228 Paij(Jit Biipu Deva S'astri — A brief account of Bhdslcam. [No. 3, 
Multiply the equinoctial shadow by the radius and divide the 
product by the cosine of the azimuth. Assuming the result as an 
equinoctial shadow, find the sine of an assumed latitude, i. e., finding 
the Alcsliaharna from this equinoctial shadow, say : — 
as the alesJiakarna 
■ the equinoctial shadow or the result 
: : the radius 
: the sine of assumed latitude. 
Now the sine of the sun’s declination multiplied by the sine of 
latitude of the given place gives the sine of assumed declination. 
Add the assumed declination to the assumed latitude, when the 
sun’s declination is south ; but when the declination is north, subtract 
it. The result will bo the zenith distance of the sun.* 
Demonstration. First of all ho found the shadow of the gnomon, 
when the sun, revolving in the equinoctial, arrived at the given vertical 
circle, i. e., when the sun has the given azimuth, as follows : — ■ 
Draw a circle on a level surface with a given radius, and draw two 
diameters perpendicular to each other, east and west and north and 
south; then, at the equinoctial day, if we place a gnomon of 12 digits 
on the level so that the end of its shadow fall on the centre, the distance 
of the gnomon’s bottom from the east and west line must be equal to the 
equinoctial shadow of the given place. Now draw a line from the 
centre to the gnomon’s bottom, and produce it. It will meet the circum- 
ference at the distance of the complement of the azimuth from the 
east or west point. 
Then say— 
as the cosine of the azimuth 
: the radius 
: : the distance of the gnomon’s bottom from the east 
and west line, i. e., the equinoctial shadow 
: the gnomon’s shadow. 
From this shadow find its hypothenuse, then say 
as the hypothenuse 
: shadow 
: : radius 
: the sine of the zenith distance when the sun is in 
the equinoctial having the same azimuth. 
Call this sine the sine of assumed latitude. 
Then by similar triangles — ■ 
as the sine of the latitude of the place in the plane of 
the meridian 
* That is, assuming the given place of the observer to be in the northern 
hemisphere. 
