19^ MEASUREMENT OF AN ARC ON THE 



difference of the angles). Therefore 92' 50' 5 \",96 

 and 86° 58' 31", 5, will be the angles at Cutmatightir 

 and Carangoohj, such as would have been observed 

 on a sphere, the latitudes and longitudes being the 

 same. Then by using these angles, with the sides 

 PC and PG, and computing spherically, the angle 

 CPG, or difference of longitude, will be48'47'',75, 

 with which, and the side PC, or co-latitude of 

 Carangaoly, in the triangle PCR, right angled at 

 C, the side CR will be had equal 0° 47" 37" A5. 



Now the chord of this arc is the distance CR, 

 equal 290837,8 feet, and therefore the arc itself is 

 290841 feet nearly. Hence 47' 37",45 : 290841 :*- 

 60' : 366355,08 feet, or 61059,2 fathoms nearly, 

 which is the length of the degree perpendicular to 

 the meridian at Carangoohj *. 



ridian be 6049 1 falhoiiis ; by using these 

 data, and computing on tlie elliptic hypo- 

 thesis, the degree perpendicular to the me- 

 ridian 12° 32' would be 60906' fathoms, 

 which for the present purpose is made use of. 



By the tiiangles, the point O is east from 

 the meridian of Trivandcporn7n 190561,12 

 feet, and norlli from the perpendicular at 

 that slaiion 480363,62 feet. Also C is east 

 63690,8 feet, and north 287100,96 feet, 

 from which, and applying the above de- 

 grees, we shall have the arc T3I 1° 19' 26",4; 

 T»i— 47' 27",o6; and therefore rrMwj 31' 

 58",84. Also OM 31' 17",13, Cw — 10' 

 27",42, and PO 76" 5.0' 56",7, the latitude 

 of the observatory bein<i 13° 04' 09",3. 



Then in the spherical triangle POM, 

 right angled at M, we have Cos OM : Rad 

 :?Cos. PO : Cos PM—76° 55' 48",72, to 

 which add the arc Mm, there will be had 

 Pm—77° 27' 47',56, the co-latitude of the 

 point m. 



Then again as rad. '. Cos Cm\\ Cos mP'. 

 Cos PC= 77" 27' 47",77; therefore the latitude of Carangooli/ 

 will be 12" 32' 12 ",23. 



* The ratio of the earth's diameters has been determined, by 

 tising the ♦legree as broiiglit out here, and the one in latitude. 50° 

 41', as deduced from the measured arc bclwcen firccnwich and 

 Paiis, which is 6085l fathoms; and these two give the ratio of 

 the polar to the etjuatrial diameters. to be 1 : 1,003567, supposing 

 the earth to be aii ellipsoid. 



