229 
1893.] Pandit Bapu Deva S'astri — A brief account of BJiaslcara. 
: the sine of the assumed latitude in the plane of the 
vertical 
: : the sine of the sun’s declination in the plane of the 
meridian 
: the sine of the assumed declination in the plane of 
the vertical. 
This is the sine of the arc of the vertical circle intercepted between the 
equinoctial and the sun’s place. 
Add this arc to the assumed latitude, or to the arc of the vertical 
circle from the zenith to the equinoctial when the declination is south ; 
hut when it is north substract the arc, the result will be the zenith 
distance of the sun. Hence the rule. 
Then he says that if the complement of the sun’s azimuth be less 
than his amplitude, when he is in the northern hemisphere, the vertical 
circle will cut the diurnal circle in two points above the horizon. 
Hence on the same day the snn will enter the same vertical circle at 
two different times, and therefore the sun’s zenith distance will admit 
of two different values. Bhaskara determined these two values thus : — 
Subtract the assumed latitude above found from 180°. The re- 
mainder will be the second value of the assumed latitude. Then from 
these two values of the assumed latitude find the two different values of 
the zenith distance. The reason is very plain. 
7. The ancient astronomers, Lalla, S'ripati, &c., erroneously used 
the versed sine and radius in finding the valana or variation (of the 
ecliptic). Bhaskara himself refuted their rules variously, and used 
the right sine and the cosine of declination in the place of the versed 
sine and the radius respectively (see the last portion following the 
29th vei’se of the 8th chapter of the Goladhydya). 
8. It is stated in the Suryasiddhdnta and other ancient astro- 
nomical works, that the end of the gnomonical shadow revolves in the 
circumference of a circle, which Bhaskara boldly refuted. 
Besides the above Bhaskara discovered many other matters which 
are not so important as to deserve mention here. He wrote an annota- 
tion called Vdsandbhdsliya on his work himself, the style of which is 
very good and plain. Before he wrote this commentary, he composed 
two other works, — one a Karana * and the other called Sarvatobhadra- 
yantra, to find the hour of the day. Both of these works are now extant. 
He wrote another Karana in the 69th year of his age, which is now very 
common. It appears, therefore, that Bhaskara lived to the age of more 
than 69 years. After him, no great astronomer has appeared among 
the Hindus up to the present time. 
* A treatise on astronomical calculation, whero the epoch is taken from the 
commencement of the work. 
