364 ACCOUNT OF trigoxomi;trical 



PRS and PSR, that is half the difference between 

 90' and the angle PRS as an observed one, we liave 

 go°-(8.o° 46- 29 ^68)^ ^, ^... J ^^ ^1^^ ^„g|^ j^S3^ H^^^g 



in triangle RSs considered as a plane one, there 

 are given tlie angles at R and S and the side SR, as 

 formerly found, from which will be had Ss and Rs 

 equal 357642.6 feet and 702.51 feet respectively ; as 

 also ]\ls (= RS — RM) equal 468.87 feet, which 

 measures the distance between the parallels of S and 

 M. But 46s. S7 feet as an arc on the meridian is 

 4".6j, which substracted from the latitude of.S gives 

 1 2' 55' 05".59 for the latitude of M, the station at 

 jllullapunna hetta. 



Hence in the triangle SPM there are given the 

 sides SP and MP (the co-latitudes of S and M) and 

 the angles PSI\I, PMS, the observed angles at S and 

 M. Then, as the tangent 77° 4' 52".085 : tangent 

 Oo0'2''.325 :: tangent 89° 53' 14". 83 : tangent 'o^ 4 

 31".26; which last applied to the half sum of the 

 observed angles, we get 89° 5^ U'.SS + 4' 3r'.26 = 

 89° 57'46".09 and 89' 53' 14".83 — 4'3l".26 = 89° 

 48' 43 .57 for the angles at Savendroog and Mulla- 

 punnahetta such as they would have been observed 

 on a sphere. Then proceeding by spherical compu- 

 tation with the sides PS, PM, and the angles PSM 

 and PMS given, the angle SPM, or difference of 

 longitude of S and M will be had equal 1° 00' 24''.44, 

 from whicli and the side SP in the right angled 

 spherical triangle PSR the side SR or arc SR per- 

 pendicular to the meridian PS at the point S will be 

 jiad equal 0° 58' 52".71. 



Now the chord of the arc SR is had = 357644.6 feet, 

 half of which will be as the sine of half the arc SR, 

 and from which is got the radius of the same arc, 

 and thence the length of the arc SR is found to be 

 357650.8 feet. Then as 58' 52".7l • 357650.8 :: 60' 

 : 364463.3 feet, or 60743.8 fathoms, for the measure 

 of the degree at right angles to the meridian of, 

 Kiaveadroog, . 



