^4 Mr Sang 07i Optimum Surveying. 



ness of the earth altogether ridiculous. The investigation, 

 however, is erroneous, as may be detected by any beginner in 

 stereometry; it has been justly characterized by Mr Ivory, 

 as " the greatest delusion that has ever prevailed in practical 

 mathematics." 



There is, by the way, something very curious connected 

 with the operations carried across the channel. On all the 

 partial triangles the curvature of the earth is carefully allowed 

 for, yet in the computations for determining the easting and 

 southing from Greenwich, computations extending over larger 

 surfaces, it is entirely neglected ! 



Leaving the survey for a little, I shall now proceed to shew, 

 first, in the case of plane surveying, how the computations must 

 be carried on so as to give the greatest exactitude ; and in do- 

 ing this, I shall merely use a method already well known, and 

 applied to much more intricate matters. 



While carrying on an extensive survey, the operator is care- 

 ful to determine the position of each new station, by the meet- 

 ing of several lines drawn towards it. If only two lines be 

 used, its position, indeed, may be set down, but there will be 

 afforded no means of knowing what degree of accuracy has 

 been attained ; a third, fourth, or fifth bearing affords means 

 for checking: the determination from the first two. It is not 

 uncommon to compute the position of several intersections, and 

 to average these for the true position ; nor is it even unusual 

 (see Trig. Surv. passim) to reject those results and observations 

 which do not happen to jump with the rest. I shall shew a 

 single operation by which the optimum position may be found, 

 whatever may be the number of intersecting lines. 



The positions of a number of stations, A, B, C, D, &c. ha- 

 ving been accurately determined, 

 we seek to ascertain that of a new 

 station, N. For this purpose, we 

 observe the bearing of N, as seen 

 from several of these stations or 

 the directions of the lines A N, 

 B N, C N, he. The intersection 

 of any two of these will give, 

 supposing that there is no error, 



