the Self-inductanee of Small Loops. 221 



tending- to increase 6. It the circuit is not plane we can 

 nevertheless associate with it a plane circuit, rigidly attached 

 to it, such that the areas of projection on any plane are 

 equal. If the circuit is suspended by a torsion fibre giving 

 a couple of fi units per radian, and a. is the deflexion pro- 

 duced by an alternating field of effective strength H, 



L/> 2 H 2 A 2 a . a 



P" — t 2 2 ■ t>' : cos sin 0. 

 ^ L 2 jr + R- 



Writing 1 for the moment of inertia of the circuit about 

 the suspending fibre, and T for the time of swing in the 

 absence of a magnetic field, we have therefore 



Lp 2 87T 2 Ia 



JJp2 -jTfi* = H 2 A 2 T 2 sin 20 ' 



It is advantageous to work near the position 6 = ^tt, when 

 sin 20 may be put equal to unity. Then we have for low 

 frequencies, where Lp/R is small, 



L =-H]Ey 2 > w 



q being the frequency of the alternating current. For high 

 frequencies, where Lp/R is large, 



L ~^LT (2) 



To measure R in situ we may substitute for the alternating 

 field a constant field H, and measure the damping about the 

 position 6 = \ir. The damping factor in a small swing is 

 e~ xt , where 



H 2 A' 2 

 \ = const + -tt^t (3) 



4RI v J 



The making and breaking of the exciting current will itself 

 provide a momentary couple for setting the coil in motion. 



2. Low- frequency experiments. 



Experiments with alternating current of low frequency 

 •showed that the effects observed are approximately of the 

 right magnitude, but several causes combine to render such 

 •experiments inaccurate. The value of R derived from che 

 damping experiments, not in themselves very accurate, is 

 squared in (1), and the same holds of the magnitude and 

 ifrequency of the exciiing current. The irregularities oJ 



