Siyya-Siddhanta We have thus found the value of MT and the two parts of SI in terrms of the general sphere, or of a circle whose radius is tabtar Yadius: jb is desired farther to reduce thern to termnx of a circle in which MI shall aqua} %he gnomion, or twelve digits. And since 8he gnommon is equa! {o the sine of attitude in a circle of which the hypothenuse of the corresponding Bhadow is I'adlius (cormpare above, iii, 25-2 etc.), bhis reduction may be sfected by multiplying the quantities in question by the hypotenuse of the sharow and diving by radius That is to say, representing the roduced value of sN and NIL by 27 and }l respectively, R : hyp.shad. : : ML : xmu। . R; hyp-shai. SN : s R: hyp.ahad. : : No : १ । Substitutingnow, in the seconal and third of these proportions the values} of s and NL found for them bove Ind substituding also in bhe bhird the value of the hypotenuse of the shadow (lerived from the first, we have ain ar. x Bip 18t R, x aum sin le ]. ३ : hyp. bhad : ४jp cd-1a lk x guom. and T. a la &in p-18 which redue to hyp . 58है. » &u Ju २३n det . and . sian lAt. A goo , in :-!at M]D col •d of he constant value of the Hence, if the perpendicular MEbe gnomon, or twelve digits, We have (IVP. khad x_a AL ३ip dec!) + (xi |at x gn. ain ey-la. In the case thus fat cmilart: 1.h! Ind noon have been supposed upon opposite sides of the equator, If they at upon the arside, the R}} setting at S, or if their sines of declination, 3 and Ne, Are of the same direction, the value of S/N, the corresponding part of the base 'L, wilt be found by threating in the Anme mann as before the difference of the sines, Ste, insteदीd of their sun. In this case, too, the value of Sys being northSVN will have zo be subtracted ften NJ, i० लiye bhe bake X/ I. Other positions of the two luminaries with #expect to one another are supposable, but those which we h४ve take ar sufficient to illustrate १]] the Ottitione of the problem, and the method of its solhution. ¥b is evident that, in two points, the proless as thus explained by the ommentator is discordant with that which the text prescribes. The latter, in the first place, tells us to take, not the sum or difference of the site: of declination, but the sine of the sum or difference of declinations, as the side bN of the triangle SNb. This seems to be a mere inceluracy on Bhe part of the text, the difference between the bwe quantities, which
