202 PIERCE. 



due to the whole vertical 'part of the antenna. In this formula, referring 

 to Figure 6, 



ro = the distance OP in cm., 

 6 = the zenith angle ZOP, 

 b = length of the horizontal flat top in meters, 

 a = length of vertical part of antenna, in meters, 

 Xo = 4 (a -{- b) = natural wave length in meters, 

 X = wave length in meters actually emitted, and differing from Xo 



by virtue of the added inductance, 

 7o = amplitude of current in absolute electrostatic units at the base 

 of the antenna and related to I by the equation, 



ttXo 



/n = / sin 



2X 



We shall reserve comment on this equation until after investigation 

 of other characteristics of the radiation. See Part IV. 



8. Total Power Radiated from the Vertical Part of the 

 Antenna. — Having obtained in equation (19) the electric and mag- 

 netic intensities at any required point at a distance from the antenna, 

 we shall next compute the total power radiated from the vertical part 

 of the antenna, and shall then obtain its radiation resistance. 



Since Eq and H^ are perpendicular to one another and perpendicu- 

 lar to ro, we have, according to Poynting's theorem for the power 

 radiated in the direction of ro through an element of surface dS per- 

 pendicular to ro the quantity 



dp = ^EgH^dS. (22) 



47r 



Let the element of surface be an elemental zone on the surface of 

 the sphere, then 



dS = 2irro^ sin Odd (23) 



This quantity, together with the values of Ee and H^ from (19), 

 substituted in (22) and properly integrated, gives for the total power 

 radiated through the whole hemisphere above the earth's surface, 

 the value in ergs per second following: 



