Dr. W. H. Eccles on Coherers. 881 



but if the resistance of the material varies with its temperature 

 the relation between electromotive force and current will not 

 be linear. A direct experiment on a film of oxide of iron 

 showed that its resistance coefficient was negative and nearly 

 1 per cent, per degree centigrade. Calculation shows that 

 a resistance-temperature coefficient of this magnitude can 

 cause the voltage-current curve to deviate considerably from 

 a straight line. The equation of the curve is deduced below. 



If a train of electrical oscillations be passed through, the 

 minute mass of oxide traversed by the steady current, its 

 energy appears as heat in the oxide. The resistance falls in 

 consequence, and the equilibrium of the direct current in its 

 circuit is disturbed. Since the rise of current enhances the 

 heating of the oxide, the subsidence of the current to equi- 

 librium is somewhat prolonged when, as in the case of iron- 

 oxide, the resistance-temperature coefficient is negative. 

 Hence the effect on a telephone diaphragm, whose natural 

 period of vibration must be regarded as great in comparison 

 with the duration of a train of oscillations, may be very large. 

 It remains to be seen whether the disturbance of the direct 

 current, caused by a small variation of resistance, can account 

 for the phenomena disclosed in the course of the above- 

 described experiments. 



Let Wi be the fraction of the energy of a single train of oscil- 

 lations given to the variable resistance p of the detector; let 

 p = p (l — ol&) where p is the value of p at the temperature 

 of the surroundings. Then k W 1 = (&6)= — (&p)/p a, where 

 k is a constant involving Joule's equivalent and the specific 

 heat and the mass of the oxide. This initial disturbance (8p) 

 of resistance is accomplished in less than 1/10000 of a second 

 and gives rise to the perturbations of current to be traced 

 immediately. 



Let the direct current circuit of the detector comprise a 

 total invariable resistance r (which includes the resistance of 

 the telephone), the variable resistance p of the detector, and 

 the inductance L of the telephone. Let c be the current at 

 any moment and e the applied electromotive force. Assume 

 that the rate of loss of heat from the warmed mass of oxide 

 to its surroundings is md, wheie, as implied above, 6 is the 

 temperature of the oxide above the temperature of the sur- 

 roundings, taken as zero. Then at any time t 



kpc 2 — m6, (1) 



dt 



and 



l^ + (r + p)c = e (2) 



