320 TRIGONOMETRICAL SURVEYS. 



of a oonsiderable arc of the meridian. Without regarding 

 ■what he had formerly done, he began anew, and fixed on a 

 tract of country for a base near Madras. It was well 

 adapted to his purpose, being an entire flat, extending in a 

 southerly direction almost eight miles. The length of the 

 base, reduced to the level of the sea and the temperature 

 32°, was 40,006.44 feet, or 7.546 miles. The latitude of the 

 north end was 13° 0' 29", and it made an angle of about 

 12° with the meridian. From this a series of triangles was 

 carried about eighty-live miles westward, extending north 

 to the parallel of 13° 19' 49", and south to Cuddalore, in 

 latitude 11° 44' 53", embracing an extent of 3700 square 

 miles. The country seems to be favourable to the choice 

 of stations, and the' climate to geodetical observations, for 

 the triangles are of considerable magnitude, the sides of 

 some being thirty or forty miles in length. They are also 

 well contrived for avoiding very acute or very obtuse angles, 

 which are unfavourable to accuracy in trigonometrical sur- 

 veys. In computincr the sides. Colonel Lambton reduced 

 the observed spherical angles to the angles of the chords of 

 the arcs, according to the method of Delambre. The chords, 

 which were the sTdes of the triangles, were then converted 

 into arcs ; and as by a very judicious arrangement,— which 

 is, however, not alw'ays practicable, — he had contrived that 

 the sides of four triangles which connected the stations at 

 the north and south extremities of the meridian should be 

 very nearly in its direction, their sum, with very little de- 

 duction, gave the length of the intercepted arc, which was 

 thus found to be 95,721.326 fathoms. 



By a series of observations for the latitude at the extrem- 

 ities of this arc, made with an excellent zenith sector of five 

 feet radius by Carey, the amplitude of the corresponding 

 arc in the heavens was found to be 1°. 58233. The length 

 of the terrestrial arc in fathoms divided by this number 

 gives 60,494 fathoms for the length of a degree in the 

 middle parallel of latitude, viz. 12° 32'. This at the time 

 it was measured was the degree nearest to the equatoi 

 (except that in Peru almost under it) which had yet been 

 measured, and on that account was highly interesting. 



The next object was to measure a degree perpendicular 

 to the meridian in the same latitude. This degree was ac- 

 cordingly derived from a distance of more than fiftj'-five 



