CHAP, v.] FIXING MARKS 169 



Given the angles between three knoAvn objects so placed as To Re- 

 to give a good fix, the position can readily be found within a Exld;*^^ 

 few yards by means of the sextant. Position 



Setting up the theodolite as near as possible to the supposed ^^ j^^g 

 position of the A, we must consider the three circles involved own 

 in the fix, and select that which is the most sensitive. tween^ 



(1) Measure the angle between the two objects lying on that Known 

 circle ; plumb the centre of the theodolite, and mark the spot 

 with a peg. 



(2) If the angle is found to be too small, a slight movement 



of the theodohte towards the fixing objects in a direction at • 

 right angles to the arc of the circle we are concerned with will 

 give a second position with an increased angle. 



(3) Measure the angle again in the new position, and mark 

 the spot with another peg. 



(4) Find a point A on the ground between the two pegs, 

 corresponding to the correct angle, by dividing the distance 

 in the proportion of the difference between that angle and 

 the angle observed at the two positions. 



(5) Now move the theodolite several feet along the arc of 

 the circle we are considering. 



Repeat the operations (1), (2), (3), and (4), and find a point B, 

 as already described. 



(6) The line joining A B will represent the arc of the circle 

 we are endeavouring to find. 



(7) We must next consider the other two circles involved 

 in the fix, and choose that which cuts the first circle at the 

 broadest angle. 



(8) Repeat the operations in connection with the two objects 

 lying on the second circle that we are now concerned with, and 

 find two other points, C and D. The intersection of the lines 

 A B and C D will be the exact position of the A required. 



Select two other stations, B and C, at both of which at some To recover 

 former period angles have been observed to the A (A) which ^^^ .■F.^^''^ 

 it is required to locate. See Fig. 46. of a a by 



Place a mark A' as near as possible to the supposed position ^^^j^g °1 

 of A. served to 



The stations B and C should be so placed with reference to ot^er"^ 

 A as to subtend a broad angle, and the distance of each from stations. 

 A should be as short as possible. 



