934 



I = av -\- bV + o l=r/-{-I, 



"ï at 



^//.^- 



W— ^ \I,dt = V= E — RI—W. 



Here W is the potential on the condensoi' C and M the coef- 

 ticient of mutual induction of the reaction coil. 



From these equations a differential equation for IF may be derived 

 d^W dW 



a 



^ _^yW=ff-\-Raf{t) ^ Laf{t). 



dt* dt 



where 



« ^ CL (1 + bR) 

 ^=CR{\^ bR) 4- 6L + aM. 

 y=\ +b{R + R) 

 rf= i^(c f bE). 

 The solution of this equation is of the form 



.., d ~^t /|/4a y— /?' ^ 



y V 2« y 



-■j- e~ " ÖJÜ J sin (2.T ?»< -j- X^ 



— e—(p-\-<') I aw B sin (2.T 7it + if'). 



If the circuit (LRC) is tuned to the incoming oscillations 



i^4:a y — /?- = 4t 7i«. Putting the damping factor ^ = Z) we find for 



2« 



the variable part of W an expression of the form: 



in whicii F, G and H are functions of <7, 9, L, /? and D only. 



The first four quantities are independent of the andion, the last 

 one D however is a function of a and b, but bj varying the coef- 

 ficient of mutual induction M of the reaction coil any value of D 

 may be obtained, so that independent of a and h the most effective 

 damping can always be obtained. 



So we come to the conclusion, that in a reaction circuit, when 



R and R' are not extraordinarily large, W^ is proportional to a 



a 

 and independent of the value -, which gave the maximum ampli- 



b 



fication in the previously treated cases. 



Eindhoven. Physical laboratory of Philips' incandescent 



lamp Works Ltd. 



