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dip (for height of eye), the semi-diameter (if any), the refraction, and parallax (if any).

Then, these corrections being applied, if the zenith distance is required, proceed as follows

For the Zenith Distance

For the Apparent Zenith Distance : Subtract the apparent (central) altitude from 90°.

For the True Zenith Distance : Subtract the true (central) altitude from

90°.

Then, if the observed object bears N., the zenith distance will be S.; if it bears S. the zenith distance will be N.

Or, otherwise, if the observer is N. of the object the zenith distance will be N.; if observer is S. of the object the zenith distance will be S.

Corrections for the Sun : (1) Apply to the observed altitude the index error, additive ( + ) or subtractive (-), as the case may be.

(2) Dip (for height of eye), subtractive (-), Dip Table ; gives the apparent altitude of the limb observed.

(3) Semi-diameter (from Nautical Almanac, p. II. of month); additive (+) when lower limb is observed; subtractive (—) if upper limb is observed. The application of these corrections gives the apparent altitude of the centre.

(4) Refraction, subtractive ( - ), Mean Refraction Table ; enter with the apparent altitude of limb observed. (5) Parallax, additive ( + ), Table of Sun's Parallax in Altitude.

Note.—These corrections when applied give the true altitude of the centre. N.B.--Refraction and parallax are combined in Table of Sun's Correction of Apparent Altitude.

All the corrections, excepting index error, are combined in Table of Sun's Total Correction of Observed Altitude, which is sufficiently accurate for sea purposes.

For the Zenith Distance see Rule above.

Example.- January 1oth : the observed altitude of the sun's lower limb was 37° 24' 30" bearing north ; index error of the sextant 1' 42" to subtract; height of the eye 19 feet. Required the true altitude, and thence the zenith distance

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90 Sun's true zen. dist. 52 26 18 S

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Corrections for the Moon : (I) To observed altitude apply index error, +

as the case may be.

(2) Dip, subtractive (-), Dip Table; gives the apparent altitude of limb observed.

(3) Semi-diameter (from Nautical Almanac, p. III. of month) to be corrected for Greenwich time, and augmented from the Moon's Augmentation Table; apply augmented semidiameter, additive ( + ) if lower limb is observed, subtractive ( - ) if upper limb is observed.

(4) Refraction, subtractive ( - ), Mean Refraction Table ; enter with apparent altitude of limb observed.

(5) Parallax, additive ( + ); to be computed as follows

Correct the horizontal parallax (from Nautical Almanac, p. III. of month) for Greenwich time, and reduce it by Table E: then, to the Proportional Logarithm of the corrected horizontal parallax add the L secant of the apparent (central) altitude, corrected for refraction; the sum will be the proportional logarithm of the parallax in altitude.

Or the parallax in altitude may also be found as indicated on p. 254.

Convert the horizontal parallax into seconds, then to the logarithm of the horizontal parallax (in seconds) add the L cosine of the apparent (central) altitude, corrected for refraction; the sum will be the logarithm of the parallax in altitude in seconds, which take out and reduce.

These corrections, when applied, give the true altitude of the centre.

N.B.—Refraction and parallax in altitude are combined in Moon's Correction Table, sufficiently accurate for sea purposes.

For the Zenith Distance see Rule, p. 255.

Example.-August 28th, about 2h. at a.m. at ship, in lat. 46° 4' S., long. 165° E. ; mean time at Greenwich by chronometer (corrected) August 27d. 3h. im. 545., the observed altitude of the moon's upper limb was 32° 45' 40" bearing north ; error of sextant 2'7" to add ; height of eye 21 feet.

Required the true altitude, and thence the zenith distance

Moon's Semi-diameter and Horizontal Parallax corrected for Greenwich time.

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16 45

I 29

Altitude and Zen. Dist.
Obs. alt. I's U.L. 32° 45' 40" N. Correction by Moon's Cor. Tables
Index error + 7
32 47 47

App. alt. (centre) 32° 26' 33"
Dip 21 ft.
4 29

Cor. (par.-ref.) + 49 42
App. alt. I's U.L. 32 43 18

True alt. (centre) 33 16 15
l's Semi-d.
App. alt. I's centre 32 26 33
Ref.

H.P. 60' 39" Prop. log. 4724 32 25 4.....

Secant 0.0736 Par. in alt + 51 12

Par. in alt. Prop. log. 0:5460
True alt. I's centre 33 16 16 N.

90
l's True zen. dist. 56 43 44 S.

Or, otherwise
H.P. 3639"-2 Log. 3.561006
Alt. 32° 25'4" Cos. 9.926426

6,0)307,2":I Log. 3.487432 Par. in alt. 51'12":1 as above.

Corrections for a Planet.You may follow the instructions as given for the Moon, but ordinarily it will be sufficient to use the usual Nautical Tables, and the quantities as given in the Nautical Almanac under the head of the given planet.

(1) To the observed altitude apply the index error, + or -, as the case

may be.

(2) Dip, subtractive ( - ).

(3) It is usual to estimate the centre in bringing it to the sea-horizon, so that semi-diameter is not required.

(4) Refraction, subtractive ( - ).

(5) Parallax, additive ( + ), to be found as follows : Enter the Nautical Almanac with the heading the name of the planet and transit at Greenwich. Opposite the day of the month in the last column take out the horizontal parallax. Enter Table of Parallax in Altitude for Planets with the horizontal parallax at the top and altitude at the side ; the quantity found is the parallax in altitude. These corrections give the true altitude of the centre.

For the Zenith Distance see Rule, p. 255.

Example.December 7th : the observed altitude of the centre of the planet Venus was 53° 14' 20" ; observer N. of the planet ; index error + 3' 46" ; height of eye 22 feet. Required the apparent and true altitudes, and the apparent and true zenith distances

By Nautical Almanac the Horizontal parallax is 33",
Obs. alt. Venus 53° 14' 20" S.

Index error +

3 46 53 18 6

4 36

Dip 22 ft.
App. alt. 53 13 30.....

53° 13' 30"
Ref.
43

90
53 12 47 App. zen. dist. 36 46 30
Par. in alt. + 20
True alt. (centre) 53 13 7 S.

90
True zen. dist. 36 46 53

Corrections for a Fixed Star : (1) Apply to the observed altitude the index error + or as the case may be.

(2) Dip, subtractive ( - ).

The application of these corrections gives the apparent altitude of the star. A star has no semi-diameter.

(3) Refraction, subtractive ( - ), Mean Refraction Table ; this correction, applied to the apparent altitude, gives the true altitude, since a fixed star has no parallax.

N.B.The dip and refraction are combined in Star's Correction Table; accurate enough for sea purposes.

For the Zenith Distance see Rule, p. 255.

Example.-- February 1oth : the observed altitude of a Canis Minoris (Procyon) was found to be 18° 46' 30" bearing south ; index error 3' 17" to subtract; height of eye 18 feet. Find the apparent and true altitudes of the star, and the apparent and true zenith distances

Whole Correction by

Star's Total Correction Table *'s Obs. alt. 18° 46' 30" S.

*'s Obs. alt. 18° 46'.5 Ind. err.

Ind. err. 3 17

3:3

18 43 13

18 43.2

Dip 18 ft.

4 9
*'s App. alt. 18 39 4
Refraction

2 47
*'s True alt. 18 36 17 S.

90
*'s True zen. dist. 71 23 43 N.

Star's Cor.

6.9
*'s True alt. 18 36.3

90
*'s True zen. dist. 71 237
*'s App. alt. 18°39'4'

90
*'s App. zen. dist. 71 20 56

CORRECTIONS OF ALTITUDE OBSERVED BY AN ARTIFICIAL HORIZON ON

SHORE

The altitude having been observed by an artificial horizon, each angle, of whichever part of the object observed, will be double what it would have been if taken by the sea-horizon ; and as it is customary to take several altitudes (3, 5, or 7) in succession, the sum of the altitudes must (in

the first place) be divided by the number observed ; this will be the mean of the observations, to which the next operation is to apply the index error, + or as the case may be ; and the result will be the correct observed angle.

But this angle being double what it would have been if the altitude had been taken direct, the correct mean observed angle must be divided by 2, and the result will be the apparent altitude of the part of the object observed, since there is no correction required for the height of the eye, or dip, the effect of the elevation of the observer being insensible.

The subsequent corrections then fall in the natural order, already given.

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(1) To the apparent altitude

apply the semi-diameter
if any; + or

case may be.
(2) Refraction ( - ).

(3) Parallax ( + ) if any.
And the result will be the true
central altitude.

Example.-November 7th, the altitudes of the sun's lower limb observed by artificial horizon were

52° 0' 45"
51 41 30

51 20 45
index error of sextant 2' 50" to sub-
tract. Find the true altitude of the
sun's centre.

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N.B.-If several altitudes are taken at about equal intervals, the difference between the altitudes will indicate if there be any serious errors in the observations.

If the sun is the object observed, and the altitude is increasing (or rising); when taking the lower limb, the images are continually separating ; but when taking the upper limb, the images are continually overlapping. The contrary effect is observed with the sun's decreasing (or falling) altitude. This leaves no doubt as to the limb observed.

For a Fixed Star : Divide by the number of observations; to the result apply the index error ; then divide by 2 for the apparent altitude ; from the apparent altitude subtract the refraction, and the result will be the true altitude.

Example.- January 20th : the following altitudes of Procyon (a Canis Minoris) were observed by artificial horizon

))

47° 0' 15"
47 17 45

47 35 30
index error of sextant 3' 10" to sub-
tract. Find the apparent and true
altitudes.

Obs. altitudes 47° 0' 15"

47 17 45

47 35 30 3)141 53 30 47 17 50

3 IO

Ind. err.

2)47 14 40

*'s App. alt.

Ref.

23 37 20

2 10

*'s True alt.

23 35 10

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