468 



HYDRO GRAPHICAL SURVEYING Fchap. xx. 



The method of rectangular co-ordinates may be used if the 

 distance east or west of the starting-point is not hkely to exceed 

 1 50 miles, and if there is no probability of accurate geographical 

 positions being required, nor of there being any further ex- 

 tension of the triangulation, and if the azimuths of the sides 

 are not wanted. 



The method is as follows : 



(a) The lengths of all the sides of the triangles are calculated 

 by plane trigonometry. 



(6) One station is selected at the initial station and the 

 meridian through that station is the initial meridian ; then, 



Fig. IIS. 



the earth's surface being treated as a plane, the co-ordinates 

 of all the stations are calculated, the co-ordinates being mea- 

 sured along, and at right angles to, the initial meridian, thus: 

 If, as in Fig. 115, A be the initial point, or origin, A Y the 

 initial meridian, and a the azimuth or true bearing, of the first 

 side A B, then 



Xi (the co-ordinate at right angles to the meridian) = A B sin a, 



and 2/i=ABcos a. 



A Y is called the axis of 2/i and A X, drawn at right angles to 

 A Y, the axis of x. 



