the Goldschmidt Dynamo. 769 



Thus to summarise sufficiently, ignoring differences in R 

 for the moment, call jpM/R = c, for all four circuits. 



# = ?/ {|c 3 sin3p£ + c(ic 2 — 1) siiij?£} . . . (3') 

 y = t Jo {3c 4 cos Apt + c 2 {2c 2 -1) cos2pt + l}. . (4') 



There are really four characteristic constants 



pM. pM pM. pM 

 R : ' R 2 ' R 3 ' R 4 ' 



which we may denote by c 1? c 2 , c 2 , c 4 , respectively, and so 

 can write the values 



x - CiJ/o{| c 2^3 sin Zpt + (ic 2 <? 3 — 1) sin pt] . . (3") 



y — ?/ =CiC 2 3/o{3c 3 c 4 cos 4p£ + (2c 3 <? 4 — 1) cos 2p£}. . (4") 



To cancel the p frequency, c 2 c 3 must equal 2, or p 2 M 2 = 2R 2 R 3 . 



To cancel the 2p frequency, c 3 c 4 must equal J, or ^> 2 M 2 = ^R 3 R 4 . 



To cancel both, 2R 2 R 3 must equal ^R 3 R 4 , or R 4 =4R 2 . 



It is not likely that these cancelling conditions can be 

 satisfied ; nor is it at all certain that it would be desirable 

 to satisfy them, since possibly if any intermediate step 

 were omitted the graduated rise of frequency might cease. 

 But the partial cancelling of merely auxiliary currents 

 is of interest, and ought to have some effect in reducing 

 unnecessary iron losses. The highest frequency losses are 

 inevitable, and the limit of practicable frequency will be 

 reached when hysteresis and other such losses become too 

 prominent in comparison with what is available for radiation. 

 But it must always be remembered that the shorter the wave 

 the more powerful is the emission ; and so, presumably, the 

 shorter the wave the more vigorous would be the reception at 

 a distance, save for difficulties connected with transmission 

 and accidents by the way. 



Part II. On the Transmission of Waves in Air. 



The rate of emission of energy from an aerial was calcu- 

 lated by Fitz Gerald for a magnetic radiator in 1883, and by 

 Hertz for an electric one in his great paper of 1888. Hertz's 



