V 
(4) Z = ^ A + AtlA when P A is greater than P Z. 
2 2 
= _. + A — ?— lA when P A. is less than P Z 
2 2 
which is in accordance with the rule given by Lieutenant Raper, R.N., in his 
“Practice of Navigation,” Art. 675, viz., 
(1) Take half the sum of the polar distance and co-latitude, and half the 
difference. 
(2) Add together the log. cot. of half the hour angle, the log. sec. of the 
half sum, and log. cos. of the half difference ; the sum (rejecting tens) 
is the log. tan. of half the sum of the azimuth and another angle A. 
When the half sum of the polar distance and co-latitude exceeds 90°, 
take the supplement of the i-esulting arc for the half sum required. 
(3) To the log. cot. already employed add the log. cosec. of the half sum, 
and the log. sin. of the half difference ; the sum (rejecting tens) is 
the log. tan. of half the difference of the same two angles. 
(4) The sum of the resulting half sum and half difference is the greater of 
the said two angles ; the difference is the lesser. 
When the polar distance exceeds the co-latitude, the greater of the two 
angles is the azimuth required ; when the polar distance is less than the 
co-latitude, the lesser of the angles is the azimuth required. 
Example. —October 11, 1894, at 8h. 36m. a.m. apparent time, or 3h. 24m. 
from noon, in lat. 49° 0' N., long. 10° 0' W., the Sun’s declination then being 
about 7° South, and consequently the north polar dist. 97° ; required the Sun’s 
true bearing or azimuth. 
Time from noon, 
h. 
m. 
or hour angle 
3 
24 
Half. 
- 1 42 
cot 
10-321504 
cot 
10-321504 
Pol. dist. 
o 
- 97 
6 
Co.-lat. 
- 41 
0 
Sum 
- 138 
0 
Diff. 
- 56 
0 
Half sum 
- 69 
0 
sec 
10-445671 
cosec 
10-029848 
Half diff. 
- 28 
0 
cos 
9-945935 
sin 
9-671609 
79 
3 
tan 
10-713110 
46° 31' tan 
10-022961 
46 31 
Azimuth N. 125 34 E.