182 LIPKA. 



Property V thus completes the characterization of an " n " system, 

 and we may finally state 



Theorem 21. In order that a triply infinite system of curves on a 

 sin-face may he identified icith an " n " system, the given system must 

 possess Properties I, II' , III, IV', T . 



Massachusetts Institute of Technology, 

 Cambridge, Mass., September, 1920. 



