aon 



by trying- n isolnlioii of liio forni ,r = J^/'' . Here the <r's are fiiiu'tions 

 of the alternating current-resistances ; .r indicates a ciineiii or a tension. 

 If at least one root p ^= p„ is a pure imaginary quantity, free nn- 

 (laniped vibrations can occnr. Where the audion is aj)plied in a receiving- 

 station for wireless telegraphy, the grid-potential is subjected to a 

 forced vibration on account of the coupling with the antenna. Instead 

 of (28) we now obtain an equation with a right-hand side of the 

 following form, in complex notation'): 



d»x d' I 



f a' 



hu'i't. 



(29) 



where // is a pure imaginary quantity. 



The particidar solution, which gives the forced vibrutioii is found 

 by putting ,v=zA'ei''^. To determine the amplitude A' , we have: 



(«o p„ f . . . . a„ 

 If })' is equal to an (imaginary) root />, of (27), we can make 

 the denominator of the right-hand side of (31) as small as we like, 

 by making the constant a' but little different from a^ etc. in (27). 

 A limit is only given by the condition, that the natui'al vibrations 

 determined by : 



«>'" f ....«'„ = (31) 



have to be sutïiciently damped; therefore it is necessary that the 

 roots of (32) have a sufficiently large real part. Hence by a coupling 

 as that of fig. 12 the object is attained of the system having' but 

 little friction for the forced vibration. 



The audion is exceedingly well 

 . -, ■ adapted to receive undamped waves. 



1 c>i According to the heterodyne-principle 



local oscillations are then excited in 

 the receiving station, which give rise 

 to beats of audible frequency which 

 can be detected in the ordinary mannei- 

 . , by rectifier and telephone. The audion 



y\ f is then tuned in such a way, that the 



natural frequency differs but slightly 

 from that of the forced vibration. It is 

 then obvious that the svstem for this 



ié0 



Fig. 12. 

 vibration has but little "friction 



1) We reserve the o's without accents for the special <ase, that these quantities 

 are chosen in such a manner that (27) has one root, which is a pure imaginary 

 quantity. 



