CHAP. I.] 



ATION POINTER 



29 



Any other position, as X^, would not allow the leg to pass 

 over H. 



It will also be seen that the farther apart A and B are, the 

 truer will be the direction of the transit line. If one object was 

 at Bj, the position pricked through at X might be a Httle right 

 or left of the true transit line, without the deviation being 

 visible on the leg of the station pointer. 



Also, it will be seen that the angle to the third object should 

 be as near 90° as possible, anything under 25° being inadmis- 

 sible, as the angle of intersection at X would permit of a false 

 position without detection. 



When using this method, the distance of the third object 

 should also be considered. It must not be too far, or both 

 theoretically and practically, by reason of the imperfection of 

 instruments, the fix may be in error. 



These conditions are illustrated in Fig. 6, in fixing the Effect of a 

 position of a point O on the line DO, by the intersection of ^j^^^ jq 



the line A 0„ 



an Inter- 

 secting 

 Angle. 



Fig. 6. 



Resulting error of position on line D due to a small error in 



angle D Aa , 



sin D O A 



and thus has its smallest value when D A = 90° and when 



A O is short. 



The principle here involved is of frequent application in 

 deciding what cuts to accept when there is a slight discrepancy 

 in the plotting of a point. 



If the value of the resulting error in position when D A = 



