NAVIGATION. 
021 
Rule. As the fine compl. of the lat. or fee. lefs radius 
Is to radius. 
So is the fine of the fun’s or liar’s declination 
To the fine of the true amplitude ; 
which is always of the fame name with the declination, 
whether north or fouth. 
Ex. Suppofe the fun’s declination to be io°43'S. in 
lat. 51° 32' N. I demand the true amplitude. 
As fine com. Iat. 51° 32' - 979383 
Is to radius - io’ooooo 
So is fi. fun’s dec. io° 43'S. - 9-26940 
To fine of true amp. 17° 24' - 9-47557 
Or thus: 
Lat. 51 0 32'N. fecant - - 0-20617 
Deck io° 40' S. log. fine - - 9-26940 
True amplitude, 17 0 24'S.= - 9‘47557 
To find the true Azimuth. 
The true azimuth is an arch of the horizon contained 
between the meridian of the place and the azimuth-circle 
palling through the centre of the fun or ftar at the 
time of obfervation ; or it is the true diftance of the fun 
or ftar from the true north or fouth points of the com- 
pafs. 
The magnetic azimuth is an arch of the horizon con¬ 
tained between the magnetic meridian and the azimuth- 
circle palling through the centre of the fun or ftar when 
obferved ; or it is the apparent diftance of the fun or ftar 
from the north or fouth points of the compafs, either in 
the forenoon or in the afternoon, when they are 5 0 , 
io°, 15 0 , &c. above the horizon ; and, the lefs the altitude 
is, the more exa£t you may perform the obfervation. The 
magnetic azimuth is found by the compafs in the fol¬ 
lowing manner: Place the compafs in a convenient part 
of the Ihip; then move it fo that the fights may be di- 
re£led to the fun’s centre; and the lhadow of the fixing 
■will fall dire£lly on the line marked on the plane which 
joins the fights; then the degree, &c. in the arch inter¬ 
cepted between the end of the index and north point of 
the card, will give the magnetic azimuth required. If 
the fun does not lliine enough to give a ftrong lhadow, 
look through one of the fights, and move the compafs 
till one of the firings cuts the fun’s centre; and then the 
intercepted arch, as before, Ihows the fun’s azimuth, and 
the like of the Itar’s. When there is a rough fea, the 
obfervation is heft made by two perfons ; and, if the card 
vibrates much, take the middle degree between the limits 
which the vibration reaches. When the azimuth is ob¬ 
ferved, the altitude of the object muft be obferved at the 
fame time. 
Having the latitude of the place of obfervation, and 
the fun or liar’s declination with the true altitude at the 
time of obfervation, the true azimuth is found as follows : 
Rule. From the half fum of the complement of the 
latitude, the complement of the altitude, and the fun or 
liar’s polar diftance, fubtraft the polar diftance, noting 
the half fum and the remainder. Then add together 
The log. fine of the Lat. co ar = co fee. lefs rad. or 
complement of the Alt. co ar — co fee. indexes. 
The log. fine of the half fum, 
And the log. fine of the remainder, into one fum. 
Half the fum of thefe four logarithms will give the log. 
co-fine of half the true azimuth, which, being doubled, 
gives the true azimuth, reckoned from the north in north 
latitude, and from the fouth in fouth latitude. 
The polar diftance of the Jun or ftar is their diftance 
from the nearcil, or elevated, pole; and, if the latitude of 
the place and the declination of the fun or ftar be both 
Eorth or both fouth, then the complement of the decli¬ 
nation is the polar diftance ; but, if the latitude and de- 
Vo-L.XVJ. No. 1140. 
clination be one north and the other fouth, the declina¬ 
tion added to 90 0 gives the polar diftance. 
Ex. In latitude 51° 32' N. the fun’s altitude was ob¬ 
ferved to be 39 0 28', his declination being then 16 0 37' N. 
Required the true azimuth. 
90 0 00' 90 0 oo , 90 0 oo’ 
Lat. 51 32 Alt. 39 28 Dec. 16 37 
Com. Alt. 50 32 Pol.dill. 73 23 
Co. lat. 38 
28 
Sine co ar 
— J Co-fecant 
{ 0-20617 
Co. alt. 50 
32 
Sine co ar 
=2 |_lefs rat i* 
J 011239 
Pol. dill. 73 
23 
Sum 162 
23 
| Sum 81 
I I 
Sine 
9-99484 
Pol. dill. 73 
23 
Rem. 7 
48 
Sine 
9-13263 
2 
>19-44603 
Log. co-fi. of \ the azimuth 
= 58 °6 
2 
9*72301 
True azimuth 
_ 
116 12 from the north. 
Of the TIDES. 
The theory of the tides will be farther illuftrated 
under that article. In this place, therefore, we fiiall 
only explain the method of calculating the time of high- 
water at a given place. 
As the tides depend upon the joint a£lion of the fun 
and moon, and therefore upon the diftance of thefe ob¬ 
jects from the earth and from each other; and as, in the 
method generally employed to find the time of high 
water, whether by the mean time of new moon, or by 
the epadls, or tables deduced therefrom, the moon is 
fuppoled to be the foie agent, and to have an uniform 
motion in the periphery of a circle, whole centre is that 
of the earth ; it is hence obvious that method cannot be 
accurate, and by obfervation the error is fometimes found 
to exceed two hours. That method is therefore rejedled, 
and another given, in which the error will feldom exceed 
a few minutes, unlefs the tides are greatly influenced by 
the winds. 
Prob. I. To reduce the times of the moon’s phafes, 
as given in the Nautical Almanac, to the meridian of a 
known place. 
Rule. To the time of the propofed phafe, as given in 
the Nautical Almanac, apply the longitude of the place 
in time, by addition or fubtradlion, according as it is eaft 
or weft, and it will give the time of the phafe at the given 
place. 
Ex. 1. Required the time of new moon at Saloniki in 
May 1793 ? 
Time of new rqoon per Naut. Aim. - 9 d 15^ 31' 
Longitude of Saloniki in time - o 1 33 E. 
Time of new moon required, in May 917 4 
Ex. 2. What is the time of the Iaft quarter of the moon 
at Refolution Bay in Odtober 1793 ? 
Time of laft quarter per Naut. Aim. z6 d 5 11 47' 
Longitude in time - - -09 17W. 
Time at Refolution Bay - - 25 20 30, or 
26th day at 8 Jl 30' A.M. 
Prob. II. To find the time of high-water at a known 
place. 
Rule. In the Nautical Almanac feek in the given 
month, or in that immediately preceding or following it, 
7 T for 
1 
