RADIATION CHARACTERISTICS OF AN ANTENNA. 193 



whole antenna and therefore is enormously large in comparison with 

 the lengths of the elemental doublets. The electric and magnetic 

 forces due to each of the doublets is determined at a distance point 

 and is summed up for all of the doublets of the antenna, with strict 

 regard to the difference of phase due to the different locations of the differ- 

 ent doublets. Such a process performed for all points of a distant 

 sphere surrounding the antenna gives the total electric and magnetic 

 forces at all points on the sphere. Then by integrating Poynting's 

 Vector over the entire sphere, we obtain the total power radiated, 

 and from this we compute the radiation resistance and other charac- 

 teristics of the antenna. 



The effect due to the vertical portion of the antenna and to the 

 horizontal flat-top portion are computed separately, so as to give 

 information as to how much energy is radiated with its electric force 

 vertical to the horizon and how much parallel to the horizon. 



In deciding as to the proper distribution of the elemental doublets 

 along the antenna, the form of the current curve from point to point 

 of the antenna is assumed independently. This process is not entirely 

 above reproach, because Maxwell's equations, if they could be properly 

 applied to the problem, would themselves give the distribution that 

 is consistent with the applied electromotive force at the base of the 

 antenna and with the shape and form of the antenna. This step of 

 accurately deriving the distribution is, however, at the present time 

 not possible of mathematical execution. 



The distribution here assumed for the current in the antenna, as a 

 function of the time and of the position along the antenna, is a 

 generalization of the distribution assumed by Abraham, and is given 

 in the next section. 



4. Assumed Current Distribution. — The form of antenna to 

 which the whole discussion is devoted is illustrated in Figure 1, and 

 consists of a vertical portion of length a and a horizontal flat-top 

 portion of length b. These quantities a and b may have any relative 

 values whatever. 



At the base of the antenna is an arbitrary inductance L for varying 

 the wavelength. 



The current at any point P' of the antenna is ass.umed to be given 

 by the equation 



, . 27rc . 27r/Xo A ,,. 



i = /sm — ^smyf- -a (1) 



