CHAP. XX.] RECTANGULAR CO-ORDINATES 469 



(Note. — This represents a great circle of the earth, and is 

 therefore not the same as the parallel of latitude of A, which 

 is a small circle.) 



If lines are drawn through B, C, D, parallel to A Y, it is 

 clear that. 



r»o=B C, sin /SI , ^ * T> r^ 

 1 T3 r^/ ViVwhere/9=ABC-a 



and 2/2 =B C, cos pj 



X3=CD,sin7|^1^^^3 BCD-^ 

 and y^—C D, cos 7 J 



The co-ordinates of A are o o 



}> J5 >j B ,, Xi 2/1 



>> >5 3> C „ a:i-{-.T2 ?/i ;?/2 



„ D „ x^+Xo+X:, '/l -2/2+2/3 



All these points can now be plotted with reference to the 

 origin, A, and its meridian. 



It is obvious from Fig. 115 that the co-ordinates of C can be 

 found direct from A, being — 



CAsin (a + BAC) 

 andCAcos(a + BAC) 



Similarly, the co-ordinates of D are — 



DBsin (180°-/3-DBC) 

 andDBcos (180°-/5-DBC) 



In this way an arithmetical check should be provided for 

 every point. 



The signs of rectangular co-ordinates are determined by two 

 conventions : 



(i.) X co-ordinates are considered as — according as the point 



IS 7 01 the origm. 



west 



(ii.) y co-ordinates are considered as — accordmg f.s the point 



. north . , 



IS 01 the origin. 



south 



The co-ordinates are usually measured in feet. It is im- 



