NAVIGATION-NAUTICAL ASTRONOMV. 



[LATITIIDB. 



DOM the observed altitude of a sUr to be 47 10', the 

 height of the eye 18 fat, mid the index ern>r of the in- 

 strument to be 3' 12" tulitractirt. Required tlio true 

 altitude. 



Observed altitude . 

 Ludez error . . 



Dip of the horizon 



Apparent altitude 

 lie-fraction . . 



True altitude . 



4r Iff 0" 

 -3' 12" 



47 6' 48" 

 -4' 11" 



47 V 37" 

 -53" 



47 1' 44" 



The refraction here taken from the table is that for 

 the mean state of the atmosphere. If the height of the 

 barometer and thermometer be observed, the mean 

 refraction may be corrected accordingly, by aid of a 

 table usually placed beside that for the mean state of the 

 Atmosphere. 



2. The observed altitude of the sun's lower limb on a 

 certain day was 16 33', the height of the eye was 17 

 feet, the index error was 3 additive ; the barometer stood 

 at 29 inches, and the thermometer at 68. Required the 

 true altitude of the sun's centre, his semi-diameter, as 

 given in the Nautital Almanac, for the day, being 

 10' 17*. 



Observed alt. sun's L. L. 

 Index error 



Dip . 



Apparent alt L.L. . 



Refraction . -3' 10' 



Correction for barom. 7' 



, therm. - 3* 



1C" 33' 0' 

 + 3' 0" 



16 36' 0- 

 -4' 4' 



16 31' 66' 



-3' 20- 



True altitude of L. L. above 



sensible horizon . . . 1C 28' 36' 



Bsad-dimmetm (\,iut. Aim). + 10' 17* 



Parallax in altitude . -f- 8" 



True alt of sun's centre . . 16 45' 1* 



The corrections for the barometer and thermometer 

 being, as in this example, always very small, they are 

 not attended to at sea when the latitude is the only thing 

 to be determined. The error in the latitude arixing 

 haw small quantities U too trilling to be 

 of any consequence. 



3. The observed altitude of the moon's lower limb 

 (index error allowed for) is 31 18 ; the horizontal 

 parallax, from the Xaiitiuil Almanac, 58' 37'; semi- 

 dwineter, 15' 58' ; and the height of the eye 10 feet. 

 Required the true altitude of the moon's centre. 



Observed alt moon's L. L. 

 Dip 



Soroi-diam. 15' 63" j 



Augmentation 8" j 



31 18' 0" 



= +12-10' 



App. alt moon's centre .... 31 30' 16* 

 Cor. for par.audref.(hor. par. 58' 37", alt. 31^ +48' 20* 



True alt moon's centre 



32" 18* 42" 



4. The observed altitude of the moon's upper limb, 

 com-cU-d for index error, was 41 25' ; the horizontal 

 i-arallax, 66' 40"; semi-diameter, 16' 10 ; and the 

 height of the eye, 16 feet Required the true altitude of 

 tho moon's oentre. 



Observed alt moon's U. L. 



Semi-diam, 15 



Augmentation 10* j 



- 3' 42* 

 -15' 20" 



41 2j' 0* 



App. alt. moon's centre . 

 Correction for parallax and refraction 



True alt moon's centre . 



- -19' 2* 



41 6' 68* 



+ 40 ;,i 



41 46' 49* 



To DETERMINE THE LATITUDE AT SEA FKOM THE 

 MERIDIAN ALTITUDE OF A CELESTIAL OBJECI H..,K 

 DECLINATION is KNOWN. The deterinina'iou of the 

 latitude of the ship by means of the altitude, when on 

 the meridian, of a celestial object of known de.-l in.vi.iii, is 

 the easiest, and in general the safest, method f.>r the pur- 

 pose. The observations and the subsequent calculations 

 being but few, they may be readily aecomplislie 1, and with 

 but little liability to error in the result. This iueth.nl, 

 therefore, is always used at sea, whenever foggy or 

 cloudy weather does not render it impracti. 



The celestial object observed must be one of which the 

 declination is given in the Nautical Almanac, for the 

 meridian of Greenwich. This declination may be re- 

 duced to the meridian of the ship or rather to the time 

 at Greenwich corresponding to that at the ship by 

 turning the longitude by a.-count into time, and then 

 applying the variation for declination due to that time, as 

 explained at page 1077 ; the hourly variation of the sun's 

 declination is given in the Suutical Almanac, at page 1, 

 of each month. Tho longitude by account is always 

 sufficiently near the truth for the determination of this 

 element, though greater precision is required for the 

 moon than for the sun, an the declination of the former 

 changes more rapidly. The decliuatiou of the object 

 observed being thus known at the time of observation, 

 and, from its altitude, the zenith distance of it heim; also 

 known, we have the distance of the oliject Ix.th from the 

 equinoctial and from the zenith of the ship : conse- 

 quently, the distance of the zenith from the equinoctial 

 that is, the distance of the ship from the equator 

 becomes known either by simple additiou or subtraction ; 

 and thus the latitude is found. 



The object observed may be either above the pole or 

 below it ; that is, it may be on either the mid-day or the 

 mid-night portion of the celestial meridian of the place ; 

 and, in the former case, it may be in either of the three 

 following positions in reference to the equinoctial and 

 the zenith, namely 



1. The zenith, and the object observed, may both be on 

 the same side of the equinoctial, and the object nearer to 

 the equinoctial than tne zenith is, as at S, in tin 

 diagram below. 



2. The zenith and the object being on the same side of 



the equinoctial, th> 

 nith may bo nearer t6 

 tin- iM|iiinoctial than the 

 object is, as at S . 



3. The zenith and the 

 object may be on dif- 

 ferent nide of the equi- 

 noctial, as at S*. 



N X H be the 

 meridian, Z the zenith 

 of the ship, N the eleva- 

 ted pole the north pule 

 suppose and E y the 

 equinoctial. 



First. Let the object 

 observed be at S, between the zenith and the equinoctial, 

 and both north of the equinoctial : then for the latitude 

 E Z, we have EZ-ES + SZ: that is, 



(1). The latitude is equal to the declination, plus 

 the co-altii. la. 



Second. Let the obje, * He at S', on the contrary side 

 of the zenith, then the latu.iJo EZisEZ-ES'-S'Z; 

 that in, 



