CHAPTER XL.                              367

calculation by 6° 50', and that this difference will in¬
crease in future by one minute every year.

These are the words of a man who either was him¬
self a most careful practical observer, or who examined
the observations of former astronomers which he had
at his disposal, and thereby found out the amount of
the annual difference. No doubt, also, other people
have perceived the same or a similar difference by
means of the calculation of the noon-shadows. There¬
fore (as this observation was already much known)
Utpala of Kashmir has taken this theory from Punjala.

This conjecture of mine is confirmed by the fact that
the Hindus prefix the samdhis of the solstices to each
of the six seasons of the year, in consequence of which
they begin already with the twenty-third degree of the
next preceding signs.

The Hindus assume a sarhdhi, too, between the dif¬
ferent yitgas and between the manvantaras ; but as the
bases of this theory are hypothetical, so everything else
derived from them is hypothetical. We shall give a
sufficient explanation of these things in the proper
place.