J302 



Bv yiil)sti(iitiiig- z^ = j\ -\- Ji/^ elc, where J - l/ — 1 and putting' 

 tlie real and tlie imaginary |)arts of (16) separately equal to zero^ 

 we obtain : 



.r, |../ + (1 f/)^\"| ^.-r(.c, f .r,)-.v,|^/ + (l + /) y," | = (17) 

 y, I -r/ f (1 -f /) .V," j 4- r (j/, + t/,) -f -t', \ .'// f ( 1 4" '^) .v/' I =- (18) 



The v's and possibly also the x's contain the frequency /i. By 

 eliminating /> from (17) and (18), we obtain a relation for the con- 

 stants of (he circuit : 



x]^ {r, R,L,(.\ . . .) = (19) 



which must be satisfied, in order that permanent allernating currents 

 may exist. Besides either of the eqiuitions (17) and {lb) can be employed 

 for the determination of the frequency. (19) gives a necesmnj condi- 

 tion ; it is also siif/icient, if (17) or (18) contains one real root. 



If /> has a real value, d\, .i.^ etc. are essentially positive as having 

 the character of ohmic resistances; r and A are positive audion- 

 constants; //i,//, ... are either positive (of the nature of a self-induc- 

 tion) or negative (capacity). From (17) and (18) it is obvious, that 

 connection 1 can oidy be made in two essentially different manners. 

 From (17) it may be concluded, that y, and i/\ -|- (1 -\- ?.) t/\ must 

 have the same sign, from (18) il follows, that ?/,=ƒ/',-(-//", and//, 

 must be of a different sign. 



First manner: 



tj^ and y'\ positive; //i' negative, whereas 



.v," + .v.<-.v/<(i ' ^).v/' im 



This connection in its simplest form is given by fig. 6. Now (20) 

 assumes the form : 



hence it follows that 



Instead of (17) and (18) we obtain: 



p L, R, (1 I /.) + r I p {L, t L,) - i j + « i - -^ + (1 I /)pL, [ .-. 



whence by elimination of /> the rather complicated condition for 

 oscillation can' be deduced. 



