460 



HYDROGRAPHICAL SURVEYING [chap. xx. 



The true position will be on the prolongation of the line 

 joining the centre object and the position found, using the 

 assumed points at a distance from the centre object pi-oportion- 

 ate to the degree of division used. 



AC 







Fig. 113. 



The following example (see Fig. 113) will explain this 

 graj)hically : 



True positions of the objects. 



Assumed positions of A, A B being divided 



ABC 



Xo Xg 



p 



Po 



p. 



2' 3^' 



Assumed positions of C, A C bemg divided 



into \,\- 



True position, using A, B, and C. 

 Position using Xg B y2 (1). 

 Position using X3 B y^ (2). 



Therefore, by (1) true position P is on the prolongation of 

 the line B P.> at the distance where P^ P=B P.,. 



And similarly by (2) true position P is on the prolongation 

 of the line B P3 at the distance where P3 P=2B P,. 



