1522 
NAVIGATION. 
for the time of that pha'fe which happens neareft to the 
given day. Reduce the time of this phafe to the meridian 
of the given place by Prob. I. and take the difference be¬ 
tween the reduced time and the noon of the given day. 
Find the equation anfwering to this difference in the 
following Table; which, applied to the time of high- 
water on the day of new or full moon at the given place, 
according as the table directs, will give the approximate 
time of high-water in the afternoon. 
Now, take the interval between the reduced time of the 
phafe and the approximate time of high-water; find the 
correfponding equation, which, applied as before to the 
fyzigy-time of high-water, will give the time of the after¬ 
noon high-water. 
If the time of the morning high-water is required, in- 
creafe the laft interval by 12 hours if the given dny falls 
before the phafe, or climinifh it by 12 hours when after 
that phafe; and the equation to this time, applied to the 
fyzigy-time, gives the morning-time of high-water. 
Ex. Required the morning and afternoon times of high- 
water at Leith, 1 ith December, 1793 ? 
Neareft phafe to 1 ith Dec. is ill quarter 9 d 2o h 29' 
Longitude of Leith in time - —o o 13 
Time at Leith of ift quarter - - 9 20 16 
Given day - - - - -/noo 
Difference - - - - -13 44 
Time of H. W. at Leith-pier on fyzigy o 2 20 
Equat. from Tab. to i d 3 11 44' - -J-o 6 32 
Approximate time of high-water - ji S 52 
Reduced time of ift quarter - 9 20 16 
Interval - - - - - 1 iz 36 
Time of high-water at Leith on fyzigy 2 20 
Equat. from the Tab. to i d u 1 * 36' 7 o 
Time of high-water at Leith - - 9 ioP.M, 
Time of H. W. at Leith at full & change 2 20 
Equat. to i d i2 !l 36'—i2 h =: i d o' 1 36' 6 22 
High-water at Leith, Dec. nth, at - 8 42 A.M. 
Table of Correction to be applied to the Time of High- 
water at Full and Change of the Moon, to find the * 
Time of High-water on any other Day. 
interval , 
Alter New 
Before 
Alter 
Before New 
of 
^ or 
ift or 3d 
ift 
or 3d 
or 
Time. 
Full Moon. 
Quarter. 
Quarter. 
Full 
Moon. 
S D. H. 
H. 
M. 
H. M. 
H. JV 1 . 
H. 
M. 
O 
0 
+° 
O 
+ 5 
6 
+ 5 
6 
-O 
O 
O 
6 
O 
8 
4 
51 
5 
22 
0 
9 
O 
12 
0 
17 
4 
37 
5 
40 
0 
18 
' O 
18 
0 
26 
4 
23 
6 
O 
0 
27 
I 
O 
0 
36 
4 
9 
6 
20 
0 
37 
1 
6 
0 
45 
3 
56 
6 
39 
0 
47 
I 
12 
0 
54 
3 
44 
6 
58 
0 
57 
I 
18 
I 
2 
3 
32 
7 
18 
I 
7 
2 
O 
1 
I I 
3 
21 
7 
37 
1 
17 
2 
6 
I 
!9 
3 
I I 
7 
56 
I 
28 
2 
I 2 
I 
28 
3 
I 
8 
14 
I 
39 
2 
18 
I 
37 
2 
5 ° 
8 
31 
T 
51 
1 3 
O 
1 
46 
2 
40 
8 
47 
2 
4 
3 
6 
I 
54 
2 
30 
9 
2 
2 
16 
3 
12 
2 
3 
2 
21 
9 
17 
2 
29 
3 
18 . 
2 
12 
2 
12 
9 
31 
2 
44 
3 4 
O 
2 
21 
2 
3 
9 
44 
2 
58 
Of Measuring a Shit’s Run. 
The method commonly ufed at'feato find the diftance 
failed in a given time is by means of the log-line and half¬ 
minute glafs. It has been already obferved, that the in-, 
terval between each knot on the line ought to he 50 feet, 
in order to adapt it to a glafs that runs 30 feconds. Rut, 
although the line and glafs be at any time perfectly ad- 
jlifted to each other, yet, as the line (brinks after being 
wet, and as the weather has a confiderable effeCl upon the 
glafs, it will therefore be peceffary to examine them from 
time to time; and the diftance given by them mull be 
corrected accordingly. The diftance failed may, there¬ 
fore, be affedled by an error in the glafs, or in the line, 
or in both. The true diftance may, however, be found as 
follows: 
Proe. I. The diftance failed by the log, and the feconds 
run by the glafs, being given, to find the true diftance,, 
the line being fuppofed right. 
Rule, Multiply the diftance given by the log by 30, and 
divide the produdt by the feconds run by the glafs, the 
quotient will be the true diftance. 
Ex. 1. The hourly rate of failing by the log is nine 
knots, and the glafs is found to run out in 35 feconds. 
Required the true rate of failing? 
9 X 30-f- 35—7-7, true rate of failing. 
Ex. 2. The diftance failed by the log is 73 miles, and 
the glafs runs out in 26 feconds. Sought the true 
diftance ? 
73X30-7-26 — 84-2, the true diftance. 
Proe. II. Given the diftance failed by the log, and the 
meafured interval between two adjacent knots on the 
line ; to find the true diftance, the glafs running exaCtly 
30 feconds. 
Rule. Multiply twice the diftance failed by the mea¬ 
fured length of a knot, point off two figures to the right, 
and the remainder will be the true diftance. 
Ex. The hourly rate of failing by the log is five knots, 
and the interval between knot and knot meafures 53 feet. 
Required the true rate of failing ? 
Meafured interval = 53 
Twice hourly rate = 10 
True rate of failing = 5-30 
Of PLANE SAILING. 
Plane failing is the art of navigating a (hip upon prin¬ 
ciples deduced from the notion of the earth’s being ars 
extended plane. On this fuppofition the meridians are 
efteemed as parallel right lines. The parallels of latitude 
are at right angles to the meridians ; the lengths of the 
degrees on the meridians, equator, and parallels of lati¬ 
tude, are every-where equal; and the degrees of longitude 
are reckoned on the parallels of latitude as well as on the 
equator.—In this failing four things are principally con¬ 
cerned, namely, the courfe, diftance, difference of latitude, 
and departure. 
The courfe is the angle contained between the meri¬ 
dian and the line defcribed by the (hip, and is ufuaily 
expreffed in points of the compafs. 
The diftance is the number of miles a (hip has failed on 
a direCt .courfe in a given time. 
The difference of latitude is the portion of a meridian 
contained between the parallels of latitude failed from 
and come to; and is reckoned either north or fouth, 
according as the courfe is in the northern or fouthern 
hemifpliere. 
The departure is the diftance of the (hip from the meri¬ 
dian of the place (he left, reckoned on a parallel of lati¬ 
tude. In this failing, the departure and difference of 
longitude are efteemed equal. 
In order toilluftrate the above, let A (fig. 1.) reprefent 
the pofition of any given place, and AB the meridian 
paffing through that place ; alfo let AC reprefent the line 
defcribed by a (hip, and C the point arrived at. From 
C draw CB perpendicular to AB. Now, in the triangle 
ABC, the angle BAC reprefents the eourle, the fide AC 
