S66 
HOROLOGY. 
equal altitudes be obferved in the morning and afternoon, 
and from thence find the correfted time of noon, as di¬ 
rected under the article Astronomy, vol. ii. p.455; allb, 
let the fun’s azimuth be obferved, by which, the variation 
of the compafs being applied, the true azimuth at the 
time of obfervation will be obtained. 
Now, to the conflant logarithm 9-2219 add the propor¬ 
tional log. of the interval of time between the equal alti¬ 
tudes, the hours and minutes being confidered as minutes 
and feconds ; the prop. log. of the hourly rate of failings 
the log. co-fine of the fliip’s latitude, the log. fecant of 
• the courfe, and the log. tangent of the fun’s azimuth; 
the fum, rejefting tens in the index, will be the prop. log. 
of the correction anfweringto the change of latitude ; and 
to the fum of the firft four logs, add the log. co-fecant of 
the courfe; the fum, rejefting tens in the index, will be 
the prop. log. of the change of longitude. The firft cor- 
reftion is to be added to, or fubtrafted from, the time of 
noon before found, accordingly as the fliip’s latitude is 
increafing or diminif^ing; and the fecond correftion is 
additive or fuhtradtive, accordingly, as the fliip’s courfe 
has been in the eaftern or weftern hemifphere. Therefult 
thus deduced will be the time per watch of apparent noon, 
under the meridian of the firft place of obfervation. 
If the two laft corredtions be applied with a contrary 
fign, the time of apparent noon, under the meridian of 
the fecond place of obfervation, will be obtained. The 
firft correftion vanifhes, if the courfe made good between 
the obfervations is either due eaft or weft ; and the fecond, 
if the fhip fails on a meridian. 
Example. Auguft 7th, 1804, equal altitudes of the fun’s 
lower limb were obferved, whereof the means w'ere 9 h 14™ 
52 s A.M. and 2 h 48“ 18 s P.M. refpeftively, the correfted 
azimuth of the fun from the l’outh was 69I 0 , the fhip’s 
courfe during the elapfed time S.W. by W. at the rate of 
8-6 knots per hour, and the fhip’s latitude and longitude 
at noon were 39 0 18' N. and 31 0 24' W. refpeftively. Re¬ 
quired the error of the w-atch for apparent noon, under 
the meridian of the place where the firft fet of obfervations 
was made? 
Conftant logarithm 9-2219 
Int.oftime=z s n 33 m 1 
or 5 m 33s p. log. J ~ 1 5110 
Hourly rate of fail-d 
ing 8 r ’ 6 m or 8 m >= 3-3208 
36s p. log. J 
Latitude 39 °.18 ; ,co-T 9 . 8g85 
fine 
1-9423 
Gourfe 3 points-, fe- ? „ r 
cant - 5 0-0801 co-fecant 
Azimuth 69° 45', 
tangent 
Pirft corredtion 
o m 38 s p. log. 3 ^ +555 
Mean of the morning fet 
-afternoon fet 
Tncorrect time of noon 
Equation of equal altitudes 
Equation of latitude 
Equation of longitude 
Time per watch of apparent noon") 
1-9423 
o -2553 
| 0-4331 fee. cor. i ra 9 s P.L. 2-1976 
]z A 
9& i4 m 52 s 
obfervation 
Watch flow- for apparent time 
Equation of time 
Watch flow for mean time 
2 
48 
18 
12, 
+ 
I 
OC» <_Kl 
00 -vj {jrt 
— 
I 
9 
I I 
59 
55 
5 
• 5 
23- 
5 
28 
The problem may otherwife be performed, by eftimating 
how many minutes the fun is higher or lower, in confe- 
quence of the change of latitude in the elapfed time, at the 
inftant it will attain the correfponding altitude in the af¬ 
ternoon, and letting the index of the quadrant accordingly. 
This quantity may be found with fufiicient accuracy from 
a traverfe-table. 
2. To find the Longitude at Sea by a Time-keeper .—Obferve 
the altitude of the fun’s limb, either in the morning or 
evening, w’hen it is at leaf?: three points of the compafs 
from the meridian, and note the time when it was ob¬ 
ferved by the time-keeper. Multiply the daily rate of 
the watch by the number of days which have elapfed fince 
that on which the laft obfervation was made for finding 
it, and add the produdt to the time fhown by the watch 
w’hen the fun’s altitude was obferved, if the -watch be 
lofing, but fubtraft it from that time if the watch be 
gaining. To the fum, or remainder, add what the watch 
was too (low, or fubtraft from it what the watch was too 
fall, for mean time at the place where its rate was found, 
on the day when the laft obfervation was made for finding 
it, and the refult will be the mean time at the place when 
the fun’s altitude was obferved. To this time add the 
longitude of the place in time, where the rate of the watch 
was found, if it be weft ; or fubtraft the longitude in time 
from it, if it be eaft, and the fum or remainder will be 
the mean time at Greenwich. To this time find the fun’s 
declination, (Astronomy, vol. ii. p. 431,) and correft 
the obferved altitude of the fun’s limb for the dip of the 
horizon, refraftion,parallax,and femi-diameter, with which, 
the latitude of the fhip, and the fun’s- declination, find the 
mean time at the flrip. Then take the difference between 
the mean time at the fhip and the mean time at Green¬ 
wich; and it will be the longitude of the fliip in time; 
eaft if the time at the fliip be greater than the time at 
Greenwich, but w'eft if it be lefs. ' 
Example. After having found the rate of a chrono¬ 
meter to be gaining i s " 67, and that it was too fall for 
mean time at Barbadoes, on the 31ft of December, 1793, 
by 4,11 ,m 49 s -7, let us fuppofe that on the 4th of February, 
1794, in the afternoon, latitude 44 0 26' N. the following 
obfervations were taken: What was the longitude of the 
fliip; the height of the oblerver’s eye above the lurface 
of the fea being ai fe.et ? 
Chr. too fall, Dec. 31, 1793, 4 h i m 49 a -7 
Gain to Feb. 4, 1794, = ? , - 
i s -67 X 35 d - - J * 5 3 
Time-keep, too faft, Feb. 4, 4 2 48 ■% 
Times by 
the Watch. 
Alt. of the 
Q’sL. L. 
5 n 2 m 5 i s 
3 44 
4 4 ° 
,5 49 
9 °i 7' 15" 
9 8 45 
8 59 3 ° 
8 50 00 
4)17 4 
36 15 30 
5416 
4 2 48 
9 3 5 - 
+ 6 i 5 
1 128 
3 5 8 45 
910 7 
5013 
Sun’s femi-diameter - 
Sun’s horizontal parallax - 
Dip of the horizon 4' 22" ? 
Refraction - 
5 4 8 
Correftion of the fun’s alt. 
True altitude. 
Longitude of Barbadoes W. 
16' 16" 
' 9 
16 25 
6 15 
Mean time at Greenwich 
Sun’s declination for noon at Greenwich 
Correftion for Time at Greenwich - - 
Sun’s correft declination — 
Ship’s latitude 44 26 N. fecant 
Co-latitude 
90 0 
'00' 
44 
26 
45 
34 
l6 
OO 
29 
9 : 
16° 3' 2 4 "S* 
— 3 31 
J 5 59 53 S. 
10-14626 
30-01715 
menu. aniLuue 29 34 4 VS 44 f 334! 3 log. 4-52393,. 
Sun s obf. alt. 9 10 N.S. 1 5931 3 a ^ j 
Apparent time at the fhip 
Equation of time add 
Mean time at the fhip 
Mean time at Greenwich. 
Longitude in time 
jh-jgm 29s Log. rifing 4-68734 
14 
26 
4 
10 
55 
S 
0 
13 
O 
49 
iS 
=ri2°i9'iW; 
Ill 
