130 CARNEGIE INSTITUTION OF WASHINGTON. 



radiated by a radiating system in quanta of hv; second, that a radiating sys- 

 tem has the statistical properties of a perfect gas, i. e., that Maxwell's dis- 

 tribution law holds for the distribution of the local values of the energy among 

 the coordinates defining the state of the radiating system. (The usual auxil- 

 iary assumptions, such as Planck's oscillators or Larmor's regions of equal 

 probability, are not only unnecessary but misleading.) 



Although these two assumptions are sufficient for deriving the Planck 

 radiation law, both of them, and particularly the latter, are very dubious, 

 it being almost unthinkable that a radiating system can have the statistical 

 properties of a perfect gas and yet not have the equipartition law hold. For 

 these and other reasons it seems necessary to give up at least the second of the 

 quantum hypotheses and to assume that the distribution of energy in a radiat- 

 ing system does not obey Maxwell's law — that is, to assume that in a radi- 

 ating sj^stem the distribution of the local values of the coordinates is a 

 function not only of the energy of the system but also of some other vari- 

 ables. If we do this and assume, for definiteness, that the distribution of the 

 local values of the generalized momenta is a function not only of the total 

 energy E of the system but also of the Helmholtz free energy A, and further 

 assume that the total energy of a radiating system can not be less than a 

 certain limiting value Eq (Eq turns out to equal hv), we can, following the 

 methods of Gibbs and Ratnowsky, derive in a very simple manner the 

 Planck radiation law, and moreover we can do this without assuming 

 discreteness of radiant energy, without contradicting clasiical mechanics 

 (equipartition does not hold for systems of this kind), without discarding 

 infinitesimal analysis or without contradicting thermo-dyn amies or the 

 direct experimental evidence of the photoelectric effect that the hv law 

 holds only as a limiting case. 



A translation of the mathematical part of "The entropy equation of sohd 

 bodies and gases and the universal quantum of activity," by Simon Ratnow- 

 sky (Ber. phys. Ges., 16, 232, 1916) is appended. 



(6) The color of inorganic compounds. F. Russell v. Bichowsky. J. Am. Chem. Soc, 40, 

 500-508 (1918). 



It is shown that every valence state of an element can be associated by 

 means of purely experimental evidence with a definite "atom color." There 

 is a marked relation between atom color thus determined and valence and 

 valence variability. The atom color of every element in its normal valence 

 state, that is, in the valence state which corresponds to its place lq the periodic 

 system, is zero (all non-variant-valence atoms have their normal valence). 

 The atom color of an element, in valence states where the valence is decreased 

 or increased by an odd number from the normal valence, lies further in the 

 blue than the atom color of the same element in any other valence state. The 

 atom color of an element in a state whose valence is removed by an even num- 

 ber from normal will be zero if compounds of the element do not exist in which 

 the valence of the element is removed by an odd number from normal; other- 

 wise the atom color will lie further in the yellow than the atom color of the 

 same element in a state of valence removed by an odd number from normal. 

 Compounds between non-variant-valence elements will be colorless. Com- 

 pounds between a non-variant-valence element and a variant-valence ele- 

 ment will have the same color as the "atom" of variant-valence element. 

 Compounds between other elements will have colors more to the blue than 

 the sum of their atom colors. All these regularities can be deduced from a 

 variation of Lewis's theory of atom structure. The almost perfect accord 

 between the deduction and the facts indicates very strongly that Lewis's 



