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Equation of Time. When it is wished to regulate a clock by means of a good sun-dial, the numbers in the following table must be subtracted from the time as indicated by the dial, and the remainder will be the time which should be shown by the clock at the same instant the dial was observed.
TABLE. Saturday, May 1st, from the time by the dial subtract 2 58 Thursday, 6th,
3 32 Tuesday, 11th,
3 51 Sunday, 16th,
3 57 Friday, 21st,
3 47 Wednesday, 26th,
3 24 Monday, 31st,
2 after 1 morning. Moon's Passage over the first Meridian. The Moon will pass the meridian of the Royal Observatory at the following times during this month; which will be convenient for observation, if the weather be favourable; viz.
May 4th, at 7 m, after 8 in the evening.
3 in the morning. 21st,
5 22d, 6
5 Phase of Venus.
7.70911 digits. Dark
4.29089 Eclipses of Jupiter's Satellites. There will be only one eclipse of the first satellite
and one of the second visible at the Royal Observatory this month, which will happen as follows :
3 Other Phenomena. Mercury will be in his inferior opposition at 4 in the morning of the 3d of this month, stationary on the 17th, and attain his greatest elongation on the 31st. Jupiter will be in quadrature at 45 m. past 6 in the morning of the 7th Mars and Venus will be in conjunction with each other at 8m. after 8 in the morning of the 2d, when Mars will be 45' south of Venus. The Moon will be in conjunction with a in Scorpio at 29 m. after 7 in the morning of the 11th ; with Saturn at 46 m. after 2 in the morning of the 19th ; with Venus at 15 m. after 8 in the morning of the 20th; with Mercury at 4 m. past9 in the evening of the 20th, with B in Taurus at 20 m. after 1 in the afternoon of the 25th; and with Pollux at 27 m. past 1 in the morning of the 28th.
On Time and its APPLICATION.
[Continued from p. 107.] From the simple exposition of the subject already given, it may readily be conceived, that in virtue of the obliquity of the ecliptic combined with the inequality in the motion of the Sun, the equation of time becomes nothing four times in the course of the year; viz. once between the winter solstice and the perigee of the Sun, twice between the vernal equinox and the summer solstice, and again between the apogee and the autumnal equinox. These epochs, however, are not fixed, but vary with the position of the major axis of the solar orbit. They are at present about the 25th of December, the 16th of April, the 16th of June, and the 1st of September. The progressive change in the position of the major axis of the apparent solar orbit ought also to produce a gradual and small corresponding variation in the absolute value of the equation of time. The causes, however, which make the equation of time vanish at certain intervals, ought still to produce their effect, notwithstanding the trifling variations which the effects of nutation may occasion; for as these variations never exceed a few seconds, they can only produce a small change in the four epochs in each year when the equation of time becomes nothing, but they can neither destroy it altogether, nor cause it to deviate from the limits above assigned to it.
If the inclination of the ecliptic to the plane of the equator were to become nothing, or the planes of the two circles to coincide with each other, that part of the equation of time which depends upon this inclination would also become nothing. Then the mean and real motions would only differ from each other by the effects produced by the inequalities of the latter motion, and which the French astronomers express by the equation of the centre. The real and the mean Sun would then meet only at the perigee and apogee, and apparent time would coincide with mean time only twice a year, when the Sun was in the line of his apsides.
From this explanation, it is easy to conceive that the instant of apparent noon, as marked by the shadow on the dial, will generally differ from that of
But as the equation of time is known for each day at this time, the direction and limit of the shadow may be marked on the dial at the instant of mean noon; and there will thus be obtained a series of points on both sides of the apparent meridian, which will mark the positions of the mean meridians at these successive instants. The curve described through all these points ought evidently to meet the meridian in four points, answering to the four times in the year in which the equation of time becomes nothing. This curve ought also to return in
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
= 59'8":33, 365 d. 5 h. 48 m. 51 s. 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 15(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 24 h. 3 m. 56-5554 is to 24 h.; and hence we have the equation
the duration of the mean hour
86400 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
1.00273791' it will therefore be expressed by a less number in mean time than in sidereal time.
From the equation, s = 1.00273791, we readily deduee s
m = 1:00273791m m = 0.0027370km; 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 9%8568 to be added to it, in order to have s-=1h. Om. 9.8568.
Again, if we suppose m = 7h. 30m., the quantity to be added to obtain s, will be 9••8568 x 7.5 = 1*. 13.926; and, consequently, s. = 7h. 30m. + Jn. 134926 -7h. 31m. 134.926.
The same result may be obtained from the previ, ous equation, in which s = 1.00273791m ; for, multipiying m by this number, we shall have the value of s. Taking the last example, 1.00273791 x 7.5 - 76.520534325 = 7n. 31m. 13-924.
Whens 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 7h. 31", 13.924, as an example, we have 75.521 * •99727 =7h. 30. Or, by the second method, we have 7h.521 .00273 = .021 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, lm, of mean time answers to 15' 2":4642, and 1. of mean time corresponds to 15".04107 of a