Effect of Pressure on Temperature of Crater of Electric Arc. 381 



times, there was undoubtedly absorption 'from this cause. We 

 certainly got no evidence that there is any appreciable increase 

 of temperature. When the arc was started in the gas at a low 

 pressure and then the pressure was raised, the radiation at the low 

 pressure was greater than at a high pressure ; but when the arc was 

 started first in the gas at high pressure, and then the pressure 

 reduced, the radiation was rather higher in the gas at high pressure. 

 From all this we concluded that the greater part of the differences 

 we were observing were due to the absorption of the light in the long 

 tube already mentioned, which increased the longer the arc was 

 kept burning, and was probably greater at high than at low pressures. 

 The best observations were made with variations of pressure from 15 

 up to 100 Ihs. per sq. in., and there seems very little evidence of much 

 change of radiation with this change of from 1 up to between 6 and 

 7 atmos. 



The whple question is surrounded with great difficulty. If the 

 carbon be really in equilibrium with its own vapour at the tempera- 

 ture of the crater and at the pressure of the surrounding atmosphere, 

 some relation must exist between the change in pressure and change 

 in temperature of the crater. If we knew the latent heat of volati- 

 lisation of carbon, we should be able to calculate the change of tem- 

 perature from the well-known thermodynamic formula 



ST Av 



Aw can certainly be approximately determined on the supposition 

 that the absolute temperature of the crater is fifteen times the abso- 

 lute temperature of the freezing point, i.e., 3800. We thus get for 

 gaseous carbon Av = 10 4 , q.p., at this temperature. For 1 atmos. f>p 



= 10 6 , q.p., so that 



cT 1Q 1U 



Hence, unless the latent heat of carbon be enormously great com- 

 pared with that of other substances, cT/T will be considerable. If X 

 be as great as the latent heat of vaporisation of carbon given by 

 Trouton's law, i.e., about 4000 calories, or 16'8 X 1C 10 ergs, T/T 

 would be about -fr, and T would be nearly 220 C. for each atmo- 

 sphere, and a change of pressure of about 18 atmos. would raise the 

 temperature of the crater to that estimated for the sun. The corre- 

 sponding increase of radiation would be very great, for the radiation 

 varies, at least approximately, as the fourth power of the absolute 

 temperature. This would lead one to expect that the radiation would 

 be nearly doubled for each 4 atmos. added. Such an increase as 

 this certainly does not take place, so that we may conclude that 

 either the temperature of the crater is not that of boiling carbon, 



