THEORY OF POLYCONIC PROJECTIONS. 83 



or by substituting the values on page 82 



dW 



_i 1 pa; d^x by b'y "]_ 1 

 i2m Wijbd dcr dX "^ d(T 5(7 dX J W 



dX 



1 _ 1 rdx d'x by b'y 1 1 bW 

 i2p FldXdXdcr + dXdXdd F^dcr' 



or, again paying no attention to sign, 



i?m b\\Wj 



in which 



W^-^f\icT + i\)f,{a-i\). 



If the meridians and parallels are to be circles', R^a must 

 be independent of cr, and i?p must be independent of X. 

 This fact is analytically expressed by 



^.(i)-«-a-xa)-»- 



These two conditions lead to the same condition; that is, to 





From this it follows that, if the projection is conformal. 

 the condition that one system of curves forming the net is to 

 be made up of circles, makes it necessary that the other set 

 should also be circular arcs; this includes, of course, straight 

 lines as special cases of circles with infinite radii and with 

 centers at infinity. 



If, in order to simplify the analysis, we set 



1 , . .^, 



