(534 
NAVIGATION. 
The moon’s declination is fet down in page the 6th of 
the month for every noon and midnight in the Nautical 
Almanac. 
Therefore find the declination for the nearell noon and 
midnight, both before and after the reduced time, and 
take the difference. Then, from Moore, Tab. XVIII. 
take out the number corresponding to the hours at top, 
and the minutes in the left-hand column, with the time 
at Greenwich, with which multiply the difference ; from 
the produft cut off" four figures from the right hand; the 
remainderis a correction to be added to the declination if 
increafing, but fubtrafted if decreafing ; the refult will be 
the declination at the given time. 
Ex. i. Suppofe, on Oft. 16, 1813, in longitude 45 °weft, 
the altitude of the moon’s lower limb, when on the meri¬ 
dian, fouth of the obferver, Ihould be 6o° 4.3' o", the eye 
being 23 feet above the lea. Required the latitude. 
The longitude 45 0 weft turned into time equal to 3 
hours, and the correction 7m. added to i8h. 7m. the time 
the moon pafies over the meridian on the given day, gives 
iSh. 54m. time at Greenwich. 
Hor. par. 58'17" P. 1 ,. 10-4897 Moon’sobf. alt. 6o°43' o" 
App. alt. Co 0 54 L.co-fi. 9-6869 M.fem.di. 15 51 } + 11 15 
-Dip - 4 36 )- 
Par. in alt. ~ 28 21 P. L. -8028 60 54 15 
Refradlion 32 
27 49 Cor. of the Moon’s alt. -f 27 49 
Moon’s dec. midnight i9°49' N. True alt. - 61 22 4 
Do. at noon - 18 55 N. 90 
Diff. in 12 hours 54 I9°49' Zen. dill. 28 37 56 
Then 54 X by *5750 gives - — 31 
Moon’s dec. at reduced time 19 18 19 18 oN 
Latitude 47 55 56 
Ex. 2. Suppofe, on Dec. 6, 1813, in longitude 6o° eajl, 
the altitude of the moon’s upper limb fhould be obferved, 
when on the meridian, being then fouth, 54 0 30', the eye 
20 feet above the fea. Required the latitude. 
The longitude 6o° eafl in time equal to 4 hours, lefs the 
correftion 10m. fubtrafted from nh. 10m. the time the 
moon pafies over the meridian on the given day, leaves 
till. om. time at Greenwich. 
Hor.par. 61' 21" P. L. 10-4675 Moon’s obf. alt. 
App.alt.54 0 18 o co-fi. 9-7661 M.fem.di. 16'44' 
—--- Dip - 4 17 
Par. in alt. 35 48 P. L. *7014 
Refradlion 41 
35 7 Moon’s correction to be added 
Moon’s dec. at noon I4°22'N. 54 52 4.0 • 
Do. at midnight - 16 18 N. 90 
1 56 14 22 Zen.dift. 35 7 20S. 
1 56—116X by-9167 gives 106—+ 146 16 8 oN. 
Moon’s dec. at reduced time 16 8 Lat. 51 15 20 
Prob. Given the apparent time of the tranfit of the 
moon’s limb over the meridian, to find the longitude of 
the place of obfervation. 
Rule. Reduce the apparent femidiameter of the moon 
to time, by Mackay’s Tables XXXIX. and XL. which 
being applied to the apparent time of tranfit of the moon’s 
limb, by addition or fubtraftion, according as the weftern 
or eaftern limb was obferved ; the fum or difference will 
be the apparent time of the tranfit of the moon’s centre. 
From the right afeenfion of the moon in time fubtraft 
that of the fun ; the remainder will be the approximate 
time of the moon’s paflage over the meridian of Green¬ 
wich. Now, to the log. of the difference between the 
change of the moon’s right afeenfion in 12 hours, and 
that of the fun’s in the fame time, reduced to feconds, 
add the ar-co. log. of the difference between the above 
quantity and 43200", and the log. of the approximate 
time in feconds; the natural number anfwering to the 
fum of thele three logs, will be the correction in feconds 
of the approximate time ; which, being added thereto, 
will give the apparent time of the moon’s paflage over 
the meridian of Greenwich. 
From the p. log. of the difference between the apparent 
times of tranfit at Greenwich and at the place of obferva¬ 
tion, fubtraft the p. log. of the difference between the 
variations of the right afeenfions of the fun and moon in 
12 hours; the remainder will be the p. log. of the lon¬ 
gitude of the place of obfervation in minutes and feconds, 
which are to be efteemed degrees and minutes. If the 
time of tranfit at the place of obfervation is earlier than 
that at Greenwich, the longitude is eaft, otherwife it is weft. 
Ex. July 2, 1792, the apparent time of the tranfit of the 
moon’s weftern limb was ioh. 43' 58". Sought the longi¬ 
tude of the place of obfervation. 
54 ° 3 °' o"' 
|— 12 27 
54 17 33 ; 
D’s R. A. at 
noon, 
0 ’s R. A. at 
noon, 
} 
i6>> 58' 20" 
6 4.8 3o - 4 
Approx, time 10 9 49-6 
S’sR.A. at| 6 o g , „ 
noon, J -> 
])’s R. A. atl 
midnight, / 
17 30 
Vr. J) ’s R. A. in 12 11 31 40 
Vr. 0 ’sR. A. in 12 h 2 3-7 
Ap. time of tran. J 
J) ’s weftern limb,J 
1 o 1 * 43' 58" 
5 ’s equal femidia. + 1 9-7 
Incr. femidia. 3-36 
Ap. t. of tr. ])’s cen. 10 45 11*3 
Difference - - - - - 29 36-5 =2 inti'-T, - log. - 3-249516 
Conllant quantity ------ 43200 
Difference -------- 41423-7 ar-co-log. 5 - 38275i 
Approximate time of tranfit - io h 9' 49"-6=36589-6 - log. - 4 - 563358 
Correction - - - - - -J- 26 9-0 - 1569-0 - - - 3-195625 
Appar. time of tranfit at Greenwich. 10 
Appar. time of tranfit at place of obferv. 10 
35 
45 
58-6 
ir 3 
Difference - 
Difference of varia. R. A. © and J) in i2 h 
9 
29 
12*7 
3 < 5’3 
t 1 
I '2909 
O7839 
Longitude ----- 
56 ° 
o' 
P.L. 
0.5070 
Which is weft, becaufe the time of tranfit by obfervation is later than the time at Greenwich. 
For any thing further on the theory and praftice of navigation, and for various ufeful tables, we recommend 
the reader to confult Moore’s Praftical Navigator, and Mackay’s Treatifes on Navigation and on the Longitude. 
1 Navigation 
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