1862.] The Trigonometrical Survey of India. 35 



With the bases so found, the triangles were, as implied, first ex- 

 perimentally computed, an accordance of the numerous common sides 

 demonstrating an identity of the several characteristic letters. In 

 those cases where any want of demonstration existed, the point 

 was rejected. 



59. Such identification imposes no experimental calculation when 

 the points observed are clearly isolated from each other. For in- 

 stance XI. or Jannoo, XIII. and Mont Everest or XV. were readily 

 identified by the angular projection. But as in the cases of XLIII., 

 XLIV. and XLV. it is evident that nothing short of actual computa- 

 tion will separate the points in the group. The numerous experi- 

 mental triangles by which non-identity was proved, as also the 

 triangles for bases are not shown in this volume. The last mention- 

 ed triangles were about 450 in number, and the former also involved 

 considerable labour. 



60. Spheroidal excess. — The two formula for spheroidal excess, 

 viz., that involving two sides and the contained angle, and the other 

 in terms of the base and the three angles, were respectively employed 

 in the triangles for bases and in those to Himalayan points. In 

 the latter case however, the spherical angle opposite the base c 

 could, in the first instance, be only roughly found from the equation 

 ir — (A -f- B) = C, wherein A and B are spherical angles. Whence 

 C was taken too small by the whole spheroidal excess. Now, as this 

 latter frequently exceeds 100 seconds, it was sometimes required to 

 find the excess approximately, next to correct the angle C, and then 

 with this value of C, to recompute the excess finally. In other 

 respects the Triangles were calculated as usually done. 



61. Synopsis of sides. — The values of the sides in feet thus obtain- 

 ed were recorded in the form of a synopsis, and this paper was 

 completed by finding the logarithm to the mean of these values, 

 as well as the miles corresponding to the same. 



62. Latitude and Longitude. — The computer was now prepared 

 to deduce the required latitudes and longitudes, which was done in 

 this wise. With the latitude and longitude of any station of 

 observation A, the aximuth thereat of point n, and the mean dis- 

 tance from the synopsis of sides A to n, the latitude and longitude 

 of n from A were found. Similarly values of latitude and longitude 

 were obtained from the other stations of observation, and a mean of 

 all these values was taken as the latitude and lonaritude of n. 



