172 HYDROGRAPHICAL SURVEYING [chap. v. 



C A D = w. At C, in A C, draw in like manner C D, making 

 ACD = m. 



When X is inside the triangle (Fig. 46) CAD, and A C D 

 must be drawn to equal 180° — w and 180°-m respectively. 



Describe a circle to pass through the points A, D, and C 



Join D B, and produce it until it cuts the circumference of 

 the circle in X. 



Then X is the position required. 



For A C D, A X D, being angles in the same segment, are 

 equal, and A C D is drawn = m 



.\ AXD = m 

 or A X B = m 

 Similarly B XC = w 



Then A D = 6 Sin . m. Cosec(w + «) . . . . , , . (1) 



^ BAG ^ /S ~(S -"a) 



Cos— -=V-^, (2) 



2 he 



BAD = BAC±CAD . (3) 



c-A D 

 Tan A (A B D - A D B) = Tan i (A B D + A D B) (4) 



c+A D 



XA = c. Sin A B D. Cosec m (5) 



SmABX- ......... . (6) 



AB • ' \ ) 



B A X=180-(m+A B X) (7) 



X can now be plotted by the angles from A, B, and C, if 

 required. 



DRAWING RECTANGULAR LINES. 



The methods of drawing a line perpendicular to another line 

 are well known, but are here repeated. 



Fig- 50. 



C ^4. It 



Measure from the point A with the beam compass any equal 

 distances right and left of A, as A B, A C. 



