284 Mr. P. E. Shaw on some 



III. The self-induction of a short flat coil, as used ior 

 sending or receiving, is 



L = 4Tr/in 2 a ( log e — — 2 U 



and for a long solenoid (neglecting a small correction for the 

 ends) 



T _ 47ryun 2 A 



' n •=■ number of turns ; 



a = radius of coil ; 



c = radius of wire; 

 I L = length of solenoid; 



A=mean sectional area. 



IV. Current Amplitude = 



V 1 + SK 2 (p -V 

 where -~ = natural frequency of circuit, 



^— = frequency of alternating-current in circuit ; 

 but "for " xa °t resonance, the current-amplitude = E /R; hence 

 for sharp resonance (since then p=p ), ^2 mil st be large. 



V. Magnification Ratio, due to resonance, is given by the 

 expression 



Y_p_L 



E ~~ R ' 



supposing the damping is small ; 



where E = impressed E.M.F. from current source, 



V = effective potential- difference at the condenser- 

 terminals. 

 Now we have as far as possible to arrange the circuits in 

 accordance with the above principles, and where these seem 

 mutually in opposition to make a judicious compromise. 



The desiderata are : — 



(1) R small, to obtain large current-amplitude, small 

 damping, sharp resonance, and large magnification- 

 ratio. Notice that R includes hysteresis if an iron 

 core is used, and eddy-currents in neighbourin " 

 circuits. 



