126 Journal of the Asiatic Society of Bengal. { March, 1908. 
reason of this, he must know bes i of these kardajat is 1/96 of 
the circle and equals 225 min Albiruni, in explaining 
another quotation from Pulisa, ele refers to this matter (ii., 74) : 
“ The last-mentioned two numbers are products of the multipli- 
cation of the yajanas of the sun and moon by 3438, which is the 
number of minutes in the sinus totus.” 
The historical order of the development of these tables is 
Hipparchus, Ptolemy, Paulisa, Pulisa ; and very probably Arya- 
bhata obtained his results from Pulisa. 
“The part of the following extract that I have put in italics is 
“sen untrue, otherwise the passage is pertinent to the matter in 
hand :— 
“The earliest institution of the sines in calculations for the 
chords, which were employed by the Greeks, is generally attributed 
to the Arab astronomer Albatgenius (al-Battani vs who flourished 
much confidence, because the substitution of the sines for the 
chords seems so natural and easy, that it may well have been hit 
upon independently by the Arabs : it is a matter of it 
as remarked by Delambre, that Ptolemy himself, who 
near it,should have failed of it, If A eigenms got ia site. 
tion from India he, at any rate, got no more than that. His table 
of sines, much more complete than that of the Hindus, was made 
from Ptolemy’s table of chords by simply halving them. The 
method, too, which in India remained ogra barren, led 
to valuable developments in the hands of the Arab mathemati- 
cians.” (Sarya Siddhanta, KE. Burgess, p. "900. 
e accompanying table shows the close connection between 
the chords of Ptolemy, the Pafcasiddhantika sines, and the table 
of differences given by Aryabhata 
13. The circle is produced a8 a rotation; the triangle and 
rectangle are each determined by their hypotenuse the horizontal 
by water and the vertical by the plumb-line 
This serves as an introduction to a section which deals with 
shadow problems. It is doubtful whether the Hindus used sun- 
look to the Mahammadans, In India a ernie form of clepsydra 
has generally been preferred. (See Paiichasijddhantika xiv., 31f; 
Sirya Sidahanta xii., 23 ; Indica 1., 337, 339 ; _ rate ’ Notes 
in 8. India, Thurston, 562 I) 
