GREAT TRIGONOMETRICAL SURVEY OF INDIA. 43 



more difficult to determine than the co-efficients in the linear 

 equations, for they consist of summations of series of terms from 

 the commencement of the circuit up to the position of the angle 

 whose error is the unknown quantity, whereas in the linear equations 

 the co-efficients are merely the co-tangents of the angles. The 

 solution of the equations was effected by Gauss's method of minimum 

 squares, in which every unknown quantity is given the weight due 

 to the facts of observation of which it represents the error. The 

 number of triangles in each circuit was so great that every equation 

 usually contained at least a hundred unknown quantities and often 

 many more, and thus the simultaneous solution of any considerable 

 number of circuits would be a matter of enormous labour, requiring 

 every precaution to ensure accuracy in the execution of so large a 

 mass of interdependent calculations. It was found practically 

 impossible to undertake the simultaneous solution of the whole of 

 the principal triangulation of India; the triangulation was there- 

 fore apportioned into five sections, of which the dividing lines were 

 the two longitudinal chains of triangles, one connecting Karachi 

 with Calcutta, and the other connecting Vizagapatam with Bombay, 

 and also the portion of the central meridional chain of triangles 

 called the Great Arc, which lies between the parallels of 18° and 30° 

 Of the sections thus obtained, the four northern ones were of a 

 quadrilateral form, and were called the North-Bast, Worth-West, 

 South-East, and South- West Quadrilaterals, the directions having 

 reference to certain points common to all the four sections at their 

 convergence in Central India, namely, the Sironj base-line, which 

 was the adopted origin of the linear element of the survey, and the 

 Kalianpur Observatory, the adopted origin of the geodetic elements 

 of azimuth, latitude and longitude. The fifth section embraced the 

 whole of the Beninsula to the south of a line from Bombay to 

 Vizagapatam, and, being triangular in form, is called the Southern 

 Trigon. Each figure presents an enormous amount of simultaneous 

 interdependent calculation, greater than had. ever been executed in 

 any survey, or probably in any investigation whatever. 



Of these sections of the triangulation the North- West, North- 

 East, and South-East Quadrilaterals were reduced, and the final 

 results printed and published at the head quarters of the Survey in 

 Dehra Dun, by Mr. Hennessey and other officers directing the 

 computing staff, under the immediate superintendence of General 

 Walker. The results are contained in Volumes II. to IV. and VI. 



