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4. 1885.- December ist, at 4h 54m P.M., Apparent Time at Ship; in

Latitude 38° 15' N. ; Longitude 1750 W. The sun's observed amplitude was W. by N. Required the true amplitude and error of the compass, and, supposing the variation to be 40° W., required the

deviation. 5. 1885 –September 21st, at 6h 3m A.M., Apparent Time at Ship:

in Latitude 51° 30' N. ; Longitude o’. The sun's observed amplitude was E. 1° 1' N. Required the true amplitude and error of the compass, and, supposing the variation to be 15o W., required the

deviation. 6. 1885:- July 1st, at 2h 14m A.M., Apparent Time at Ship, in Latitude

63° 25' N.; Longitude 79° 29' W. The sun's observed amplitude was N. W. Required the true amplitude and error of the compass, and,

supposing the variation to be 27° E., required the deviation. 7. 1885.—August 16th, at_7h 12m P.M., Apparent Time at Ship; in

Latitude 51° 10' N.; Longitude o. The sun's observed amplitude was N.W. by W. Required the true amplitude and error of the compass, and, supposing the variation to be 11° 52' E., required the

deviation. 8. 1885. -October 20th, at 6h 39m A.M., Apparent Time at Ship; in

Latitude 44° 50' N.; Longitude 71° 5' E. The sun's observed amplitude was N.E. by E. E, Required the true amplitude and error of the compass, and, supposing the variation to be 41° E., required the deviation.

9. 1885.—November 27th, at 6h 41m A.M., Apparent Time at Ship; in

Latitude 25° 50' N.; Longitude 170° W. The sun's observed amplitude was E. Required the true amplitude and error of the compass, and, supposing the variation to be 6° 14' W., required the deviation.

10.

1885.—January 31st, at 7h im P.M., Apparent Time at Ship; in Latitude

45° 19' S.; Longitude 160° E. The sun's observed amplitude was W. by S. Required the true amplitude and error of the compass, and, supposing the variation to be oo o', required the deviation.

II.

1885.–March 21st, at 6b om A.M , Apparent Time at Ship; in Latitude

63° 59' N.; Longitude 10° E. The sun's observed amplitude was E.S.E. Required the true amplitude and error of the compass, and, supposing the variation to be 27° W., required the deviation.

12.

1885:- July 1st, at 6h 27m A.M., Apparent Time at Ship; in Latitude

24° 1''S. ; Longitude 84° 15' E. The sun's observed amplitude was N.E. by E. E. Required the true amplitude and error of the compass, and, supposing the variation to be 21° 1' W., required the deviation.

LONGITUDE BY CHRONOMETER. If the daily rate of the Chronometer is not given, proceed to find it thus :

TO FIND THE DAILY RATE:-Write down the two errors, one below the other.

If both are fast or both slow, subtract;

If one is fast and the other slow, add. Bring the sum or remainder into seconds, and divide by the number of days between the dates of the two errors, the result is the daily rate. To tell if the daily rate of the Chronometer is gaining or losing, consider the following rules :

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TO FIND THE GREENWICH MEAN TIME.—To the time by chronometer, apply the last error.

If fast, subtract it; if slow, add it, then apply the

accumulated rate.
If gaining, subtract it; if losing, add it.

The result is the Greenwich mean time.

TO FIND THE ACCUMULATED RATE.—Having found the daily rate, or having it given it must be multiplied by the number of days and tenths of days between the date of the last error and the day of the chronometer time.

The product (brought into minutes if necessary) gives the accumulated rate, which is applied to the time by chronometer as before stated.

TO FIND THE TRUE ALTITUDE.—Proceed exactly as in finding the true alt. in the Latitude by the Sun's meridian altitude.

TO FIND THE POLAR DISTANCE.—Find the declination by the same method as used in the meridian altitude, taking care to take the declination from page II. of the Nautical Almanac.

Lat.)
Dec.

Same name, subtract dec. from goo.
Lat.
Dec.

Diff. names, add 90° to dec.

Note.--If both Lat. and Dec, are o, or if one of them is o, use either rule.

TO FIND THE EQUATION OF TIME.—Take from page II. of the month, the equation of time for the Greenwich day of the chronometer time. Take out also the hourly difference for the same day from page 1, and multiply this hourly diff. by the hours and tenths in the Greenwich time, being careful to mark off from the right-hand side of the product as many decimal figures as there are decimals in the two numbers you have multiplied together. This is the correction (always less than 60) to be added to the equation if equation is increasing, but subtracted if decreasing

TO FIND THE APPARENT TIME AT SHIP.—Write down the true altitude, below it place the latitude and the polar distance; add these three together; divide the sum by 2. The result is half sum. From half sum subtract the true

altitude. The result is the remainder. Then take out from Table XXV. the following logs. to seconds :

Secant of latitude.
Cosecant of polar distance.
Cosine of half sum.

Sine of remainder. Note-If polar distance is greater than 90? take out the log. secant of the corrected declination instead,

Add the above four logs. together, cast off the tens from the index, and seek the sum of the logs. in Table XXXI., which gives the hour angle, or time from nearest noon.

Question.-Is it A.M. Or P.M. at ship?

If A.M.

If P.M. Subtract the hour angle To the left-hand side of from 24 hours, and to the the hour angle put the same left-hand side

of the re

day as at ship. mainder put a day less than the day at ship.

This gives Apparent Time at the ship.

TO FIND THE MEAN TIME AT SHIP.--Below the

app:

time at ship place the corrected equation of time, and apply it as stated on page 1 of the given month. The result is the mean time at ship.

TO FIND THE LONGITUDE.-Below the mean time at ship place the mean time at Greenwich, taking care always to have the day as well as the hours, &c.; then subtract the less from the greater. The remainder brought into degrees, &c., is the Longitude of the ship.

The Long. is East if the Greenwich time is less than the mean time at ship.

The Long. is West if the Greenwich time is more than the mean time at ship.

The following rhyme is often used to tell the name of the Long. :

" Greenwich Time least Long East,

Greenwich Time best Long West."

EXAMPLE, 1885.–February 6th.—A.M. at Ship in Latitude 28° 40' N. The observed altitude of the sun's lower limb 42° 50' 10"; height of eye 15 feet. Time by a chronometer, February 6d 7h 2m os which was im Os fast for mean noon at Greenwich on November ioth, 1884, and on January 2nd, 1885, it was om go. slow for mean noon at Greenwich. Required the Longitude.

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-5 28

Altitude.

H. diff. Eqn. Time. H. diff. 42° 50' 10" Dec. Feb. 6th 15° 28' 0" S. 46”.56 14 206.28 .144 Dip. -3 42 Cor.

7.05

1.01 7.05 42 46 28

15 22 32
23280 14 21.29

720 Ref. I I

90
325920

10080

To be added to 42 45 27 Pol. dist..... 105 22 32 6,0)32,8.2480 App. Time, 1.01520 Sem. + 16 15 Par.

7

5' 28"

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NOTE.-In Chronometer" all Logs. must be taken out to seconds.

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