220 Mr. F. B. Pidduck on a Method of Measuring 



(d) The effect of varying the reaction coupling on the- 

 form of the anode and grid current variations is studiq.d and. 

 the results explained in terms of the simple theory (a) 

 and the filament cooling effect (c). Secondary emission is- 

 found to play an important part in the action of a triode 

 even at low anode potentials. 



(e) A method of investigating the Joulean heating effect 

 of the filament by the emission current is described, and it is- 

 shown that when the emission current flows through the 

 filament in the same direction as the filament current 

 the emission is 25 per cent, greater than when it flows in 

 opposition. 



(/) A further discussion of the thermal alterations pro- 

 duced in the filament on closing the anode circuit shows the 

 possibility of running the electronic discharge without a fila- 

 ment heating battery, the filament being maintained at an 

 emitting temperature by the effect of the emission current 

 itself. A special method of starting such a discharge would 

 be required. 



XXVI. A Method of Measuring the Self-inductance of Small 

 Loops. By F. B. Pidduck, M.A., University Lecturer 

 in Applied Mathematics and Fellow of Queen s College, 

 Oxford *. 



1. Introduction. 



THE suggestion has several times been made of an alter- 

 nating current galvanometer based on the couple ex- 

 perienced by a ring or disk suspended in an alternating 

 magnetic field f. It appeared to the writer that the method 

 could be advantageously used to determine small self-induc- 

 tances in absolute measure, as considerable forces can be 

 developed in quite small rings J. If a plane circuit of area A 

 lies in a uniform magnetic field of strength H cos pt at time t r . 

 its normal making an angle 6 with the field, it is easy to show § 

 that the mean couple on the circuit is 



L» 2 H 2 A 2 

 2(Ly + R*j C0S * sin *' 



* Communicated by the Author. 



t J. A. Fleming, Electrician, xviii. p. 561 (1887) ; Elihu Thomson,. 

 Trans. Amer. Inst. Electr. Eng. iv. p. 160 (1887). 



J On the measurement of small inductance, see L. Prerauer, Wied. 

 Ann. liii. p. 772 (1894); M. Wien, Wied. Ann. liii. p. 928 (1894);, 

 F. Dolezalek, Zeitschr. f. Instrument enkunde, xxiii. p. 246 (1903); A. H. 

 Taylor, Phys. Rev. xix. p. 273 (1904) ; E. Giebe, Ann. d. Phys. [4] xxiv_ 

 p. 941 (1907). 



§ Cf. G. T. Walker, Phil. Trans. A. 183, p. 290 (1891). 



