﻿APPENDIX, 493 



" that, by adding of the differences, the arcs them- 

 " selves may be found nearly ; the reason will appear 

 " from the following investigation. Let N be the equa- 

 " torial shadow of the Bramlns in Bmrles, then 720 the 

 " length of the Gnomon, or twelve On vies, will be to N 

 '* the shadow, as radius to the tangent of the latitude ; 

 " and radius to the tangent of the latitude as the tangent 

 " of the declination to the sine of the ascensional dif- 

 " ference ; consequently 720 is to N as the tangent of 

 " declination to the sine of the ascensional difference. 

 " Now if the declinations for one, two, and three sines 

 «' be substituted in the last proportion, we get the sines 

 M of the three ascensional differences in terms of N 

 " and known quantities ; and, if these values be sub- 

 *« stituted in the Newtonian form for finding the arc 

 " from the sine, we get the arcs in parts of the radius ; 

 i( and if each of these be multiplied by 36C0 and 

 '* divided by 6,28318, the values comes out in puis 

 " of a Gurry if N be in Bingks, but in parts of a 

 t* Gurry if N be in Ongles j and by taking the doubles, 

 " we ?et the values nearly as follows : 



O J 



I Fakes. \ Difference. 



p,oooco N 



0,33056 N 0,33056 N — 1-3 N nearly, ~\ the values 



0,59928 N 0,26872. N = 4-5 of 1-3 N nearly, Ui led by the 



jo, 70860 Nl 0,10932 N = 1-3 N nearly, J Bramins. 



" Now, because the values in the first column are 

 " doubles of the ascensional differences for one, two, 

 " and three sines, their halves are the ascensional dif- 

 " ferences in parts of a Gurry, supposing N to be 

 " in Ongles; and if each of these halves be mul- 

 tiplied by sixty, the products, namely, 9,9168 N, 

 17,9784 N, and 21,2580 N will be the same in 

 puis of a Gurry ; and if to get each of these nearly 

 in round numbers, the whole be multiplied by three, 

 and afterwards divided by three, the three products 



it 



a 



