of Ether Waves in Air. 11] 



The current amplitude is therefore 



The average current depends on how it is measured ; its 

 square may be ^C 2 . Bat if it is considered as the quantity 

 passing in half a swing, C = */JT, the radiation expression 

 becomes 



16ttVFu 4tt 4 C 2 / 2 400 /nvGH 2 400 x 10 1( yCT 2 



~3K*?~ = 3K,\ 2 = - IST ■ = " ~X 2 ergs per sec. 



But in electromagnetic measure the unit of current is 

 10 amperes, and 10 10 ergs per second is a kilowatt, so the 

 formula for radiation power is proved; and the true radiation 

 (subject to correction for the numerical factor) is 



I 2 

 4 x (mean amperes) 2 x r-g kilowatts, . . . (5) 



I being the effective height, or linear factor of the electric 

 moment, of the radiator. 



There are many circumstances which it would seem 

 necessary to take into account besides those which appear in 

 this formula. Capacity, for instance, and self-induction, and 

 arrangement of antenna generally. But they are all im- 

 plicitly involved in the wave-length, and there is no need 

 specially to attend to them except in considering the design 

 of an antenna. For that purpose it must be remembered 

 that in true waves the electric and magnetic energies are 

 equal, and in any region where they are not equal the excess 

 of one is useless for wave emission. At great distances the 

 electric and magnetic intensities are necessarily and auto- 

 matically equal, because any other part of the energy has 

 returned to the oscillator and is promoting persistence of 

 vibration, which in the case of shock-excitation is a useful 

 thing to do. 



But to determine the conditions which assist radiation we 

 may calculate separately the electric and magnetic intensities 

 at points on the equator fairly near the oscillator, within 

 say a quarter wave-length ; or perhaps most simply at the 

 critical distance r = \/7r x /2, characterized by m 2 r 2 = 2 3 the 

 place at which progressive radiation really begins. 



It is manifest that the shorter the wave-length the stronger 

 will these intensities be, and hence the stronger the radiation, 

 other things being equal ; for the radiation through unit 

 area at every place is by Poyn ting's theorem EH/47T. 



Consider therefore the circumstances on the equator of a 



