870 



3. The temperafnre coefficient was small: 1.06 — 1.11 for 10°. 



4. The velocity of the pinacone formation is greatly dependent on 

 the alcohol; for instance, tiie methyl alcohol and the ally] 

 alcohol were oxidised much more slowly than other primary 

 and secondary alcohols. 



5. The velocity of the pinacone formation is greatly dependent 

 on the ketone, Ihe benzophenone is attacked rapidly, most of 

 the ketones as yet examined less rapidly, many not at all. 



6. The ratio of these velocities in different alcohols is constant. 



7. The active light of ihe ketone reduction is sure to be situated 

 in the specti'iun between 400 and 430 mi and very probably 

 in, or adjacent to, the rays 404.7 and 407.8 of the mercury 

 quartz lamp. 



8. The ratio of the velocities of the pinacone formation in sun- 

 light and in mercnry light is the same. 



9. When two ketones are present simultaneously one of them 

 absorbs a part of the i*ays recpiired by the other ketone; this 

 also appears when the light passes through a solution of the 

 one ketone and falls on that of the other. 



Particularly in the case of the powerfully absorbing ketones 

 the hindrances are stronger than was to be expected. 

 Delft, October 1914. 



Physics. — ''Simplified deduction of the formula from the theory 

 of comhinatioiu ivhich Planck uses as the basis of his radiation- 

 theory."" By Prof. P. Ehrenfest and Prof. H. Kameriingh Onnes. 

 (Communicated in the meeting of Oct. 31, 1914). 



We refer to the expression 



V' {N-l-\-P)f 



p Ff{N-iy ^ ^ 



which gives the number of ways in which X monochromatic reso- 

 nators R^, R,^, . . . Ry may be distributed over the various degrees 

 of energy, determined by the series of mnltipies 0, f, 2e . . . of the 

 unit energy e, when the resonators together must each time contain 

 the given multiple Fe. Two methods of distribution will be called 

 identical, and only then, when the first resonator in the one distri- 

 bution is at the same grade of energy as the same resonator in the 

 second and similarly the second, third, .... and the Xth resonator 

 are each at the same energy-grades in the two distributions. 



Taking a special example, we shall introduce a symbol for the 

 distribution. Let ^Y=4, andP = 7. One of the possible distributions 



