CHAP, v.] USE OF THE SHIP FOR TRIANGULATION 163 

 The error involved in this method is due — 



(1) To any movement of the ship. 



(2) To the error in the assumed distance of the peak. 



As regards (1), the error is inherent to any method of floating 

 triangulation, and cannot altogether be avoided, although it 

 may be minimised by mooring the ship taut. 



As regards (2), the following investigation shows what it is 

 likely to amount to at any given distance from the ship : 



In Fig. 45, A being the ship, B the true position of the peak, 

 D its assumed position, draw A C at right angles to A B, the 



Fig- 45 



point C representing the limit of distance to which the sound- 

 ings extend from the ship. 



Join B C, C D, and from B drop the perpendicular B E on 

 C D produced. 



Let angle A D C - a, and B C E = j3. 



A C 

 Then, tan a = 



AD 

 B E = D B . sin a 



BC= VAB2 + AC2 



BE DB.s ing 

 ^"^~BC" VATB^+XC^ 



error in assumed distance of B x sin a 



J A B2+AC2 



j3 represents the difference between the correct bearing of A 

 from C, and its bearing as deduced by erroneously assuming 

 the position of the peak to be at D. 



The resulting error in the fix will be represented by the 

 arc of the circle at the distance from the ship corresponding 

 to the mast-head angle, intercepted by two radii separated by 

 the angle |3. 



11—2 



