CHAPTER XXXI.                             313

dian. Hereby people are frequently misled to think
that the 4800 yojanas are the corrected circumference
for the city of Ujain, If we calculate it (according to
Brahmagupta's correction), we find the latitude of Ujain
to be i6\ degrees, whilst in reality it is 24 degrees.

The author of the canon Karana-tilaka makes this
correction in the following way. He multiplies the
diameter of the earth by 12 and divides the product
by the equinoctial shadow of the place. The gnomon
stands in the same relation to this shadow as the radius
of the parallel circle of the place to the sine of the lati¬
tude of the place, not to the sinus totus. Evidently the
author of this method thinks that we have here the
same kind of equation as that which the Hindus call Theequa-

•    /1/-7-         77              ■        -,                        7             •         iiowvyasta-

vyastatrairasika, i.e. the places with the retrograde motion. traird.iika.
An example of it is the following.

If the price of a harlot of 15 years be, e.g. 10 denars,
how much will it be when she is 40 years old ?

The method is this, that you multiply the first number
by the second (15 x 10 = 150), and divide the pro¬
duct by the third number (150 : 40 = 3|-). Then the
quotient or fourth number is her price when she has
become old, viz. 3f denars.

Now the author of the ICctr an a-tilaka, after having
found that the straight shadow increases with the lati¬
tude, whilst the diameter of the circle decreases, thought,
according to the analogy of the just mentioned calcula¬
tion, that between this increase and decrease there is a
certain ratio. Therefore he maintains that the diameter
of the circle decreases, i.e. becomes gradually smaller
than the diameter of the earth, at the same rate as the
straight shadow'i?7C7'gases. Thereupon he calculates the
corrected circumference from the corrected diameter.

After having thus found the longitudinal difference
between two places, he observes a lunar eclipse, and
fixes in day-minutes the difference between the time of
its appearance in the two places.    Pulisa multiplies