MERIDIAN ON THE COAST OF COROMANDEL. 191 



But to find the small space Rs on the meridian 

 of Curnatighur, between the perpendicular arc and 

 parallel from Carangooly, let the triangle CR^ be 

 taken as a plane one. Then if to the corrected 

 angle CRs (89' 49' i^4",01) be added the supple- 

 ment to the spherical excess in the triangle 'i^C^G 

 (0",5), we shall have 89" 49' 24", 5 1 for the angle 

 sRC. Dr2L\v Rt parallel to sC, meeting the me- 

 ridian of Carangoolj/, produced in f. Then since 

 the angles PtR and PsC are equal by construc- 

 tion; and the triangles sCR, CRt considered as 

 plane ones, the angle CRt is equal half the diffe- 

 rence of the angles PCR and FRC, that is = 

 poo.-(goo 4 0- C4".5\)_.Q» 5' 17'; 74. Hence is given 



the two angles CRs, sCR, and the side CR, by 

 which the small side Rs is had, equal to 448,02 

 feet, which, deducted from GR, gives Gs— 

 14780,72 feet, equal to an arc of 2' 26",58 on the 

 meridian, and this is the difference of the latitudes 

 of Carafjgoolij and Curnafighur. Hence if the la- 

 titude of *Carangooly be ^12° 32' 12",27, that of 

 Curnatighur\Y\\\he 12° 34' 38", 85, and their re- 

 spective complements will be 77° 27' 47",73 and 

 77° 25' 2 1", 15. Hence in the triangle PCG, on the 

 spheroid, is given the two sides PG and PC, the 

 co-latitudes of G and C, and the two observed 

 angles PCG and PGC. 



Then as the tan. T?'' 26' 34",44 (half the sum of 

 the sides PG and PC) to tan. 0° 1' 13", 29 (half 

 their difference) so is tan. 89° 54' 41", 73 (half the 

 sum of the angles), to tan. 2° 56' 10",23 (the half 



* When the polar star observations were made r\t Carangoolyy 

 no doable azimuths could be taken, and therefore the latitude of 

 the place v.as necessary to compute the azimuths, in order to get 

 the direction of the meridian. As I wished to dedijce the latitude 

 of Carangooly from that of the observatory at Madras, the fol- 

 lowing method was usefl to obtain it. 



Let P be the pole, PT the meridian of Trivnndeporum, O the 

 observatory at Madras; and let C be tiie station at Carans'Gob/, 

 T Ihiit zt Trivandcpornm, 03/ an arc of a great circle, perpendi- 

 cular to PT, falling from the observatory, and Cm another per- 

 pendicular arc from Carangooly . Tlien if the ratio of the earth'? 

 diameters be taken as 1 to 1,003567, and the degree on the ni««> 



