Appar. Time at Greenwich, Feb. 1855, 3d. 2h. 43m 36.
Equation of time by Table XII, -

100yrs. 13s. (Sec. Var. Table XIII)
:: 15yrs. 1.9s. -

Approx. Mean Time at Greenwich,
24h. 6s. (change of equa. for 1° of
long.) 14m. : 0.1s. -

+14

8.6

1.9

3 2 57 42.7

+0.1

0.8

1.0

0.4

0.3

0.1

3.0

Mean Time at Greenwich

3 2 57 42.4

4. On the 18th of November, 1841, when it is 2h. 12. 26sec. A. M. mean time at Greenwich, what is the apparent time at Philadelphia? Ans. Nov. 17th, 9h. 26m. 24s. P. M.

5. On the 2d of February, 1839, when it is 6h. 32m. 35sec. P.M. apparent time at New Haven, what is the mean time at the same place? Ans. 6h. 46m. 3Ss. P. M.

6. On the 23d of September, 1850, when it is 9h. 10m. 12sec. mean time at Boston, what is the exact apparent time at the same place? Ans. 9h. 8m. 1.0s.

PROBLEM VII.

To correct the Observed Altitude of a Heavenly Body for

Refraction.

With the given altitude take the corresponding refraction from Table VIII. Subtract the refraction from the given altitude, and the result will be the true altitude of the body at the given station.

This rule will give exact results if the barometer stands at 30 inches, and Fahrenheit's thermometer at 50°, and results sufficiently exact for ordinary purposes in any state of the atmosphere. When there is occasion for greater precision, take from Table IX

the corrections for + 1 inch in the height of the barometer, and -1° in the height of Fahrenheit's thermometer, and compute the corrections for the difference between the observed height of the barometer and 30 in. and for the difference between the observed height of the thermometer and 50°. Add these to the mean refraction taken from Table VIII, if the barometer stands higher than 30 in. and the thermometer lower than 50°; but in the opposite case, subtract them, and the result will be the true refraction, which subtract from the observed altitude.

Exam. 1. The observed altitude of the sun being 32° 10′ 25′′, what is its true altitude at the place of observation?

2. The observed altitude of Sirius being 20° 42′ 11", the barometer 29.5 inches, and the thermometer of Fahrenheit 70°, required the true altitude at the place of observation. The difference between 29.5 inches and 30 inches is 0.5 inches, and the difference between 70° and 50° is 20°.

Refrac. (Table VIII), 2′ 33′′.0; Bar.+1in., 5".12; ther.—1°, 0′′.310 Corr. for-0.5 in. bar. 2.6

Corr. for+20°, ther. -6.2

5

20

6.20

3. The observed altitude of the moon on the 11th of April, 1838, being 14° 17' 20", required the true altitude at the place of observation. Ans. 14° 13′ 35′′.

4. Let the observed altitude of Aldebaran be 48° 35' 52", the barometer at the same time standing at 30.7 inches, and the thermometer at 42°, required the true altitude.

Ans. 48° 34' 58".8.

PROBLEM VIII.

The Apparent Altitude of a Heavenly Body being given, to find its True Altitude.

Correct the observed altitude for refraction by the foregoing problem. Then,

1. If the sun is the body whose altitude is taken, find its parallax in altitude by Table X, and add it to the observed altitude corrected for refraction. The result will be the true altitude, sought.

2. If it is the altitude of the moon that is taken, and the horizontal parallax at the time of the observation is known, find the parallax in altitude by the following formula:

log. sin (par. in alt.) = log. sin (hor. par.) + log. cos. (app. alt.)—10; and add it, as before, to the apparent altitude corrected for refraction.

3. If one of the planets is the body observed, the following formula will serve for the determination of the parallax in altitude when the horizontal parallax is known:

log. (par. in alt.) = log. (hor. par.) + log. (cos appar. alt.) —— 10.

Note 1. The equatorial horizontal parallax of the moon at any given time may be obtained from the tables appended to the work. (See Problem XIV). But it can be had much more readily from the Nautical Almanac. The equatorial horizontal parallax being known, the horizontal parallax at any given latitude may be obtained by subtracting the Reduction of Parallax, to be found in Table LXIV. The horizontal parallax of any planet, the altitude of which is measured, may also be derived from the Nautical Almanac.

Note 2. The fixed stars have no sensible parallax, and thus the observed altitude of a star, corrected for refraction, will be its true altitude at the centre of the earth as well as at the station of the observer.

Note 3. If the true altitude of a heavenly body is given, and it is required to find the apparent, the rules for finding the parallax in altitude and the refraction are the same as when the

apparent altitude is given; the true altitude being used in place of the apparent. Tut these corrections are to be applied with the opposite signs from those used in the determination of the true altitude from the apparent; that is, the parallax is to be subtracted, and the refraction added. It will also be more accurate to make use of equa. (12), p. 44, in the case of the moon. Exam. 1. The observed altitude of the sun on the 1st of May, 1837, being 25° 40' 20", what is its true altitude?

2. Let the apparent altitude of the moon at New York on the 17th of March, 1837, 8h. P. M., be 66° 10' 44"; the barometer 30.4 in. and the thermometer 62°; required the true altitude.

3. On the 18th of February, 1837, the true meridian altitude of the planet Jupiter at Greenwich was 56° 54' 57", what was its apparent altitude at the time of the meridian passage, the horizontal parallax being taken at 1".9 as given by the Nautical Almanac ?

4. What will be the true altitude of the sun on the 22d of September, 1840, at the time its apparent altitude is 39° 17' 50"? Ans. 39° 16' 46".

5. Given 29° 33' 30" the apparent altitude of the moon at Philadelphia on the 15th of June, 1837, at 9h. 30m. P. M., and 58' 33" the equatorial parallax of the moon at the same time, to find the true altitude. Ans. 30° 22′ 41′′.

6. Given 15° 24′ 23" the true altitude of Venus, and 8" its horizontal parallax, to find the apparent altitude.

Ans. 15° 27' 41".

PROBLEM IX.

To find the Sun's Longitude, Semi-diameter, and Hourly Motion, for a given time, from the Tables.

For the Longitude.

When the given time is not for the meridian of Greenwich, reduce it to that meridian by Problem V; and when it is apparent time, convert it into mean time by the last problem.

With the mean time at Greenwich, take from Tables XVIII, XIX, XX, and XXI, the quantities corresponding to the year, month, day, hour, minute, and second (omitting those in the last two columns), and place them in separate columns headed as in Table XVIII, and take their sums.* The sum in the column entitled M. Long, will be the tabular mean longitude of

• In adding quantities that are expressed in signs, degrees, &c. reject 12 or 24 signs whenever the sum exceeds either of these quantities. In adding arguments expressed in 100 or 1000, &c. parts of the circle, when they consist of two figures, reject the hundreds from the sum; when of three figures, the thousands; and when of four figures, the ten thousands.