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already stated, those obtained by the methods of the present paper, employ- 

 ing numerical integration. 



From detailed inspection of Table 5.1 it will presumably be considered 

 that the agreement between the two sets of values of Q*{R\b) = pb(R'>R) 

 is to be regarded as satisfactory, at least from the practical viewpoint, the 

 largest deviation being less than one per cent (for R = 0.8, b — 0.9). 



Table 5.1 

 Valxjes of Q*{R) = p{R' > R) 



6. The Distribution Function For The Angle 



The distribution function P{d \ Rn) = P{d) for the angle 9 of any complex 

 variate W = R{cos 6 -\- i sin 9) is defined by equation (1.10) on setting 

 p = 6, a = R, (Xi — Ri = and ao — R^ — 'x, -^ thus 



P{9)d9 = p{d<9'<d-\-d9,0<R'<x). (6.1) 



An integral formula for P(9) is immediately obtainable from (1.6) by 

 setting p — 9, a = R, as = (Xi — Ri = and 0-4 = ao — R2 = °o ', thus 



p(e) = [ P{R, 9) (JR. 



(6.2) 



