876 Prof. H. L. Callendar on 



simplest relations between the various quantities, in addition 

 to giving very good agreement with experiment. The in- 

 trinsic energy of a volume v such that ]jv = 1R,T, is simply 

 Rbv, and the corresponding expression for the entropy is 

 R(l + bv/T). 



If the latent heat equation, T(d^/6?T) v = E/r -\-p, is integrated 

 at constant frequency on the assumption E/pv = Z>v/T, we 

 obtain immediately the expressions previously given (loc. 

 at.) for the partial pressure, intrinsic energy, and latent 

 heat, per unit range of v, namely, 



Partial Pressure, pdv=Cv 2 Te-W T dv, ... (4) 



Intrinsic Energy, (E/v)dv=Obv i e- bv l T dv, . . (5) 



Latent Heat, Idv = 2 T(1 + bv/T)e~ bv ' T dv, (6) 



The partial pressure p is proportional to the energy- 

 stream q in an isothermal enclosure, and is identical in form 

 with the expression originally proposed by Lord Rayleigh 

 (Phil. Mag. xlix. p. 539, 1900) to represent the energy- 

 stream. His method was founded on the doctrine of the 

 equipartition of energy, and gave no explanation of the 

 exponential term. This factor arises in the present inves- 

 tigation directly from Carnot's principle, and is explained by 

 the continual degradation of the higher frequencies owing to 

 the Doppler effect in isothermal emission, which appears 

 to afford a possible way out of the difficulty raised by Jeans 

 in discussing the problem from the point of view of equi- 

 partition. 



Comparison with Experiment. 

 The quantity measured in experimental work is either the 

 rate of loss of heat of a more or less perfect adiator, or else 

 the rate of reception of heat by a receiver absorbing a known 

 fraction of the radiation from a source of the "black body''' 

 type. In either case the quantity measured is proportional 

 to the latent heat of emission as already defined^ and not to 

 the energy-stream existing in the state of equilibrium, except 

 in the case of full radiation for which T(^Q/<iT) = 4Q. The 

 full stream, Q = crT 4 , emitted per second per sq. cm. from a 

 small aperture in a black body at a uniform temperature T, 

 is equal to c/4 of the full energy density U, or to 3c/4 of the 

 full pressure P, and is the same as T(dQ/<iT)/4. But the 

 quantity measured for each separate frequency per unit range 

 is not q = cw/4 = 3c/>/4, as generally assumed, but T(dq/dT) v /4:, 

 which is proportional to the latent heat of emission T(dp/dT) v 

 per unit volume. The value of the full pressure P, obtained 



