793 



n' 1 1 



E cos pt = EI cos (pt -\- ^) 5T7<r" ^ *^"^* (P^ + ^) -^ - 



p8H"-I '^ '^^ s^(n/_p2) 

 from which / can be found. The sum in the second member can 

 be put in a wa}' analogous to that of § 3, into a form identical 

 witii (18). Our result does not agree with that of Crehore (compare 

 p. 214). In our solution the retardation of phase is the same for all 

 vibrations, which is not the case in Crehore's paper. 



It may be observed that in our problem we have to do with a 

 system of an intinite number of variables in which a dissipation- 

 function couples the variables; for eliminating J from (12) and (13), 

 we obtain 



ffs -\- ns' */ = ^ — * • 



sjzqR s 



The dissipation F takes the form 



8//^ / (fs 



Groningen, Sept. 1914. 



Physics. - — ''Accidental deviations of density and opalescence at 

 the critical point of a single substance." By Dr. L. S. Ornstein 

 and F. Zernike. (Communicated by Prof. H. A. Lorentz.) 



(Communicated in the meeting of September 26, 1914). 



I . The accidental deviations for a single substance as well as 



for mixtures have been treated by Smoi.uciiowski ^) and Einstein ") 



with the aid of Boltzmann's principle ; by Ornstein -') with the aid 



of statistical mechanics. It appears as if the considerations used and 



the results obtained remain valid in the critical point. Smolücho\\ski 



has applied the formula found for the probability of a deviation 



to the critical point itself, and has found for the average deviation 



of density 



_ 1.13 

 6 = 



He has used this formula to express in terms of the mean density 



^) M. Smolughowski, Theorie Cinétique de I'opalescence. Bull. Crac 1907 p. 1057. 

 Ann. der Phys. Bd. 25, 1908, p. 205. Phil. Mag. 1912. On opalescence of gases in 

 the critical state. W. H. Keesom, Ann. der Pbys. 1911 p. 591, 



2) A. Einstein. Ann. der Phys. Bd. 33, 1910, p. 1276. 



3) Ornstein, These Proc, 15, p. 54 (1912), 



