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' - 22a + a^ 



2ro 

 x'^ - 2xx' + 2za + 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^, = dHz = 



= ?^ h; r/ - 



ro(^ I 



/i {t - r'/c) + /2 (t - r"/c) , (47) 



where /i(0 and/2(0 are the moments of the two doublets respectively. 



Figure 8. 



The angles cp and 2 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 



