actuated hy Resistance-temperature Variations. 129 



and the telephone; it is supposed constant. Let c be the 

 current when the electromotive force applied to the detector 

 is e. Assume that the rate of loss of heat from the warmed 

 contact is m0, where 6 is the temperature of the contact 

 above that of the surroundings. Then it was shown that in 

 the steady state 



. -(l4§? + ')< V 



where p is the resistance of the contact when cold and q is a 

 constant. If the curve e=/o c/(l + qac 2 ) be plotted with e as 

 abscissae and c as ordinates, it is seen to rise from the origin of 

 coordinates with an increasing gradient till at a definite value 

 of e it becomes vertical. Then as c increases, the curve bends 

 towards the axis of c and approaches it asymptotically. 

 Along this latter part of the curve, increasing current is 

 associated with decreasing electromotive force — an unstable 

 state of affairs. Any conductor possessing a negative tem- 

 perature-coefficient of resistance exhibits these properties. 

 In such conductors an increase of current produces, in ac- 

 cordance with Joule's law, an increase of temperature, and 

 consequently a diminution of the resistance. The curve 

 shows that after a certain stage is passed the diminution of 

 the resistance which accompanies increasing current is great 

 enough to lead to a catastrophe. Stability can, however, be 

 obtained by introducing into the circuit of the variable re- 

 sistance p a sufficiently large constant resistance r. The 

 phenomenon resembles that of the electric arc. The unstable 

 portion of the above curve corresponds, in fact, to the " falling- 

 characteristic " of the arc. 



If the resistance r is large the e, c curve has a positive 

 gradient throughout, and the gradient has a maximum at 

 some value of e. Near this point the contact is found to 

 >vork best as a detector of oscillations. The hypothesis put 

 forward by the author supposes that a train of oscillations, 

 by yielding its energy as heat to the contact, raises the 

 temperature there and disturbs the existing equilibrium of 

 current and voltage. The dissipation of a train of oscillations 

 is accomplished in a time of the order of a fifty-thousandth 

 of a second ; the ensuing fluctuation of the current causes 

 the sound in the telephone. In the paper cited, the energy w 

 given to the telephone circuit was shown to be connected 

 with the energy W delivered by the train of waves by the 

 equation 



w=m(W-a), (2) 



where m and a are constants for any fixed value of the 

 Phil Mag. S. 6. Vol. 20. No. 115. July 1910. K 



