LATITUDE.] 



KAVIGATION NAUTICAL ASTRONOMY. 



1083 



was Ch. 56m. 



was 7h. 59m. 



26 38' 17" N. 



26 54' 39" N. 

 16' 12" 

 59' 32* 



2 44' 20* N. 

 2 57' 38" N. 



15' 12- 



55' 13' 



The moon's passage over the merid. 



of Greenwich, Feb. 19th 

 The moon's passage over the merid. 



of Greenwich, Feb. 20th 

 Declination, Feb. 19th, at noon 



midnight 



Semi-diameter . . . . . 

 Horizontal parallax ... 



Required the latitude to the nearest minute. 



Ans. Latitude, 61 1' N. 

 6. On November 12th, 1853, at 2h. 20m. mean time, 

 in longitude 60 42' W., the meridian altitude of the 

 moon's lower limb was observed to be 30 30' 40' (zenith 

 N.) ; the index, correction was -(- 10' 42" ; and the height 

 of the eye 16 feet. 



Moon's declination, Nov. 12, at 6h. 



. .1 7h. 



Semi-diameter . . . > 



Horizontal parallax .... 



Required the latitude to the nearest minute. 



Ans. Latitude, 61 11' N. 

 To determine the latitude from the meridian altitude of 

 a celestial object when below the pole In the diagram 

 (Fig. 26), at page 1078, let s be the position of a celestial 

 object when on the meridian of the place whose zenith is 

 Z, and below the elevated pole N ; the altitude of it will 

 be H s, and N will be the complement of its declination 

 Q s. Consequently, the altitude added to the co-declina- 

 tion will be the latitude H N of the place whose zenith is 

 Z (page 1078). The sun is on the meridian of any place, 

 below the pole, 12 hours after the apparent noon at that 

 place; consequently, 12 hours, increased or diminished by 

 the longitude in time, according as the place is W. or E. 

 of Greenwich, will be the apparent time at Greenwich 

 when the observation was made ; and the declination 

 corresponding to this time may be found as in the fore- 

 going examples. 



For a star, the declination will be the same as that 

 given for the day, in the Nautical Almanac ; since, as 

 before remarked, the change in the declination of a fixed 

 star is insensible till after the lapse of several days. 



For the moon, the time of transit over the mid-day 

 portion of the meridian of the place may be found as at 

 page 1081 ; and this time increased by 12 hours, and by 

 half the daily difference of time, will be the time of her 

 returning to the meridian below the pole; and the 

 proper reduction being made for longitude, as in the 

 case of the sun, the time at Greenwich, and thence 

 the corresponding declination, may be found. The rule 

 for computing the latitude is therefore as follows : 



RULE. 1. Find the declination of the object at the 

 time of observation. 



2. To the observed altitude apply the proper correc- 

 tions for deducing the true altitude. 



3. To the true altitude add the co-declination ; the 

 sum will be the latitude, of the same name as the de- 

 clination. 



LATITUDE TROM THE SDK WHEN BELOW THE POLE. 

 As the rule just given applies equally to the sun, moon, 

 or star, special directions for each case will be unneces- 

 sary ; we shall, therefore, give a practical illustration of 

 the mode of working for each object separately, and 

 then add an example or two for exercise. The following 

 is an example when the object is the sun : 



Example. On June 18th, 1853, in north latitude, 

 and in longitude 96 W., the meridian altitude of the 

 sun's lower limb, at apparent midnight, was observed to 

 be 8 36' ; the index correction was 2* ; and the height 

 of the eye 20 feet. Required the latitude. 

 For the declination at the Greenwich time of observation. 

 Apparent time at ship, June 18 . . 12h. Om. 

 Longitude 96 W. in time .... Oh. 24m. 

 Apparent time at Greenwich . . . 18h. 24m. 

 Sun's declination at noon, June 18 . 23 25'36"N. (inc.) 

 Correction for 18h. 24in. . . . 

 Declination at time of observation 



49" 



23 26' 25" N. 

 90 



Co-declination 66 33' 36* 



Observed alt. of sun's L. L. 

 Index cor. % 

 Dip . . - 4' 24" 

 Semi-diam.-t-15'46", 

 App. alt. of centre 

 Refraction and parallax 



True alt. of centre 

 Sun's co-decliiiation 



8 45' 22" 

 -5' 49" 



8 39' 33" 

 66 33' 35" 



Latitude .... 75 13' 8" N. 



LATITUDE FROM A STAR WHEN BELOW THE POLE. In 

 northern latitudes, the star called the pole star is very 

 convenient for the purpose of finding the latitude of 

 the ship, and is, therefore, frequently observed by 

 mariners for this object. The following is an example: 



Example. On March 1st, 1823, the observed altitude 

 of the pole star when on the meridian below the pole, 

 was 30 7'; the index correction was + 2'; and the height 

 of the eye 18 feet. Required the latitude. 



Observed altitude of pole star 



Index cor. + 2' ) 



Dip . .4' 11"] ' ' 



Refraction 



True altitude of star . . 

 Co-declination Mar. 1, 1823 



Latitude 



30 7' 0* 

 2' 11" 



30 4' 49" 

 1'38* 



30 3' 11* 

 138' 2" 



31 41' 13" N. 



LATITUDE FROM THE MOON WHEN BELOW THE POLE. 

 The preliminary corrections for the moon, as already 

 seen, are more numerous than those for the sun or for a 

 star ; a specimen of them is given in Example 1, p. 1082. 

 These corrections are of course the same, whether the 

 moon be observed on the meridian above the pole or 

 below it. In the following example the moon's decli- 

 nation is found as at the page just referred to, so that 

 the reductions need not be repeated here. 



Example On the 27th of May, 1846, in longitude 

 49 W., the meridian altitude of the moon's lower limb, 

 when below the pole, was found to be 7 12'; the index 

 correction was 1' 40"; and the height of the eye 20 feet. 

 Required the latitude. 



The moon's declination at the time when the observation 

 was made, was found, at page 1082, to be 18 55' 28" N. : 

 leuce the operation for finding the true altitude of the 

 moon's centre, and thence the latitude of the place, is as 

 follows : 



Observed alt. of moon's L. L. 

 Index cor. . 1' 40" \ 

 Dip ... 4' 24" ( 

 Semi-diam. ) i it-ifi'M ' 

 augmented j " & lb ) 

 App. alt. of centre ... 

 Parallax and refraction . , 



712 / 0* 

 + 9' 12* 



7 21' 12" 

 + 47' 31" 



True alt. of moon's centre 

 Co-declination, . . 



Latitude 



8 

 71 



8' 43" 

 4' 32* 



79 13' 15" N. 



Examples for Exercise. 



1. On June 28th, 1841, in longitude 126 W., the alti- 

 lude 0^ the sun's lower limb at midnight was 6 28' ; the 

 ndex correction was + 2" 15"; and the height of the eye 



20 feet. Required the latitude to the nearest minute, the 

 un's declination at noon, Greenwich time, on the 28th, 



being 23 17' 59" N. decreasing, and his semi. diameter 



15' 45* 



Ans. Latitude, 73 19' N. 



2. The observed altitude of the sun's lower limb, when 

 on the meridian below the pole, was 7 5' ; its declination 

 at the time of observation was 23 8' 17" N. ; its semi- 

 diameter 15' 45", and the height of the eye 20 feet. Re- 

 quired the latitude, the index error of the instrument 

 being 0. Ans. Latitude, 74 1' N. 



