94 



goes along the hyperbolic circles, the elliptic circles interchanging. If 

 mod. = 1, amp. =f o, motion goes along elliptic circles, the hyperbolic 

 system being invariant. If mod. ±1, amp. =fO, motion is along neither family 

 but passes diagonally from curvilinear rectangle to curvilinear rectangle. 

 These respective transformations may be named hyperbolic, elliptic, loxodromic. 

 The circles about and tlirough the fundamental points are potential lines 

 and lines of flow in the well known problem of electricity of equal source 

 and sink. 



Bloomington, Ind., Nov. 28, 1906 



