NAVIGATION. 
here be obferved, that, if the change of declination be 
confiderable during the elapfed time, it muft be allowed 
for by adding the difference to, or fubtra&ing it from, 
the fecond altitude, according as it is increafing or de- 
creafing. Left that an altitude, taken in the forenoon, 
cannot, by the interpofition of the clouds, have a corre- 
fponding one in the afternoon, it is advifeable to take fe- 
veral in the forenoon, in order to fecure a correfponding 
one in the afternoon. And, if feveral altitudes can be 
taken on both fides of the meridian, it will be beft to find 
the noons for each pair, and the mean of all the noons 
thus found, for the true noon. 
Ex. i. June 20, 1818, fuppofe that at 8h. 40m. in the 
forenoon, and 3I1. 16m. afternoon, by watch, the fun 
had equal altitudes, and the going of the watch be re¬ 
quired. 
Add together 
12 0 
8 40 
3 16 
2)23 56 
§ gives noon per watch 
True noon 
II 58 
32 O 
Watch flow 
O Z 
Ex. 2. March 17, 1818, fuppofe at 8h. 11m. forenoon, 
and at 3I1. 58m. 32f. afternoon, you have equal altitudes 
of the fun. Required the going of the watch. 
The diftance of the time from noon when the firft alt. 
was taken, is 3I1. 49m. and the daily decreafe of deck at 
this time is 23' 41"= 1421", which multiplied by 1590, (half 
the number correfponding to 3I1. 49m. in Moore, Tab. 
XVIII.) cut off four figures to the right hand, leaves 
Hence the index of the quadrant muft be 
fet 3' 46" forward on the arch, to correfpond with the 
morn. alt. whence the watch will be found 4' 46" too 
faff. 
Here it is fuppofed that the fhip is lying-to, or makes 
no way through the water; but, if (lie is failing to or 
from the fun, proper allowance muft be made for her run¬ 
ning during the elapfed time. 
To find the Apparent Time by the Sun's Altitude. 
Find the fliip’s latitude and longitude by account, at 
the time of obfervation, by carrying the reckoning for¬ 
ward to that time. 
With a quadrant well adjufted, take the altitude of the 
fun’s lowerlimb. 
Take the difference between the femi-diameter and dip 
of the horizon, and add it to the obferved altitude; the 
fum will be the fun’s apparent altitude. 
Take the difference between the fun’s refraction and 
parallax in altitude, and fubtraCl it from the apparent 
altitude ; the remainder will be the true altitude of the 
fun’s centre ; hence the true zenith-diftance. 
Turn the fhip’s longitude into time, and either fubtraCl 
it from, or add it to, the time per watch, accordingas it is 
eaft or weft; the fum or difference will be the reduced or 
luppofed time at the place of obfervation. 
Look in the Nautical Almanac, page 2 of the month, 
for the fun’s declination on the noon immediately preced¬ 
ing and the noon immediately following the reduced 
time, and find their difference. 
With half the reduced time take out (from Tab. XVIII. 
Moore) the number correfponding to the hours at top and 
minutes in the left-hand column, with which multiply 
the diff. of deck cut oft' four figures from the right-hand 
of the produCt, the remainder is the correction to be added 
or fubtraCted according as the deck is increafing or de- 
creafing, the refult is the deck or reduced time at the 
fhip > with this deck find the polar diftance-, then add 
together the zen. dift, co-lat. and polar dift. into one 
fum. 
Vol. XVI. No. 1141. 
G29 
From half this fum fubtraCt the zenith-diftance, noting 
the half-fum and remainder; then add together 
The log. co-fecantof the comp, of thelat. 7 Rejecting 
The log. co-fecantof the polar diftance, J their indices. 
The log. fine of the half-fum, and 
The log. fine of the difference, into one fum. 
Find the log. fine of half the fum of the four logarithms, 
which being doubled, and brought into time, as before, 
will give the time from the midnight before the altitude 
was taken. 
Ex. Suppofe on the 7th May, .1818, at 5I1. 30m. 32k 
P. M. per watch, in lat. 39 0 54' N. and Ion. 35 0 30' W. of 
Greenwich, by account, the altitude of the fun’s lower 
limb lhould be found to be i5°45', the eye being 18 
feet above the furface of the fea, and the true apparent 
time when the obfervation was made were required ? 
Obf. alt. fun 
’s 1 . 1 . 
15 
°4c' o ' 1 
'Lat. 
39 ° 54 ' 0" 
Sem.i5'jz" 
Dip 4 4 
| Dif. 
+ 0 
II 
48 
— • 
90 O Q 
Co. lat. 
50 6 0 
Ap. alt. fun 
’s 1. 1. 
>5 
48 
Reft. 4' 17" 
( 
Sun’s deck May 7th 
16 46 53N 
Par. 0 8 
3 
9 
Ditto - 8th 
17 3 22N 
Sun’s true alt. 
G 
53 
39 
Diff. in 24 hours 
0 16 28 
90 
O 
0 
Zenith dift. 
74 
6 
21 
J6' 26"x 3281 gives 324 : 
— 0 5 24 
—. 
Sun’s deck 7th May 
16 46 54 
H. 
M. 
s. 
Time at fhip 
C 
30 
2 Z 
True dec. for Ion. and time 16 52 18 
Lon. W. in 
time 
+ 2 
22 
O 
O 
O 
O 
O 
Reduced time 
7 
5 '~ 
32 
Polar dift. 
73 7 4 2 
Co. lat. 
Polar dift. 
• 
5 ° 
73 
6 
7 
O 
42 
Co. fee. 9 - . r , - 
Co. fee. 1 - lefs rad ’ - 
0*II5H 
0 01911 
Zen. dift. 
74 
6 
21 
Sum 
*) 
197 
20 
3 
i Sum 
• 
98 
40 
I 
Log. fine 
9 ' 995 01 
Zen. dift. 
- 
74 
6 
21 
Remainder 
24 
33 
40 
Log. fine ... 
9-61874 
Sum 4 log. 
2 )»9 74797 
4 i 
34 
10 
z 
log. co. fi. \ Horary angle 
; 9-87398 
H. M. S a 
Hour-angle 
*3 
8 
20 
in time • 
5 32 33 
Time at fhip per watch 
5 3 ° 32 
Watch flow - o 2 r 
Of finding the Longitude by the Moon's Difiance from the 
Sun or a fixed Star, commonly called the Lunar Ob¬ 
servations. 
A variety of methods for difcovering the longitude 
have at different times been brought forward, the moft 
celebrated and practicable of which is that by means of 
meafuring the angular diftance of the moon from the fun 
ora fixed liar. This method was originally propofed by 
John Werner; but, owing to the imperfection of inftru- 
ments for meafuring the angular diftance, and the inluf- 
ficient knowledge of the moon’s true place, it could not, 
in his time, be brought to the degree of accuracy to which 
it is at prefent arrived. 
Finding the difference of longitude between any two 
places may be reduced to the problem of finding the dif¬ 
ference of time between two places. For, as it is evident 
that the fun pafies over a whole circle of the earth, or 360°, 
in 24 hours, it follows that the difference of the time be¬ 
tween the noon of one place and another will always be 
the fame proportional part of 24 hours as the difference 
of their longitude is of 360°: and the difference betioeen 
7 X any 
