Behaviour of Air $c. under Powerful Electric Stress 243 

 A = — B ; hence 



# = A (cos n^— cos fi 2 0> 



f=-^-(cosIl 1 * + coslV).j ^ 36) 



If s is small, H l and fl 2 are nearly equal, and each pendulum 

 oscillates with amplitude varying between zero and a maxi- 

 mum, the maximum of one coinciding with the zero of the 

 other. The maximum amplitude is 2A for a?, and 2A/y/s 

 for f. The phases are, at first, a quarter-period earlier for £ 

 than for #. (See equations (26).) 



If the initial conditions are altered by making f vanish 

 instead of x, the plus and minus in the expressions for x and £ 

 win be interchanged, and the phases will, at first, be a quarter- 

 period earlier for x than for f, the equations being now 

 reducible to the forms 



tf=2Acbsi(f2 2 — Hj)* . cosi(n 2 + X2 1 )^ •) 



^^sini(V^.^P 2 + ^. )' * (37) 



This investigation applies to the experiment described in 

 Rayleigh on Sound, 2nd edition § 62 ; but the experiment 

 appears to have been stopped as soon as the lower pendulum 

 attained its first maximum. 



§ 14. Sellmeier (Pogg. Ann. vol. cxlv. p. 534) refers to 

 the transference of energy which goes on from one pendulum 

 to the other when the amplitudes vanish alternately, and 

 maintains that a similar transference of energy between par- 

 ticles embedded in the aether and particles of a fluorescent 

 body is the cause of fluorescence. He works out the case in 

 which sis small, a = 6, and one of the pendulums is initially at 

 rest in the zero position. 



XIX. The Behaviour of Air and Bare fed Gases under 

 Poiverful Electric Stress. By John Trowbridge*. 



IN the Philosophical Magazine for May 1897 I gave the 

 results of some experiments with high electromotive 

 force. I have lately increased the number of condensers in 

 my apparatus to one hundred and twenty, thus enabling me 

 to obtain an electromotive force in the neighbourhood of three 

 million volts. The behaviour of air under this electrical stress 

 is very interesting. Its initial resistance is greatly reduced ; 

 and the curve expressing the relation between spark-length 



* Communicated by the Author. 





