Mr Sang on Optimum Surveijing. 331 



us to determine the angles of the 

 . jj rectilineal trigon ABC, and from 



these we could compute the pro- 

 ' portion of the sides. D being 



another station, the usual obser- 

 vations would enable us to deter- 

 mine the angles of BCD, and also 

 ^ the inclination of the plane BCD 



to ABC. Having referred the 

 .J) positions of A, B and C to an ar- 

 bitrary system of co-ordinates, 

 the position of D could be found in reference to the same system. 

 And so on we might proceed to many new stations. Having thus 

 obtained the x, y, z's of a great number of points situate on {or 

 near) the surface of the terrestrial spheroid, we might then seek, 

 by the known method of minimum squares, for that spheroid 

 whose surface would pass most nearly through all the stations. 

 In this way the proportions which exist between AB and the axis 

 of the spheroid would be known, and even the inclination of 

 AB to the meridian, and that without a single astronomical 

 observation. Then, comparing the length of AB with the na- 

 tional standard, the dimensions of the globe in French toises or 

 in English feet would be known. Now here, although it would 

 be convenient to express all the distances from the commence- 

 ment, according to the national measure, that accident of con- 

 venience does not change the nature of the process, or render 

 the knowledge of the earth's form dependent on the measured 

 length of the base. This method is, on account of the irregu- 

 larities of refraction, useless in practice ; but in idea it serves 

 excellently to bring the true character of the operations before 

 the mind. 



The horizontal angles being the only ones that are much to 

 be depended on, it becomes an interesting problem to discover 

 whether these alone be sufficient to give the form or dimension 

 of tlie earth ? On the supposition that the earth is a sphere, we 

 may devise a very simple metliod of computing its radius. 

 There is this known property of spherical polygons, that their 

 surfaces are proportional to the excess of their angles above 

 those of a plane polygon having the same number of sides. 



y2 



