature's carpet is fresh laid, and nothing can be more grateful than to press its velvet surface. The scenery of a May morning is, not unfrequently, as beautiful as possibly can be conceived; a serene sky, a refreshing fragrance arising from the face of the earth, and the melody of

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