CONDITIONS UNDER WHICH Hj, = 1 

 iY 



291 



Boundary of geometrical image of particle 



Fig. VII. 13. The area S and the inscribed circle of greatest radius R which can be 

 drawn about a point x, y in the interior of the geometrical image of the particle. 



that P(p, q) = he^^ in the conjugate area, one finds that in a straight- 

 forward manner 



Jnpm n2Tt 

 Jo 



i/O Jo 



= 2;rp„r ^r V 2Trpi~{he''' - 1) -— (15.4) 



^T^rpni zivrpi 



From Eq. 14.2 



Hp{x, y, 0, 0) ^ //p(.r, ?/) = ffli^, v) d^ dv (15.5) 



in which the integral extends over the area of the geometrical image of 

 the particle with f, rj measured from the point x, y as in Fig. ^^II.13. 

 Consequently, 



Hp{x, y) = Hr{x, y) + Hs{x, y) (15.6) 



where 



Hr^x, y) ^Jf r (r, 7?) rfr drj = 2ir£ U{r)r dr; (15.7) 



Hsix, y) ^J£ U{^, rj) d^ drj =f£ U{r)r dd dr. (15.8) 



