190 



MEASUREMENT OF AN ARC ON THE 



Let PC and PG be two meridians, and let C 

 and G be the stations at Carangooly and CurnatU 

 ghur. Let Cs be a parallel of latitude at C, meet- 

 ing the meridian of Curnatighur produced, and let 

 CR be a great circle perpendicular to the meridian 

 of Carangooly falling from that place, till it meet 

 PG produced in R, 



Now GCR is a jt 



spheroidical trian- 

 gle, and the chord 

 of the arc GC is gi- 

 ven from the thirty- 

 fourth triangle; and 

 since the angle PGC 

 is known, the angle 

 CGR is known, be- 

 ing equal 1 80° minus 

 the observed angle 

 at Curnatighur, or 

 87''10'44",07.— And 

 by the same reason- 

 ing the angle GCR 

 will be given, being 

 equal the angle PCR 

 (90"") miyius the ob- 

 served angle at Ca- 

 rangooly, that is SB"" 



.59' 52",4:6 — Hence, by first considering this as a 

 plane triangle, and taking the angle at R, the 

 supplement to the other two, the sides CR and 

 GR may be obtained, and used as arcs for cor- 

 recting the angles at C and G, which will then be 

 2" 59' 52",2 and 87^ 10' 43", 79 respectively, which 

 are the angles made ])y the chords of the arcs CG 

 and RG at C and G. Hence the supplement to 

 these (89" 49' ^4",00 xvill be the angle at R made 

 by the chords of the arcs RC and RG, From 

 these data will be had 7^C=290837,8, and RG= 

 15228,74 feet. 



