Formulation of the Principle of Huygens. 



26$ 



As an example, let there be a single source at A the centre 

 of a sphere of radius b } fig. 3, and let PB = r, and denote the 

 angle BPN by 6. 



Fig. 3. 



The formula gives 



♦(-D-£jJIKi*Sr>(- i ?) 



l + oos0 d 



ah 



>♦(--;-)] 



rfS. 



Let 



then 



M . 2tto/ 



R Sln -X 



+ £(l + oo.fleoB^(«-^Y]«*S. 



o\ K y X \ a /J 



If /> is very small in comparison with the other linear 

 magnitudes involved, the right-hand side of the equation 

 becomes 



2ira / r+b y 



±TjJrb 2Sl 



\d$ 



M . 2tt« 



fr 



E m -xr('~> 



If all the linear magnitudes are large in comparison 

 with X, the right-hand side becomes 



M ff l + cos0 2™/ b + r\ ja 



2bx)) — — cos irl'~^rr s ' 



which is Stokes's expression for the secondary disturbance. 



