ON ABSORPTION SPECTRA OK OROAMIC COMPOUNDS. 303 



As regards the effect of temperature on the phase in which molecules exist, 

 it must be remembered that the only method by which a molecule can absorb 

 cr evolve energy is in terms of its atomic quanta, or of integral multiples of 

 these. Whatever may be the phases co-existing, increase of temperature means 

 the supply of whole numbers of atomic quanta, and therefore an inevitable 

 change of phase in some of the molecules. This is evidenced by the change in 

 refractivity observed with change in temperature, and it has been found possible 

 in this way to express the specific heat of a compound in terms of its molecular 

 quantum. Since the frequencies of all the absorption bands shown by a sub- 

 stance in the visible and ultra-violet are exact multiples of the molecular fre- 

 quency, the calculation of the constants in the Sellmeyer formula is very simple. 

 Let a substance having a molecular frequency of r^. exist as an equilibrium 

 mixture of two phases, the phase frequencies of which are xv ^ and yi\ re- 

 spectively. ,r and y being two whole numbers. Further, let the freciuency xv ^^ 

 lie in the near ultra-vio]et and therefore be known, and let the volume of the 

 molecules existing in this phase be 1 and the volume of those existing in the 

 phase with frequency yi\ be V. The formula then becomes 



(n - 1) (V + 1) 



and since xv^ is known the values of N. V. and //c^ can readily be found 

 from four measurements of the refractive index. When the temperature of the 

 substance is raised, the amount of energy absorbed can readily be calculated 

 from the molecular specific heat and the rise in temperature, and from this 

 the number of molecular quanta that have been absorbed can be found. Since 

 the absorption of one molecular quantum changes one molecule from one phase 

 into the next, the total number of molecules that have changed phase can be 

 determined. 



This method of calculation has been proved to be correct in the case of 

 methyl hexyl ketone, the refractive indices of which have been determined at 

 10° and SO'^. It liappens that the amount of energy necessary to raise the tem- 

 perature of one gram-molecule of the ketone from 10° to 80° is very nearly equal 

 to two molecular quanta per molecule, and, therefore, very nearly the whole 

 of the molecules undergo a change from their original phase into the next phase 

 but one. The ketone exhibits an absorption band in the near ultra-violet, and, 

 since this band does not change when the substance is warmed, the phase change 

 is restricted to the molecules which exist in the phase with frequency in the 

 extreme ultra-violet. As the number of molecules in this phase is relatively 

 very large, it will be sufficiently accurate to assume that all these undergo the 

 two changes of phase. 



At 10° the refractivity of methyl hexyl ketone is very accurately expressed 

 by the genera] formula 



fn-l)(V+l)=-N_ , NV 



xi\^ — v'^ yr^^ — r"'" 



and at 80° the refractivity (duly corrected for the change in density) is expressed 

 by the formula 



the accuracy being well within the experimental error. This phase change 

 produced by temperature change has also been proved with other substances, and 

 the phenomenon is one of great importance. It not only affords conclusive 

 proof of the existence of a large proportion of the molecules in a phase with 

 frequency in the extreme ultra-violet, even when the compound shows an absorp- 

 tion band in the visible or near ultra-violet, but it also proves that the specific 

 heat of a substance can be quantitatively expressed in terms of the molecular 

 quantum of that substance. It may be noted in passing that, whilst it is a 

 general rule that the greater proportion of the molecules of a substance exist 

 in a phase with frequency in the extreme ultra-violet, there are .some molecules 

 the greater proportion of which exist in a phase with frequency in the visible 

 region. This is the case with the dyestuffs. the extraordinary intensity of colour 

 1022 V 



