4 Lamb, A New Version of Argand's Proof. 



through zeros off(s), vanishes, whether the circuit include 

 such zeros or not. 



3. Another proof of our theorem, still simpler than 

 that of §r, in that it does not involve the logarithmic 

 function, may be obtained as follows. 



We have 



I I u - iv 



f{z) u + iv u^ + t 



(II). 



The function ul{u^-\-v'^) vanishes at infinity, and it 

 cannot have a finite upper or lower limit since it satis- 

 fies (4). It follows that there must be some point for 

 which u=-o, v = o, simultaneously. 



