198 Problems by Bapu Deva Shastri. 
These tables may be carried ne any degree of accuracy by in- 
seeing the subdivision of the a 
The arc = 9 . 
eord = 8 : to find the sagitta. 
100,000 x 4 : 
8 = 112500 
112733 — 110383 = 1895 
148629 - 141721=6908 
33087 — 29289 =3798 
1662 x 6908 . 
1895 = 6059 
1662 x 3798 naa 
ta05.: °° 
6059+ 141721 = 147780. 
3331+429289 =32620 
32620-+8 5659 3 
“47780 =] 7381 a] a nearly 
. the value of the sagitta required. 
ha minimum ratio of the are and its sagitta may thus be de- 
_ termined by the differential calculus. 
Let are =2r 
tt len ——— sagitta of 2" versa will be the minimum ratio requi 
& cee L eee du vers¢—£. sin gue 
vers & ae vers? 
~~ which gives 2=133° 33/ 48” 29” = 2.331122 
when the rad =1 and sagitta =1.6891576. 
. The minimum ratio of the arc and its sagitta is 
Qe 4.6622444 
sagitta Qe — 1.689176 7 00 1004 
2.7601004 x 100,000 = 276010-04 
¢ a nd it may be proved by reference to the table that this, which — 
the differential calculus gives as a minimum, is the minimum, for — 
u be seen to be less than any other number in the column. 
t- t= 
