42 GREAT TRIGONOMETRICAL SURVEY OF INDIA. 



He was appointed an assistant in the Great Trigonometrical 

 Survey on the 1st December 1853, took a share in the measurement 

 of the Chach base line in the valley of the Indus near Attock, 

 and for some years was conducting the principal triangulation 

 along the Indus and on the meridian of 73^°, and in carrying a 

 line of levels to connect the stations of the triangulation with the 

 sea. 



In 1861, when Colonel Walker became superintendent of the Great 

 Trigonometrical Survey, the greater portion of the principal triangu- 

 lation had already been completed, and the time had arrived for 

 determining the procedure by which the fallible values of the several 

 angles and base-lines, as obtained by actual measurement on the 

 ground, were to be rendered consistent, and final values were to be 

 determined for the lengths and azimuths of the sides of the triangles 

 and also for the latitudes and longitudes of the stations, which is 

 the ultimate object of all first-class triangulation. Already pro- 

 visional corrections had been applied to the angles of certain chains 

 of triangles directly connecting base-lines for the linear error 

 generated between the base lines, whereby the length of one base, 

 as computed through the triangles from the other, was brought into 

 accordance with the measured length. But this was only a small 

 part of the requisite reductions for general consistency. The 

 triangulation being formed of a large number of meridional chains 

 tied together by a few longitudinal chains — forming sections some- 

 what resembling a gridiron in shape — presented a large number of 

 circuits ; and at the closing side of each circuit two values were 

 forthcoming not only of the length of the side but also of its 

 azimuth, and two values were also forthcoming of the latitudes and 

 longitudes of the stations at its extremities. Thus three geodetic 

 errors — as they have been called — Lad to be recognised and disposed 

 of by a process of dispersion throughout the angles, as well as the 

 linear error ; and the question arose, and a most embarrassing 

 question it was. as to how the requisite angular corrections to 

 produce consistency throughout could be legitimately computed. 



The procedure adopted was to form equations of condition 

 expressing the errors of the angles in each circuit as unknown 

 quantities in terms of the closing error of the circuit, for the three 

 geodetic as well as the linear errors. In forming the geodetic 

 equations — now done for the first time in any survey — it was found 

 that the co-efficients of the unknown quantities in them were greatly 



