O Son !

(1/2) H=28°54' and H=57°48' and multiplying this by 4 we get
231.2 minutes of time, that is, 3 hours 51 minutes, which is the
period of fadl-i dâir (hour angle) for the ’asr awwal on August
13th in Istanbul. Since the true time is 00:00 at the time of true
zawâl, it is directly the time of true ’asr awwal in true time and is
three hours and fifty-one minutes, which is equal to the time for
the rod’s shadow to lengthen by a length equal to its height after
the time of true zuhr. Shar’î time of ’asr awwal in reference to
shar’î zuhr is later than this by the amount of the Tamkin of that
location. Since equation of time is -5 minutes, it is 16:10 in
standard mean time. If the time of sunset in standard mean time,
7:12, is subtracted from this standard mean time, time for the late
afternoon prayer in Istanbul is obtained in adhânî time to be
8:58, using equation (5) a few pages earlier. When the (time
termed) fadl-i-dâir is added to the adhânî time of zuhr, i.e. the
true time of zawâl with respect to the ghurûbî time, which is five
hours and seven minutes, the result is both the true time of late
afternoon prayer in ghurûbî time and the shar’î time of ’asr-iawwal
in adhânî time. For, although the shar’î time of ’asr-iawwal
is one unit of Tamkin later than this sum, i.e., than the
ghurûbî true time, its shar’î time in adhânî time is one unit of
Tamkin earlier than that ghurûbî shar’î time. Similarly, the shar’î
times of early afternoon, evening and night prayers in adhânî
time are the same as their true times found by calculation in
ghurûbî time.
Another method applicable for determining the altitude for the
’asr-i-awwal (the early time for late afternoon prayer) is as follows:
the time when the Sun reaches maximum altitude, (i.e. its
culmination,) is determined graphically by measuring or
calculating, and using the relation
Length of shadow = cot h,
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.)
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