NAVIGATION NAUTICAL ASTRONOMY. 



[lATITCDB. 



altitude* at this wwond place, taken at the stated times, 



36 2 40" and 41 3 



.'. Z S - 63 6r 20- and Z S' - 48 29' ff. 

 2. For tk eo-dtelinatiotu P8,P 8: 



Ship's time, Feb. 6 

 Long, ill time 



Time at Greenwich 

 Deo., Feb. 6. 



16 38 9" 

 17' 49' 



15 20 20" S. 

 90 



PS -105 2020- 



Ship's time, Feb. 6 . 

 Long, in time . . 



Gr. time, Feb. 7 . . 



Dec. Feb. 7 . 15 19' 32" 

 1'68' 



201i. 9m. 4. 

 3h. 8m. Of. W. 



23h. 17m. 4s. 



Tar. 40" -5 

 23 



1395 

 MO 



Declination 



15 17' 34- a 



90' 



P S- = 105 17 34' 



23h. 30m. 18s. 

 3k Sin. Os. 



2h. 38m. 18s. 



var. 47' '2 

 2* 



M4 



236 



6)11-80 

 1-97 



The decimal part of the minutes, in the correction for 



declination, is reduced to seconds by multiplying by CO. 

 3. For the angle S P S.' 



Time of first ob- 

 servation . . . 



Time of second 

 observation. . 



Interval of time 3h. 21m. 14s. 



8h. 9m. 4s. 3h. = 45" 

 llh. 30m. 18s. 21m * = 6 15' 



14s. = 



3' 30" 



.'. the angle S P S', in degrees, = 50 18' 30" 

 Hence in the isosceles triangle P M S, we have for each 

 of the equal sides i (P S + P S') = 105 18' 57', and for 

 half the vertical angle, 25 9' 15". 



1. In the triangle P M S to find S M. 

 in. PS, 105 20' 20" . . 9-9842479 

 sin. P, 25 9' 15' . . 9-6284454 



SM, 



24 11' 68' 

 2 



9-C12C934 



88'- 48 23' 56" 



2. In the triangle P S S' to find the angle P S S'. 

 sin. S S', 48 23' 56" Arith. Comp. -1262231 

 *in. 1'S', 105 17' 34" 99843431 

 in. 8 PS', 60 18' 30" 9'8862044 



in. PSS', 83 1'17" 99967706 

 3. In the triangle Z S S', find the angle Z S S'. 



28, 48 29* 8' 



rill. ZS, 63 67' 20' Arith. Comp. -0922566 

 in. KS'. 4X 3 IS fifl* .19i;-">::ii 



in. B S , 



2)150 60' 24' 



i ram - 75 25 12' 

 in. (1 sum- ZS), 21 27 ' W 

 in. (J .urn -88'), 27" 1' 16' 



1262230 



95633906 

 9-6673607 



2)194392309 



Mrld, i.y , u>d ndua 



31 3T 2T 97196154 



ernj unit of reminder u IS minuttt, U 

 t or MM**, If MoaaiU be Uw dividend. 



.'. '/. S S' - 63 14' 54' 

 1' S .S - 83 1' 17* 



.'. PSZ- 19 46 23' 



4. In the triangle Z S P, to find Z P. 



tan. PS 105 20' 20" 

 cos. PSZ J 



cot. 16 15' 2" 

 ZS- 63 57' 20" 



10-5017760 



+ZS-37 42 1 18" 



cos. PS . . 

 sin. u, Ar. Comp . . 

 in. (, + Z S) . 



sin. ZP, 35 2tf . 

 Hence the latitude is 35 20' N. 



9-422n'-M. r 



tsoM9 



9-7804647 

 9-7621821 



NOTE. It may happen, in low latitudes, that the arc 

 SS', if prolonged, would cut the meridian PZ between 

 P and Z, in which case the angle PSZ will not bo the 

 difference between the angles PSS', Z S S' ; and the sum 

 of these angles must be taken instead. Incases of doulit, 

 therefore, the last portion of the work should be modified 

 on this second supposition, and that one of the two re- 

 sulting latitudes taken which best agrees with the lati- 

 tude by account. (See Fig. 27, page 1084). 



It may be also noticed that the error of a few minutes 

 in the estimated mean time at the ship will be of no con- 

 sequence in deducing the declination ; but as an error in 

 the elapsed time, and therefore in the corresponding 

 polar angle, is to be avoided, the elapsed time should bo 

 taken from the chronometer, or a good watch. 



3. The two corrected altitudes of the sun are 42 14- 

 and 16 5' 47' ; the corresponding declinations aro 

 8' 16' 30' K, and 8 15' N., and the time between the 

 observations is three hours. Required the latitude of the 

 place. Ans. Latitude, 48 64' 27" N. 



4. The two corrected zenith distances are 54 39' and 

 19 69' ; the corresponding declinations are 6" 31' <i S. 

 and 5 28' 64' S., and the interval of time 21i. 2Hni. 

 Required the N. latitude. Aus. Latitude, 1 29' 28' N. 



6. In latitude 29 10* S. by account, and longitude 

 124 W., the sun being obscured at noon, its altitude 

 was taken at about 20in. past noon, the chronometer at 

 the time showing 9h. 49m. 20s. : at lOh. 44m. 45s., by 

 the same chronometer, the altitude was again taken, hi 

 the first observation the altitude of the upper limb was 

 found to be 45 33' ; in the second, the altitude of the 

 lower limb was 42 8' 30", at which second observation 

 the sun bore N. i E. The ship's course between the- 

 observations was N.W. J W., and her run 6 miles ; the 

 allowance for dip was 4' 30", and the Nautical Almanac 

 gave the following particulars for noon of the day at 

 Greenwich : 



Sun's declination from Naut. Aim., 16 34' 4" N. ; 



hourly var. 42"' 8. 

 Semi-diameter from ditto, 15' 52". 



Required the latitude of tho ship, when the greater alti- 

 tude was taken. Ans. Latitude, 28 0' S. 



NOTE. When, as in this last example, the latitude 

 at the first observation is to be found, and the sun's 

 bearing is taken at the second observation, the point 

 opposite to that of the shin's course from the first posi- 

 tion, is to be used in reducing the second altitude to 

 what it would have been, if taken at tho first position of 

 the ship. 



If the sun's true bearing, or azimuth, could be taken 

 with precision at either place of observation, there would 

 bo no necessity for a second altitude, because in the 

 spherical triangle V, I' .S, formed by the co-latitude V. I', 

 tho co-declination 1' S, and tho co-altitudu Z S, the auglo 



