Electric Waves along Wires. 663 



The relation between the maximum strength of the mag- 

 netic force at R and the length of the double secondary circuit 

 (provided resonance be undisturbed) is given by a curve whose 

 inclination at any point to the axis of x is given by 

 — X ■ (n + l)X __ X 



tan 



-{ 



n* 



(3) 



Now as in the demagnetization curve the maximum does not 

 appear as a cusp but is rounded off, the slope of the curve on 

 which it is superposed must displace it to the left (towards 

 the vibrator) by an amount depending on the slope of this 

 damping curve, and the shape of the curve near the position 

 of maximum intensity. The true position of the bridge for 

 resonance is that in which the slope of the experimental curve 

 is the same as that of the damping curve. 



Now (f> is known approximately in terms of ae~% Kx , for cj> is 

 the amplitude of oscillation when the circuits are tuned, and 

 ae~* Kx is the amplitude when there is no accumulation of effect 

 due to resonance. 



Let cf> = kae~^ kx . Then 



7.w+l p -(n+l)\x 



»-,-*■ =/< « 



Considering the extreme case in which the damping in the 

 secondary was greatest, i. e. with a secondary circuit of 

 platinum of diameter *0025 cm., by taking 6 = 1 in (4), an 

 inferior limit to. the value of e~ kx is obtained. 



The slope of the damping curve is, in this case, less than 

 the value given by 



As an approximation we write 



(1 — 6) being small in comparison with (1 



tan0=(- 

 \e> 



or 



tan0={^lo ge (l-i)}f 



(5) 



The position of the bridge for resonance is approximately that 

 in which the slope of the demagnetization curve is given by this 

 expression. With this wire, however, exact measurements 

 were impossible, and only an attempt at the order of result 

 was made *". 



* In these experiments the demagnetization was not accurately pro- 

 portional to the amplitude of oscillation for vibrations of the" same 

 frequency, as a uniform felt was not produced by the few turns round 

 the detector-needle. 



