688 iiiKKKi.ANn. 'ini: NOK\YI-:<;I.\.N AIKOKA POLARIS KXTI nn IO.N, 1902 1903. 



l!v integration of this, we obtain 



/ ' r i, 



+ r' 



ilr = i'(/'l , we can write 



Since iiioi'<_'ovi.-r 



= 1 + ; 



t/rf 



It no\\- tin: partirk- appi'oaclics a boundary-circle, then necessarily 



iv/r 



when ; is the ratlins <>[ the boundary-circle. As ///;/ r = I , and //;// r = r . , then also 



= co . 



lint as r certainly possesses a continuous 1st ilcrivativc (see (IV)), the necessary and sufficient 

 condition tor the last integral heini; infinite is that 



-,(r. i / -/I ?- ) - 



c \e j "'sin a, 



