Thermodynamical Theory of Radiation. 2#T> 



propagated with the velocity of light. The ratio dtjdt is 

 thus found to be introduced as a denominator into the velocity 

 of the oscillating nias^, since Doppler's factor modifies the 

 duration of the oscillation propagated. Now the momentum 

 being proportional to the velocity, it is momentum in the 

 electromagnetic field that fulfils the requirements outlined 

 above, and this involves the assumption that field-intensity is 

 of the nature of momentum. 



In a memoir published by Bjerknes *, on the analogy 

 between the steady electromagnetic field and the hydro - 

 dynamic field, the author shows that field-intensity in the 

 electromagnetic field is analogous to momentum in the hydro- 

 dynamic one. There is between his conclusions, to which I 

 would draw attention, and the necessity of introducing 

 Doppler's factor, a concordance which is worthy of notice. 



XIX. On the Thermodynamical Theory of Radiation. 

 To the Editors of the Philosophical Magazine. 



Gentlemen, — 

 Mr. Tuckerman's criticisms f appear to be based on a mis- 

 understanding of my position. He brings as an objection 

 to my argument, that the temperature T is " a quantity which 

 is and can be defined only in terms of the properties of 

 matter." 



My argument was directed against the thermodynamical 

 proof of the laws of radiation. It is therefore sufficient for 

 my reductio ad absurdum that according to the thermo- 

 dynamical theory underlying this proof it is possible to 

 attribute temperature to the pether. (In the thermodynamical 

 proof in question we are concerned with an imaginary neat- 

 engine, using aether as working substance, and working 

 between temperatures T 1 and T 2 .) 



Apart from this, however, 1 wish to take this opportunity 

 of remarking that it is quite easy to eliminate the idea of 

 temperature completely from my original paper f. Let us 

 agree to measure the warmth of the radiator by a quantity E, 

 which is to be equal to the average energy of a principal degree 

 of freedom in ihe radiator, and therefore in the ordinary 

 notation, to -g-RT. 



The radiation-function <£ must be a function of X, E, V, e, 

 7n, and K. There are now six independent quantities and 

 four independent physical units, namely those of length, 

 mass, time, and inductive capacity. As before, we can 

 combine the six quantities in two independent ways so as to 

 * Archives des Sciences phys. et nat. 1005, t. xx. p. 325. 

 t Phil. Mag. Nov. 1906, p. 498. 

 X Proc. Roy. Soc. A. lxxvi. p. 545. 



Phil. Mag. S. G. Vol. 13. No. 74. Feb. 1<»07. X 



