226 



Measuring the Self-inductance of Small Loops. 



corresponded to the position 6 = %7r of the ring. The fol- 

 lowing figures for ring (1) will show how the experiments- 

 were conducted : — 



Zero 46-60 cm. 



Final position 27'02 cm. 



Thermo-ammeter 58*2. 



Calibration '0509 ampere =49*2 on scale. 



Time of 10 swings 135-2, 134-8, 135*0. T = 13-50 sees.. 



True H = 1-003 x 6"47 x ^| x *0509 =0*3907 gauss. 



Angular deflexion of ring, reduced to arc, ^(-1923). 

 L _ ( 3907 x 12-95 X13-50) 2 



39-48 x 7-565 x '1923 ~ b 2 cm " 



The resistance of the ring at 3250 metres (p = 5'8x 10 5 ) is 

 calculated to be 1*8 X 10 6 absolute E.M.U. The correction 

 H 2 /Lp 2 is 0'12, giving L = 811 cm. from the experiments. 

 Repetition also gave 81*1. The theoretical inductance* at 

 the same frequency is 81*7 cm. 



The aluminium ring gave L=*52'4 cm. and 51*8 cm. in 

 two experiments. The theoretical inductance for a ring of 

 circular cross-seclion and the same area is 51'0 cm. at 

 3250 metres. The copper ring (4) gave L = 22"56 cm. and 

 22*68 cm. in two experiments uncorrected for resistance. 

 A quartz fibre was used. The resistance correction is rather 

 high, 0*93 cm. On the mean we have therefore 21*7 cm. 

 for the inductance at 3250 metres. Calculation gives 

 21*7 cm. The small solenoid (5) gave L = 51700 cm. before 

 correction. The low-frequency resistance was 1-04 ohms. 

 A rough experiment to ascertain the resistance at 3250 

 metres gave values 1*0 and 1*2 ohms. Since ~Lp is about 

 30 ohms, the resistance correction is hardly appreciable. 

 The calculated inductance, with spacing correction, is 

 53,700 cm. Ti:e correction for frequency is not known, 

 but not likely to exceed 100 cm. An experiment with a 

 known capacity, waveineter, and buzzer, gave L = 52,000 cm. 



Collecting these results, we have : — 



Inductance at 3250 metres. 



Obs. Calc. 



Ring (1) 81-1 81-7 



Ring (2) 52-1 51*0 



Ring (4) 21-7 21-7 



Solenoid (5) 51700 53700 



* NeglectiDg the effect of curvature. For tables, see Jakuke-Emde^ 

 Funktionentafebi, p. 147. 



