I 



TRANSACTIONS OF SECTION A. 659 



all angles, we find that the pressure exerted is one third of the total density of 

 radiant energy. 



Adiabatics of an enclosed Mass of Radiation, and resultinrj General Laics. — Now 

 consider an enclosure of volume V containing radiant energy traveUing indiilerently 

 in all directions, and of total density E ; and let its volume be shrunk by SV. Thia 

 req^uires mechanical work ^ ESV, which is changed into radiant energy : thus 



EV + AESV = (E-8E)(V-8V), 



•where E-8E is the new density at volume V-8V. This gives | ESV = VSE, or 

 EocV-i. 



As already explained, if tlie original state has the constitution as regards wave- 

 lengths corresponding to a teniperature,T, the new state must correspond to some 

 other temperature T — ST. Thus we can gain work \>y absorbing the radiation 

 into the working substance of a thermal engine at the one temperature, and extract- 

 ing it at the other; as the process is reversible, we have by Carnot's principle 



iESy/EV=-8T/T, 



so that Tec V-i^. 



Thus EgcT'', which is Stefan's law for the relation of the aggregate natural 

 radiation to the temperature. 



Moreover the Doppler principle has shown us that in the uniform shrinkage of 

 a spherical enclosure the wave-lengths diminish as the linear dimensions, and 

 therefore as Yi, or inversely as T by the above result. Thus in the radiations 

 at different temperatures, if the scale of wave-length is reduced inversely as the 

 temperature the curves of constitution of the radiation become homologous, i.e., 

 their ordinates are all in the same ratio. This is Wien's law. 



These relations show that the energy of the radiation corresponding to the 

 temperature T, which lies between wave-lengtlis X and X + h\, is of the form 

 X '"/(yV) 8X. The investigation, theoretical (Wien, Planck, Rayleigh, etc.) and 

 experimental (Lummer and Pringsheim, Paschen, etc.) of the form of this function 

 f\& perhaps the most fundamental and interesting problem now outstanding in the 

 general theory of the relation of radiation to temperature. The theoretical 

 relations on which this expression is founded have been shown to be in agreement 

 with fact ; and it appears that the form c^e~''-'^'^ fairly represents y (XT) over a wide 

 range of temperature. These relations have been derived, as usual, from a 

 dynamical discussion of the aggregate intensity of radiation belonging to the 

 temperature ; it may be shown that the same results, but nothing in addition, will 

 be gained by applying the same principles to each constituent of range SX by 

 itself, assigning to each its own temperature. 



6. On the Infra-red of the Solar Si^^ctrum. ByTyr. S. P. Langley, F.R.S. 



DEPARTMENT OF ASTRONOMY. 

 Chaiemax : Dr. A. A. Cojimox, F.R.S., F.R.A.S. 



FRIDAY, SEPTEMBER 7. 



The Chairman delivered the following Address : — 



It has been decided to form a Department of Astronomy under Section A, and I 

 have been requested to give an Address on the occasion. In looking up the 

 records of the British Association to see what position Asutromimy has occupied, I 

 was delighted to fii d, in the very first volume, ' A Pteport on" the I'rogres.s of 

 Astronomy during the Pre-eat Century,' made by the late Sir Geor-e Airy, so 



U u3 



