Seadet-i Ebediyye - Endless Bliss Fourth Fascicle

the length of the shadow of a 1 m long (vertical) rod (erected on a
level ground) is measured; the maximum altitude and the length of
the shadow are recorded daily. Hence, a table of “altitude” versus
“shadow length” is obtained. Since the maximum altitude of the
Sun is 64° on August 13, the minimum length of shadow is 0.49 m
as can be read off from the table. The length of the shadow is 1.49
m and the altitude is 34°. A table of altitude versus length of
shadow exists in the appendix of the book Taqwîm-i sâl printed in
1924. (Please see Appendix VI.)
The ’asr thânî time of early afternoon prayer (, i.e. the later
time for late afternoon prayer,) can be found by utilizing the same
formula, yet in this case:
tan Z 2 = 2 + fay-i zawâl = SAT
where Z 2 is the angle complementary to the Sun’s altitude for ’asr
thânî = azimuthal distance, and SAT is the [length of the
gnomon’s] shadow at ’asr thânî.
Z 2 = 68° 8'. Hence.
M = 96°09' and
H= 73° 43'.
The time of fadl-i dâir is 4 hours 55 minutes. When the Tamkin
is added to this, the ’asr thânî comes out to be 5:05 for Istanbul in
true solar time.
To determine the time of the ’asr-i-awwal for late afternoon
prayer, first the angle Z, complementary to altitude h, and then
fadl-i dâir are calculated using the formula:
Z 1 = complementary to the Sun’s altitude (bud’-i semt =
azimuthal distance) = arc tan (1 + tan Δ),
and for the ’asr-i-thânî:
Z 2 = arc tan (2 + tan Δ),
where tan Δ is fay-i zawâl. The angle whose tangent is equal to the
sum of tan Δ and 1 or 2 is the value of Z 1 and Z 2 , respectively,
(complementary to the altitude) for late afternoon prayer.
At the ’ishâ awwal of night prayer, the center of the Sun is 17°
below the true horizon; in other words, its true altitude is -17°.
Since the declination plus 90° is taken into account instead of the
angle complementary to the declination:
and the time of fadl-i dâir = hour angle is 3 hours 24 minutes,
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