35 
1862.] The Trigonometrical Survey of India. 
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 XY. were readily 
identified by the angular projection. But as in the cases of XLIII., 
XLIV. and XLY. 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 
trianodes for bases are not shown in this volume. The last mention- 
ed trianodes were about 450 in number, and the former also involved 
considerable labour. 
60. Spheroidal excess. —The two formulas 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 
t r — (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 longitude of n. 
