60 Prof. Max Planck : New Paths 



Now m= (p—ft— l)n — u and a.<n — 1. For, ii' a = n — 1 

 the integration in (4) could be effected without separation 

 into partial fractions. Therefore m — 1 contains n as a factor 

 p—fi—2 times. 



We then obtain 



1 1 ' n r -Bi+1 p-p-2 (—1)* 



And 



rn-S-l 



r* ^ lL 4 J r 2k + 1 < nji / 2 o 2k+1 .a 

 J, s^tt) = ^ n Jo L cos ~ir w (m ~ T) i lo s V 1 ' - 2 * cos -r- w + V 



-2 log Asin^t^ 



\ 2?z / j 



2/c+l 



_ . 2a: +1 , in \ r _i w 2x;+l 

 + 2 sm 7T{m — 1) ^ tan * = — — — 





. 2,e + l 2n 



sm ir 



S^ — 1( >g-9(^+l)+ * 



X 



=0 (/> — (3—K— l)w — a — 1 



-L__-i[i_ ( -i)^] ( J 



The required Integral (1) is obtained by combining (18) 

 (19) with (7) (due regard being paid to the limits). 



University of Pennsylvania, 

 Philadelphia, Pa., U.S.A. 



IX. New Paths of Physical Knowledge : being the Address 

 delivered on commencing the Pectorate of the Friedrich- 

 Wilhelm University, Berlin, on October 15th, 1913. By 

 Dr. Max Planck, Professor of Theoretical Physics *. 



The Rector began his Oration thus : — 



Honoured Assembly, Esteemed Colleagues, Dear Comrades : 



Called to the head of the Administration by the confidence of 

 the accredited representatives of our Corporation, I have under- 

 taken as my first official duty the task of greeting the members 

 and friends of our Alma Mater at the commencement of the new 



* Communicated after revision by Sir Oliver Lodge, on the basis of a 

 translation by Dr. Fournier d'Albe. 



