lATlTUDE.] 



NAVIGATION NAUTICAL ASTRONOMY. 



1079 



! 



(2). The latitude is equal to the declination, minus 

 the co-altitiule. 



Third. Let the object be at S", on the contrary side of 

 the equinoctial ; that is, let its declination be south, then 

 the latitude is E Z = S" Z - E S ' : that is, 



(3). The latitude is equal to the co-altitude, minus 

 the declination. 



Hence, if we call the co-altitude, or zenith distance of 

 the object, north, when the zenith is north of it, and 

 south, when the zenith is south of it, we shall have the 

 following rule for all the three cases namely, 



RULE. When the object observed is above the pole, 

 if the zenith distance and the declination have the same 

 name, that is, be both north or both south, their sum 

 will be the latitude. If the zenith distance and the 

 declination have different names, their difference will be 

 the latitude, of the same name as the greater. 



It is assumed above that the north is the elevated pole ; 

 but if it be the south, then, by merely writing south for 

 north and north for south, the reasoning will remain the 

 same : the rule will require no modification. 



It is obvious that the elevation of the pole above the 

 horizon of any place is always equal to the latitude of 

 that place, for Z N is equally the complement of the 

 latitude E Z, and of H N the elevation of the pole. The 

 elevation of the equator, or the angle it makes with the 

 horizon, is also clearly equal to the co-latitude. 



It should be remarked, that when celestial objects are 

 near the horizon, they are in a position less favourable 

 for observation than when they are more elevated, 

 because the refraction near the horizon is very variable 

 in its effects. 



LATITUDE FROM THE Srif WHEN ABOVE THE POLE. 

 The sun is the celestial object most commonly appealed 

 to by mariners for the determination of the latitude of 

 the ship : it is more frequently visible in the daytime, 

 when, except in bad weather, the sea horizon is more 

 clearly denned, and the corrections to be applied to the 

 observed, in order to get the true altitude, are few and 

 simple. The corrections for a star are still fewer ; but, 

 as the horizon is usually getting obscure when the stars 

 begin to appear, a star is, in general, less favourable for 

 the purpose than the sun : the moon, however, is often 

 on the meridian under favourable circumstances, but the 

 corrections necessary are more in number, and require to 

 be made with greater care. We shall give suitable 

 directions for each of these objects separately, detailing 

 the proper corrections to be made preparatively to 

 inferring the latitude, as briefly indicated by the general 

 rule given above. 



RULE 1. From the longitude by account, find the 

 apparent time at Greenwich ; this is called the Greenwich 

 daft. 



2. From page 1 of the Nautical Almanac get the 

 noon declination at Greenwich ; and, by means of the 

 hourly difference in declination there piven, and the 

 previously found Greenwich date, find the correction due 

 to that date ; the declination at the time of observation 

 will thus be discovered. 



3. Apply to the observed altitude the proper correc- 

 tions for dip and semi diameter ; the apparent altitude of 

 the centre will then be obtained ; and the corrections for 

 refraction and parallax will reduce the apparent to the 

 true altitude. 



4. Mark the zenith distance N. or S. according as it is 

 N. or S. of the sun : then, if the declination and zenith 

 distance have the same marks, their sum will be the 

 latitude ; if they have different inarms, their difference 

 will be the latitude. 



NOTE. The first step in the foregoing rule requires 

 the con version of degrees, minutes, itc., of longitude into 

 time, which is readily done from the known relations 



15 = lh., 15' = 1m., 15" = Is.; 



for from these it is evident that if we multiply the 

 degrees of longitude by 2, and then divide by 30, the 

 quotient will be hours, and so many thirtieths of an 

 hour ; so that twice these thirtieths will be the additional 

 minutes of time. 



In like manner, if we multiply the minutes of longi- 



6h. It 30-73" 



tude by 2, and divide by 30, the quotient will be the I 

 minutes of time, and so many thirtieths ; that is, twice ! 

 that number of seconds of time. 



Suppose, for instance, the longitude is 93 37' 41", we 

 may easily convert it into time, as 

 in the margin, thus: multiplying 3x^3 g 174.' 32* 

 the degrees, minutes, and seconds ' 

 by 2, we have 186 74' 82". ~~I ~ 



Dividing each, separately, by 3, ^ no 



cutting off the unit figure of each 

 for the suppressed in the 30, we 

 have, for the first quotient, 6 hours 

 and 6 thirtieths that is, 6h. 12m. ; 

 for the second quotient, 2 minutes 

 and 14 thirtieths that is, 2m. 28->. ; and for the third 

 quotient, 2 '73s. decimals of a second being always 

 used instead of thirds: hence the 'time corresponding to 

 93 37' 41" of longitude is 6h. 14m. 30 73s. 



Examples. 



1. On April 27, 1853, in north latitude, and in longi- 

 tude 87 42" W., the observed meridian altitude of the 

 sun's lower limb was 48 42' 30" (zenith N.), the index 

 correction was + 1' 42", and the height of the eye 18 

 feet. Required the latitude. 



1. For the apparent time at Greenwich. 

 Long, by account . . .87 42' W. 



2 



3)17,4 8,4 



6 48 

 248 



5h. 50' 48". 



The variation for this time to be added as the declina- 

 tion is increasing. 



2. For the sun's declination. 

 Dec. at app. noon (Naut. Aim.) 

 13 43' 53* N. var. in lh. 47" 7 increasing 

 + 4' 38* 6 



13 48' 31* N. in6h. . 286-2 

 in 10m. . 7D 



in 6h. 50m. 278 -3 second 



or 4' 38" 



Observed altitude of sun's L.L. . 48 42' 30' 



Index cor. + 1' 42" \ 



Dip . . 4'11 . . . . +13' 25" 

 Semi-diatn.-f- 15' 54" ) 



App. alt. of gun's centre . 

 Refraction and parallax 



True alt. of centra . . 



True zenith distance 

 Sun's reduced declination 



Latitude 



48 55' 55" 

 44" 



48 55' 11* 

 90 



41 4'49"N. 

 13 48' 31" N. 



54 53' 20" N. 



As noticed in the Introduction, page 1048, it is always 

 advisable to make all the use we can of Tables when they 

 are once in hand. The first Table referred to in the 

 foregoing operation, is that given at page 1 of the 

 Nautical A Imanac for the sun's declination at apparent 

 noon at Greenwich, with the hourly variation ; the semi- 

 diameter should bo taken out at the same time, and 

 inserted in its proper place ; but seamen, in general, use 

 invariably 16' for the sun's semi-diameter. A blank 

 form of the several particulars in such operations is of 

 considerable assistance, as the work is thereby facilitated, 

 and the risk of mistake diminished. The "correction in 

 altitude" that is, the allowance for refraction and 

 parallax should be taken from the Nautical Tables at 

 the same time as that for dip in working examples; 



