76 U. S. COAST AND GEODETIC SURVEY. 



In the expression for r' (X) on page 73, if we let ^ 

 represent the second constant, we have 



(dp du\ cos <p _ n 

 or, by substitution in the equation on page 73, 



r'(x)=|[i + rnx)] 



by integration, 



or 



Hence 



T'(X)d\ _n. 



1 + rHx) 2^^' 



tan-^ T{\)=^\ + c' 



r(X)=tan0X + c'y 

 tan|=itan(|x + c'). 



Since for X = 0, we have ^ = ; therefore, c' = and 



and 



r(X)=tan 2 X 



^ 1 , n . 

 tan ?r = — tan ^ X' 

 2 u 2 



To determine u, we may write 



du\ cos <^ w 



((Zp du\ 



in the form 



But 

 and 



2pu2 2 



(Z (up) cos <p _ ri 

 ~5^ 2p'w2 ~ ~2' 



