O Son !

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:
104° 50' + 49° + 73°
M = = 113° 25' and H = 50° 53'
2
and the time of fadl-i dâir = hour angle is 3 hours 24 minutes, which
is the interval from the time for night prayer in true time to
midnight. 10 minutes of Tamkin at the time of ’ishâ for Istanbul is
added to the difference between that time [of fadl-i dâir] and 12
hours, since the center of the Sun leaves the shar’î horizon later
and naturally its following limb leaves the horizons even later. On
August 13, the time for the night prayer is 8:46 in true solar time
and 20:55 in standard time. Subtracting the time of fadl-i dâir from
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