( 740 ) 



sin - 

 du 



'd{cos(py 

 d{cosi) 



We iiiaj fiirlher deduce from the consideration of the spherical 

 triangle, defined by the directions OJSF, OQ and OP, that for m = 



d(cos(p) 



so that 



and 









f(0)cosh 



2T 



2nt r «b^'T 



The real part of the expression (9), added to this result gives 

 exactly zero, so that, as we could have expected, there remains in 

 Qj: no term with only cos2ri</T. We need hardly add that this is 

 equally the case with ^'y and S^. 



Finally we have to determine f{Uo)- Let us denote by 52 the 

 solid angle of a cone, formed by directions for which ti is constant, 

 then 



dii 



<P^dtp 



(15) 



= du I sin 

 

 Now by (12) we have 







and with a view to (15) we may write for this 



•'^"^ T'V,'cos{hXduJu = u, 



The solid angle dSi^ of an intinitely small cone with axis OQ may 

 be found in the following manner. We imagine the wave-surface ]V, 

 passing through P, and the polar surface 7^ of W with respect to 

 a sphere of radius unity. Then the point corresponding to P will be 

 the point of intersection Q oi OQ and R, Further we take a point 

 P' on OP prolonged, close to P and describe from P' the cone 

 tangent to W. The normals drawn from to this cone will lie on 

 a second cone and this is the locus of all directions for which u 

 has the constant value 



