( 116 ) 



living and a well-known shallow water form and was also observed 

 in glacial deposits and in Red and Coralline Crag in England as 

 well; a second species is found according to Darwin in tertiary 

 formations in Patagonia ; a third ( Verruca prisca) in the chalk of 

 England and Belgium. As far as we know the last-named species, 

 a certain affinity of this extinct species with several of the deepsea- 

 species of Verruca cannot be denied. But for V. stro'mia, the genus 

 Verruca, therefore, in this regard also would show a greater analogy 

 with Scalpel! tnn than with Pollicipes. 



Physics. — "Calculation of the pressure of a mixture of two gases 

 by means of Gibbs'.* statist lea I mechanics." By Dr. L. S. Ornstein. 

 (Communicated by Prof. H. A. Lorentz). 



By the method of statistical mechanics I have calculated in my 

 dissertation *) the pressure of a mixture of two gases, neglecting 

 terms of an order higher than the first with respect to tf, 3 , a 3 ' 

 and o'. The quantities <j, and ^ 3 are the diameters of the mole- 

 cules of the gases composing the mixture, and a has been put 



for . 



2 



In a recent paper') H. Happel has determined the pressure of a 

 mixture by means of a method due to L. Boltzmann, retaining terms 

 of higher order with respect to the above quantities. 



As the method of statistical mechanics seems to me more exact 

 than the one used by Happel, I have been led to apply it to the problem 

 which he has treated. 



J. W. Gibbs has shown 3 ) that the pressure of a gas is given by 

 the equation 



dW 



>'=-Jv < ! > 



where V is the volume, and '/' what may be called the statistical 

 free energy. We have therefore to determine this quantity W. 



Let us suppose that the volume V contains n x molecules of the 

 first kind with the diameter tf, and the mass m A , and n^ molecules 

 of the second kind with the diameter a. and the mass m„. 



*) Toepassing der statistische mechanica van Gibbs op molekulair-theoretische 

 vraagstukken. Leiden 1908. 



2 ) H. Happel. Zur Kinetik und Thermodynamik der Gemische. Ann. der Phys. 1908 

 Bd. 26 p. 95. 



3 ) J. W. Gibbs. Elementary principles in statistical Mechanics. New-York 190:2. 



