252 PIERCE. 



the larger values of the relative length of flat-top. This diminished 

 value of the intensity factor should be compensated by the use of a 

 slightly larger transmitting current. The required increase of current 

 may be easily computed by equation (111). 



27. Summary. — This paper contains a mathematical theory of 

 the flat-top antenna. The process employed consists in the integra- 

 tion of the effects of an aggregate of doublets assumed to be distributed 

 along the antenna so as to give a current distribution described by 

 equation (1) and illustrated in Figure 2. The electric and magnetic 

 field intensity due to each of the doublets is determined by the Maxwell 

 and Hertz Theories for all distant points in space. These field in- 

 tensities are summed up for all the doublets with strict allowance for 

 the differences of phase due to different doublets; the summation 

 gives the resultant field intensities. Then by Poynting'^ theorem 

 the power radiated from the antenna tlirough a distant hemisphere 

 (bounded by the earth's stu-face assumed plane) is computed by the 

 integration of a number of intricate expressions. From the radiated 

 power the radiation resistance is obtained by dividing by the mean 

 square of the current at the base of the antenna. Tables of coeffi- 

 cients for computing radiation resistance are given, and curves are 

 plotted of the calculated values of radiation resistance for different 

 ratios of the length of the flat-top to the total length of the antenna 

 and for different relative wavelengths obtained by loading the antenna 

 with inductance. Curves are also given for determining the relative 

 electric and magnetic field intensities in the horizontal plane for 

 dift'erently proportioned antennae variously loaded. Various equa- 

 tions developed in the treatment may find application to problems 

 in the design of radiotelegraphic stations. .Although this investiga- 

 tion was undertaken in ignorance of a simple case investigated by 

 Professor Max Abraham, by a similar fundamental method, his work 

 M'as discovered early in the course of the treatment and served as a 

 check on one of the resistance values here given. This paper may be 

 regarded as an extension of the remarkable work of Professor Abraham. 



Cruft High Tensiox Electrical Laboratory, 

 Harvard Uxiversity, Cambridge, Mass. 



