1839.] Description of an Astronomical Instrument. 



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bered from left to right. By this, the index-rod being adjusted as in 

 the last case, the zenith distance may be readily found ; but when 

 taken in connexion with other parts of the instrument, the latitude of 

 places is also easily found. Before describing the manner in which 

 this is done, however, it may be as well to enter into a brief exposi- 

 tion of the principles involved. 



Of all the observations which the Indian astronomer makes, none are 

 so generally important to him as those made with his gnomon and 

 graduated horizontal plane, for any error committed here vitiates 

 almost every calculation to which he is accustomed. When the 

 practical imperfection of this instrument is considered, and the 

 difficulty which the Indian artist has to encounter in its construc- 

 tion and adjustment from the rude tools he uses, it is a matter of 

 much astonishment that he attains such accuracy as he will be pre- 

 sently seen to do. 



Having fixed a conical gnomon perpendicularly upon a plane, which 

 he graduates into ungolas, or digits, each equal to a twelfth part of the 

 height of the gnomon, he again subdivides these into beungols or 

 60ths of an ungol. Thus provided, he proceeds at noon on the day 

 of the equinox, to measure the length of the sun's shadow — an opera- 

 tion upon the accuracy of which depends his reputation as an astrono- 

 mer. Having carefully ascertained the length of the shadow, he next 

 proceeds to the determination of his latitude, which he effects in the 

 following manner : — 



Let A B be the gnomon, B C 

 the graduated plane upon which 

 the shadow is to be measured, 

 S A D a ray from the sun S, then 

 B D is the shadow. 



Draw D G at right angles to B D, 

 and upon it let fall the perpen- 

 dicular S E, and from G draw 

 G F perpendicular to D G. 



Then \/A B* + B D* = A D by the 47th of Euclid (a proposition 

 well known to Indian mathematicians, and probably borrowed from 

 them) and — = jp^ = the sine of the zenith distance. 



Indian mathematicians do not appear to have been acquainted with 

 the nature and use of tangents ; had they been so, they would cer- 



