128 Journal of the Asiatic Society of Bengal. [March, 1908. 
The following extracts will serve as a comment on this rule, 
which is ange oe with the construction of some form of dial :— 
“Ha y s of water, levelled a raised surface, on 
which the "direelione are marked, and having placed on its 
equal to any required number of the digits of the gnomon . . . 
raw a circumscribing square, by means of lines going out from 
the centre . The square-root of the sum of the squares of 
the gnomon and shadow is the hypotenuse ....” (Sur. Siddh. 
iii., 
‘The fundamental arrangements of all instruments depend 
upon strings, water, and bits of earth. By means of them one may 
make, on a level surface, er shaped like a tortoise, a man 
and so on.” (Pajfch. Siddh. , 27. See also Rae Siddh. xii., 
19.23 and Warren’s Kala Sonkalitis p- 92.) 
14. The square-root of the sum pit the gn of the ‘age of 
the style and shadow is the radius of its 
is rule occurs, in some form or are in all the early Hindu 
the rule cannot be a mere statement of the Pythagorean theorem, 
and I am inclined to believe that it has a definite connection ze 
the subject in hand. All the shadow problems given by A 
bhata and Brahmagupta relate to vertical gnomons, but the fo tiie. 
placing his eye at the base of the straight gnomon, is to incline it 
in such a way that the top of the gnomon is in a straight line 
joining the eye and the pole star.” (xii., 
Now the equinoctial shadow of a vertical gnomon gives the 
latitude of a place, z.e., the tangent of the latitude is equal to the 
shadow divided by the gnomon ; ‘and to mark out the hour angles 
on an ordinary sun-dial, it is necessary to describe two circles, one 
of which has its radius equal to the vertical gnomon and the other 
with radius equal to the hypotenuse of the triangle formed by the 
equinoctial shadow nie the gnomon, It is this circle whose radius 
is the * the square-root of the sum of the squares of the length of 
the style and shadow” ‘that 3 is referred to in our text. 
15. Multiply by ee style the distance between the style and the 
height and divide by he difference between the style and the height ; 
the =i obtanced bi give the shadow reckoned from the origin 
of the 
Bs agupta gives the same rule thus: “The itisthnge be- 
tween the ‘foot of the light and the bottom of the gnomon, multi- 
plied by the gnomon of given length, and divided by the difference 
between the height of the light and the gnomon is the shadow 
(XIL., ix., 53.) 
