( ^08 ) 



Physics. — Prof, van deu Waals presents for tlie Proceedings 

 of the meeting a paper of Prof. L. Poltzmann, foreign 

 member of the Academy,: "0/< the characteristic equation of 

 V. D. Waals," with an accompanying letter from which the 

 following extract has been taken. 



Vienna, IMarch 2'"i 1899. 

 Dear Sir, 



Mr. VAN Laar has sent me from Utrecht a calculation which he 

 undertook at your demand. From this I have calculated the next 

 correction term of your formula in the same way as I have followed 

 in the second part of my gas-theory, and I take the liberty of sending 

 the MS. to you. The result will differ in some respects from the one 

 you obtained, but I should consider a discussion about it very inte- 

 resting on mathematical grounds ; not so much on physical grounds, 

 as the further correction terms are certainly not calculable. Under 

 slight pressures the observations are too inaccurate for this term to 

 be useful, while for high pressures more approximation terms would 

 be required. Moreover no observations have been made on //,7-vapour, 

 argon, helium, where spherical molecules may be presumed. I should 

 be pleased if you would lay my MS. before the Amsterdam Academy 

 of Sciences and I should like it to be printed in its Proceedings, 

 because I think this the best way to attain my purpose, viz. to 

 incite those who are interested in this question to a discussion which 

 mi"'ht be useful to science 



Yours truly 



LUDWIO BOLTZMANN. 



At the demand of Prof, van der Waals, Mr. van Laar has 

 calculated a formula which may be used for the calculation of a 

 further approximation term in the former's formula. I shall show 

 how Mr. VAN Laar's formula may be used for the further deve- 

 lopment of my calculation relating to this subject, and make use of 

 the same notations as in the second part of my "Lectures on Gas- 

 theory", which I shall always briefly quote as 1. c. 



L Calculation of the space left for the centre of a new 

 molecule to he introduced into the gas. 



Let F be the volume of a vessel, in which there are found n very 



