Hav z = hav (L~d) + cos L cos d hav h

which is derived from the well-known expression:

Cos z = sin L sin d + cos L cos d cos h

where z = zenith distance; L = the latitude; and h = the hour angle.

Solution

Dec. Arcturus 19° 42´ 29´´.
Lat. 55° 00 N. (Assumed). G. M. T. 20 d.  6 h. 20 m. 03 s.
R. A. M. ⊙︎  3 51 42
Acceleration  1 02

Lat. 55° 00´ 00´´. G. S. T. 10 12 47
Dec. 19  42  29 Long.  7 28 32
——————
L~d  35  17  31 L. S. T. 17 41 19
R. A. ⁜ 14 11 03

H. A. ⁜  3 30 16 W.
(Observer) 52 34 00
Lat. 55° 00´ 00´´ = cos. 9.75859
Dec. 19 42 29 = cos. 9.97378
H. A. ⁜ 52 34 00 = hav. 9.29244
9.02481 = nat. hav. .10588
nat. hav. 35° 17´ 31´´ .09189
z = 52° 48´ 35´´ = nat. hav. .19777
90 00 00
Computed altitude 37 11 25
Observed altitude 37 14 50
Altitude difference  =   3´ 25´´.

Fig. 11.

A ship’s position is usually obtained by plotting the lines of azimuth and the position lines much in the manner shown in the chartlet. The azimuth of the body at the moment of observation is readily taken by inspection from the azimuth tables or better still from Weir’s Azimuth Diagram, both published by the U. S. Hydrographic Office.