240 PIERCE. 



21. Curves of Resistance Due to Radiation from the Flat- 

 top. — We shall now proceed to discuss the curves of radiation re- 

 sistance of variously proportioned antennae when employed at various 

 wavelengths relative to the natural wavelength. As preliminary, 

 the resistance due to radiation from the flat-topped portion of the 

 antennae is first computed. The equation for this is the summation 

 of terms in (107) containing the small r's as factors; that is, 



R^^ = -—^^ \ r.A~ + ^3.4^ - r,A' - r,A' + 'v4« + • • • • |- (109) 

 ' sm2(g/2) ( \ 



due to 

 flat-top 



in which 



. 2xa 



9 = '^' = 2(^ + 5)- 



Since the coefficients (small r's) are functions of B only, as given in 

 Table II, it follows that when k and B are given, the value of the flat- 

 top R may be computed. The results of the computations for various 

 values of A and B are plotted in Figure 1 1 . 



In this figure values of B are the abscissae, while the flat-top 

 resistances in ohms are ordinates. The separate curves numbered 

 .1, .2, .3, etc. to .9 are for values of ^ = .1, .2, .3, etc. to .9. 



The outside end-points of these several curves, through which a 

 limiting curve is drawn, are determined l)y the equality of the im- 

 pressed wavelength X and the natural wavelength of the antenna Xo; 

 that is, by the value of ^ + 5 = 7r/2, which is the lai'gest value 

 A-\- B can have for the fundamental oscillation of the antenna. 



22. Curves of Total Radiation Resistance. — The iiext 

 step consists in computing the radiation resistance of the vertical 

 portion of the antenna, using the first three terms of equation (107), 

 and employing a large number of values of A and B. To these values 

 of resistance due to the vertical portion of the antenna the correspond- 

 ing resistance of the flat-top are added so as to give the total resistance 



