226 Pandit Bapu Deva S'astri — A brief account of Bhdskara. [No. 3, 
Chapter XII. The seasons. 
Chapter XIII. Useful questions, — a collection of problems. Ed.]. 
In this work Bhaskara has variously exposed the errors of Lalla, 
whose work he had formerly annotated. 
We now proceed to mention the discoveries of Bhaskara. 
1. He discovered that the earth has the inherent property of 
attracting all things around it,* and 
2. r I hat portion of the equation of time which is due to the 
inclination of the ecliptic to the equinoctial. "f 
3. He found out the tatkalika, or instantaneous motion of the 
variable quantities — the planet’s longitude, and the sine of the arc. 
Bhaskara says “ the difference between the longitudes of a planet 
found at any time on a certain day, and at the same time on the follow- 
ing day, is called its rough motion during that interval of time ; and 
its tatkalika motion is its exact motion.” 
The tatkalika , or instantaneous motion of a planet, is the motion 
which it would have in a day, had its velocity at any given instant of 
time remained uniform. This is clear from the meaning of the term 
tatkalika, and it is plain enough to those who are acquainted with the 
principles of the differential calculus, that this tatkalika motion can be 
no other than the differential of the longitude of a planet. This tatkalika 
motion is determined by Bhaskara in the following manner.^ 
* ***#*#*# 
Now, the term tdtkalika applied by Bhaskara to the velocity of 
a planet, and his method of determining it, correspond exactly to the 
differential of the longitude of a planet and the way for finding it. 
Hence it is plain that Bhaskara was fully acquainted with the prin- 
ciple of the differential calculus. § The subject, however, was only inci- 
* ISiddhanta-S'iromatni. Chap. Ill, 6. — Ed.] 
t [ Siddhanta-S' iromaifi . Chap. V, 16, 17. Ed.] 
I [The calculations given by the author are omitted, as they have already 
been published in J. A. S., B., Yol. XXVII, pp. 21 3 and ff.-Ed.] 
§ [See, however, two papers by Spottiswoode in the Journal of the Royal 
Asiatic Society, Vol. XVII, p. 222 and Vol. XX, p. 345. Mr. Spottiswoode con- 
sidered that the pandit had overstated his case. He added ‘ Bhaskara undoubtedly 
conceived the idea of comparing the successive positions of a planet in its path, and 
of regarding its motion as constant during the interval, and ho may be said to have 
had some rudimentary notion of representing the arc of a curve by means of auxi- 
liary straight lines. But on the other hand, in the method here given, he makes no 
allusion to one of the most essential features of the Differential Calculus, viz., the 
infinitesimal magnitude of the intervals of time and space therein employed. Nor 
indeed is anything specifically said about the fact that the method is an approxima- 
tive one. 
‘ Nevertheless, with those reservations, it must be admitted, that the penetration 
