250 



PIERCE. 



PART V. 

 Field Intensities and Summary. 



26. The Electric and Magnetic Intensities at a Distant Point 

 in the Horizontal Plane. — Equation (19) gives the values of the 

 electric and magnetic intensities at a distant point due to the vertical 

 portion of the antenna. If we replace I of that eciuation by its value 

 in terms of lo from equation (6), and make cos 6 = 0, we have the 

 intensities in the horizontal plane in terms of lo, which is the amplitude 

 of the current at the base of the antenna. This gives 



Ee = H^ = — cos — (ct — To) 

 cro X 



cos B — cos G 



sm 



ttXq 

 2X 



(111) 



The quantities outside the square brackets are constant for a given 

 distance Tq and a given amplitude of transmitting current lo. The 

 relative intensities are therefore determined by the factor in the square 

 brackets, which we may designate by 



X = 



cos B — cos G 



sm 



2X 



(112) 



Using the values of B, G, given in equation (20) and the value of 7 in 

 (110), this equation (112) becomes 



cos 7 



X = 



ttXo \ xXo 



2X j - "°^ 2X 



sin 



ttXq 

 2X 



(113) 



This quantity X we shall call " The Intensity Factor in the Hori- 

 zontal Plane." It is to be noted that the electric and magnetic 

 intensities in the horizon plane are not eflFected by radiation from the 

 flat-top; for, by equation (55), the field intensities from the flat-top 

 are zero for z = 0; that is, all over the horizontal plane through the 

 origin. 



