78 U. S. COAST AND GEODETIC SURVEY. 



or 



fctan^d + l^+l 



fctan-(j+|)-l 



2^ «>' P tan- (1 + 0-1 

 ^ 2^tan-Q+|) 



(M) 



T(X)=tan|\ 



^ 9 r(X) ^tan'(|+|)-l 



tan o = = / ( — —tan ~k • 



2 « ,tan-Q + |) + l 2 



The value of s gives the distance of the center for the 

 circle that is to represent the parallel of latitude (p from the 

 intersection of the central meridian with the parallel that is 

 represented by a straight line; p is the radius of this 

 parallel; the parallel is therefore fully determiQed by 

 these two quantities, since the centers of the parallels must 

 lie on the central meridian. In order to construct the 

 meridians, we must determine on the parallel of <p the 

 value of 6, the angle at the center of parallel <pj that corre- 

 sponds to the meridian of longitude X; this method of 

 plottrug the meridians by coordinates will be imnecessary, 

 however, if we determine the equation of the meridians. 



We have 



X = p siu 6. 



y = s — p cos d. 

 But 



. e r(x) 



tan o=— ^^^ 

 2 u 



or 



u = r(X) cot 2 = tan ^ X cot k* 



