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THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



common, and their orientations, for which they are independent. It is 

 knowTi that in integrating over the two angles defining an orientation 

 the polar axis may be chosen freely. We shall, in the following, adopt c as 

 our polar axis with yp, k being pole distances of y and y' to c and ^, co the 

 corresponding azimuths. In Fig. 8 these angles are exhibited on the 

 unit sphere. All vectors are assumed to be plotted from the center of the 

 sphere, and show up through their piercing points. The angles between 

 the vectors then show up as sides and the azimuths as angles. The ex- 

 pression (32) becomes then 



7 dy sin \}/ d^ dip sin k dK dw 



The main transformation consists now in introducing the three com- 

 ponents of C in the place k, \f/ and <p. The transformation formulas 

 follow from the vector identity 



M 



m 



C = c — Y — y 



(33) 



and read in full 



^/ ^ _ My 



M -{- m 

 ^, ^ My 



sin yj/ cos (p 



sin ^ sin <^ 



my 



M -\- m 



my 



M -\- m 



sin K cos CO 



sm K sin CO 



Fig. 8 — Definition of the angles employed in the formulations of the Boltz- 

 mann equation for the high field case. 



