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Ex. 6. 1865, June 1st, at 9h 40m A.M. mean time at ship, latitude 60o N., longitude 40° 20′ W., observed altitude sun's L.L. 44° 48′ 50′′, index correction + 3′ 17′′, height of eye 18 feet, sun's bearing by compass S. W.

The Greenwich date is June id oh 21m 20s. True altitude, by Norie, 45° 3' 0". Decl. 1st, 22° 5′ 56′′ N., decl. 2nd, 22° 13′ 48′′ N., daily var. +7′ 52′′, corr. + o'′ 7′′, Red. decl. 22° 6' 3" W. Sum of logs. 19217523, true azimuth S. 47° 56′ 8′′ E. True azimuth S. 47° 56' 8" E.

S. 3 point W. — Mag, azimuth S. 5 37 30 W.

Variation 53 33 38 W.

The true azimuth being to the left of magnetic.

EXAMPLES FOR PRACTICE.

In each of the following examples it is required to find the true azimuth and variation :

No. Civil date, 1865.

:

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M. T. ship. 1. Jan. 24th, 8h22m35s A.M, 2, Feb. 28th, 3 14 o P.M. 3. Mar. 27th, 4 6 40 P.M. 4. April 3rd, 6 20 O P.M. 5. May 27th, 9 3 20 A.M. 6. June 20th, 6 10 O P.M. 7. July 31st, 8 46 30 A.M. 8. Aug. 23rd, 5 54 58 A.M. 9. Sept. 1st, 3 47 50 P.M. 10. Nov. 25th, 4 7 O P.M. 11. Dec. 17th, 9 10 30 A.M. 12. July 3rd, 8 26 50 A.M.

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S.

26 57 14

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29 30 50 20

I 33 W. 11 26 W.

W. 14° 10'S.
S. 36 0 E.

38 18 N.

65 4 W.

51 10 N.

135 40 W.

10 40 S.

138 42 E.

N. 50 20 W.
S. 69 20 E.
N. 56 20 E.
W. by N & N.

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39 58 S.

50 52 W.

29 10 S.

26 53 W.

32 10 S.

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47 46 S.

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62 o E. 33 11 E. 86 43 W. 49 18 W. 20 37 E. 51 2 W. 167 。 E.

66

40 N.

55 20 W.

O A.M. 10. A.M.

37

。 S.

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O 25 E.

o W.

W. 9° 10'S.
S. 79 20 E.
N. 62 o E.
N. 64 40 W.
E. 12 10 N.
W. 17 o S.
N. 70 50 W.
S. 34 30 E.
N. 128 15 W.
S. 50 o W.
N. 44 50 E.
S.E. by S.

7 38 0 30 4 10 33 51 O 14 51 I 13 14 11 37 26 37 27 18 44 55 30 13 38 46 39 56 10 32 40 O 18 60 37 O 19 15 38 O 18 42 28 O 20

15

15

16

19 28

4698

16

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ON FINDING THE LATITUDE BY REDUCTION

TO THE MERIDIAN.

THE latitude of a place is most simply determined by observation of the meridian altitude of a known heavenly body. When such an observation cannot be obtained by reason of the state of the weather, the altitude of the body may often be obtained a little before or a little after its meridian passage. And if at the time of observing such an altitude near the meridian, the hour-angle of the body is known, we may find by computation very nearly the difference of altitude by which to reduce the observed to the meridian altitude. The correction is called the "Reduction to the Meridian." This method, in point of simplicity, is little inferior to the meridian altitude, to which it is next in importance. The term "near the meridian" implies a meridian distance limited according to the latitude and declination, and also the degree of precision with which the time is known.

RULE LX.

1o. To the time shown by the watch, expressed astronomically, apply the error of the watch for apparent time: adding when the watch is slow (rejecting 24h when the sum exceeds 24a and putting the day one forward), subtracting when watch is fast (increasing the time shown by watch by 24", if necessary, and putting the day one back).

2°. Next turn into time the difference of longitude made since the error of the watch was determined; adding when the difference of longitude is East, subtracting when difference of longitude is West: the result is apparent time at ship when the observation was made.

3°. If apparent time at ship is P.M., it is the time from noon; when it is A.M., subtract it from 24", the remainder is the time from noon.

Ex. 1. Suppose it is P.M. at ship, and the watch when corrected shows January 2d oh 25m 56s (see example 1 following); then the time from noon is 25m 56s past noon of the 2nd.

Ex. 2. Again, suppose it is A.M. at ship, and the watch when corrected indicates February 5d 23h 17m 163 (see example 2 following), then we have 24h om os 23 17 16

42 44

In this instance it is 42m 44s before noon of the 6th.

4. With apparent time at ship and longitude, find Greenwich date in

apparent time (Rule XLII). A A

5°. Take out of Nautical Almanac, page 1, the declination, and reduce it to the Greenwich date (Rule XLIII or XLIV).

6°. Correct the observed altitude of sun's upper or lower limb, and so get the true altitude of sun's centre (Rule XLVIII).

7°. Take out log. rising of time from noon (Table 29, Norie),* log. cos. declination (Table 25, Norie), and log. cos. of latitude (Table 25, Norie). 8°. Take the sum of these and find the natural number corresponding thereto.

9°. To the natural number just found add the natural sine of the true altitude (Table 26, Norie): the sum is natural cosine of meridian zenith distance, which take out of the Table, and name it North or South, according as the observer is North or South of the sun.

10°. Apply the reduced declination to the zenith distance, taking their sum if they are of the same name, but their difference if of contrary names: the result, in either case, is the latitude of the same name as the greater.

BY RAPER.

1°. Find the time from noon, as directed in the preceding rule.

2o. Get a Greenwich date by means of apparent time at ship and longitude. 3°. Reduce declination to Greenwich date.

4. Correct the observed altitude, and so get the true altitude of sun's centre.

5°. With the latitude and declination find the logarithm in Table to 70, which add the logarithm sine square of the time from noon, Table 69: the sum is sine of the reduction, which take out of Table 66.

6°. Add the reduction to the true altitude: the result is the approximate meridian altitude.

7°. To compute the 2nd reduction.-Double the log. sine of the reduction, add to it log. tangent of meridian altitude found (No. 6), and the constant 9.699; the sum (rejecting 10) is the log. sine of 2nd reduction.

8°. Subtract the 2nd reduction from the approximate meridian altitude found (No. 6); the result is meridian altitude at the place where the altitude was observed.

9°. Having the meridian altitude, find the latitude as directed in 10° of the preceding Rule.

* When the natural sine is used to 6 places, the index of the log, rising must be increased by 1, and when to 7 places, it must be increased by 2.

EXAMPLES.

Ex. 1. 1865, January 2nd, P.M. at ship, latitude account 52°6′S., longitude 71°23′W. observed altitude sun's L.L. North of observer 60° 10' 30", index correction +3' 10", height of eye 20 feet, time by watch 2d 5h 48m 228, which was found to be 5h 20m 163 fast on apparent time at ship, difference of longitude 32.4 miles to West: required the latitude by reduction to meridian.

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Ex. 2. 1865, February 6th, A.M. at ship, latitude account 51° 50′ N., longitude 118° 36′ W., observed altitude sun's L.L. South of observer 21° 50', index correction +56", height of eye 22 feet, time by watch 6d 4h 4m 4s, which was found to be 4h 48m 47s fast on apparent time at ship, difference of longitude made to East was 29.8 miles since error of watch on apparent time at ship was determined: required the latitude by reduction to meridian,

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Diff, long.

29' 8 X 4
60

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By Raper Index corr. + 56",

4' 30",

:

ref. - 2′ 26′′, par. +

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16° 15', True altitude

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Zen. dist. 67 21 10 N. nat, cos. 385058 2nd reduction
Decl.
15 24 54 S.

Latitude 51 56 16 N.

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Mer, altitude

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0'108

log.
sin. sq. 7'938

sine 8.046

2

6.092

tang. 9'620 const. 9'699

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