212 



PIERCE. 



As an approximation, let us multiply by the sum of these radicals and 

 divide by the approximate value of this sum for large values of tq; 

 namely, by 2ro, obtaining 



r' = ro + 



r" = ro + 



x'^ - 2xx' - 2za + a^ 



2ro 

 x'^ - 2xx' + 22a + a^ 

 2ro 



(45) 

 (46) 



13. Determination of Electric and Magnetic Intensities due 

 to Flat-top. — The values of r' and r" in (45) and (46). may be re- 

 placed by ro in intensity factors, but not in phase terms, and give 

 for the sum of the effects of a doublet at P' and another at P" (the 

 image doublet) the electric and magnetic intensities 



dE^ = dH^ = '^\f^it- ^Vc) + /2 (t - t"/c) I , (47) 

 where /i(f) and f2(t) are the moments of the two doublets respectively. 



Figure 8. 



The angles (p and S correspond to the angles 6 and </> of Figure 3, except 

 that the figure is turned on its side, so as to put the polar diameter 



