. Add together the log haversine of the S.H.A. (Table 45), the log
cosine of the Lat. (Table 44), and the log cosine of the Dec. (Table 44)
and call the sum S. S is a log haversine and must always be less than
10. If greater than 10, subtract 10 or 20 to bring it less than 10.

III. With the log haversine S enter table 45 in the adjacent parallel
column, take out the corresponding Natural Haversine, which mark N_{S}.

IV. Find the algebraic difference of the Latitude and Declination, and
from Table 45 take out the Natural Haversine of this algebraic
difference angle. Mark it N_{D+-L}

V. Add the N_{S} to the N_{D+-L}, and the result will be the Natural
Haversine of the calculated zenith distance. Formula N_{ZD} = N_{S} +
N_{D+-L}

VI. Subtract this calculated zenith distance from 90 deg. to get the
calculated altitude.

VII. Find the difference between the calculated altitude and the true
altitude and call it the altitude difference.

VIII. In your Azimuth Table, find the azimuth for the proper "t," L and
D.

IX. Lay off the altitude difference along the azimuth either away from
or toward the body observed, according as to whether the true altitude,
observed by sextant, is less or greater than the calculated altitude.

[Illustration]

X. Through the point thus reached, draw a line at right angles to the
azimuth. This line will be your Line of Position, and the point thus
reached, which may be read from the chart or obtained by use of Table 2
from the D. R. Position, is the nearest to the actual position of the
observer which you can obtain by the use of any method from one sight
only.

Example:

At sea, May 18th, 1919, A.M. (_) 29 deg. 41' 00". D.R. Latitude 41 deg. 30' N,
Longitude 33 deg. 38' 45" W. WT 7h 20m 45s A.M. C-W 2h 17m 06s CC + 4m 59s.
IE--30". HE 23 ft. Required Line of Position and most probable position
of ship.

WT 18d -- 7h -- 20m -- 45s A.M.
-- 12
------------------------
WT 17d -- 19h -- 20m -- 45s
C-W 2 -- 17 -- 06 Corr. + 9' 34"
------------------------ IE -- 30
CT 17d -- 21h -- 37m -- 51s ------------
CC + 4 -- 59 + 9' 04"
------------------------
G.M.T. 17d -- 21h -- 42m -- 50s (_) 29 deg. 41' 00"
Eq. T. + 3 -- 47 + 9 04