J 304 



/. V = [ r -]- — — ~ I I 

 z=z — J p M /, =z — j p M 



(23) 

 (24) 



^1 r -^j 

 From [To) uiid (24) it follows that 



XpM y, — r (.f, + .6',) f .c, .c, — ,y, y, .... (25) 

 -).p M.v^ = r Cv, 4- ./J + .r, y^ 4- ..•, .(/,.... (26) 

 These equations can only be satisfied in two manners, vvhicli by 

 substitution B can be deduced from each other: 

 First manner: //, pos., y, neg., M neg. 

 Second mannei-; //, neg.. //, pos., M pos. 

 'I'hey are given by fig. 9 and 10. 



Fig. 10. Fig. 11. 



The connection of fig. 9 is also frequently made use of. It was 

 thoroughly discussed by Vat.laiiri ')• That of fig. 10 so far has 

 apparently not been used. 



If the indirect coupling is applied and there is also a current in 

 the grid-circuit, the arbitrariness is so great, that it seems rather 

 difficidt to establish any general rules, except the substitution-rules 

 A and /i. Still for every special case the above calculation leads 

 directly to the result and gives a better survey than the solution 

 of a set of simultaneous differential equations. A simple instance of 

 these connections is given by fig. J 1 ; they occur very often. 



The same connections, which will make the audion generate, 

 are also exceedingly suitable for giving a good amplifying action. 

 Wlietlier an audion acts as a generator, depends in the end on the 

 roots of an algebraic equation of the //,'•' degree: 



o. p" + a, p" -'.... + a„ = 0. . . . . . (27) 



This equation has been obtained from a homogeneous linear 

 diffei-entia! oqiuition of the /i^'' order: 

 d'lw (J»—^.v 



dt" 



dtr^--^ 



-+.... + a„ z= 0, 



(28) 



'} See I.e. 



