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Physics. — ■ ^Calculation of the second correction to the quantity b 

 of the equation of condition of Yk'S dee Waals. " By 

 ^{v. J. J. VAN Laar. (Communicated by Prof. J. D. van dee 

 Waals.) 



In a paper, published in the Proceedings of the Meeting of the 

 Section for Mathematics and Physics of the Royal Academy of 

 Sciences 29* of Oct. 1898 (appeared Nov. 9"' 1898), Prof, van 

 DEE Waals has pointed out among others how a second correction 

 to the quantity b of his equation of condition might be found. The 

 integrations necessary to it, proving to be extremely tedious and 

 lengthy, have not been calculated at full length. 



I then tried to Avork out these integrations ; I shall communicate 

 in short the results found, referring, with respect to the various 

 mathematical developments which led to my results, to a more 

 extensive treatment that will shortly be published elsewhere (in the 

 "Archives du Musee Teyler"). 



The form to be integrated ') ran as follows (see pages 142 — 143 

 of the cited Proceedings) : 



ƒƒ- 



N 



. 2 71 (/*-(- a cos Oy dh dO X P^i"'- "f segment, 



ill which that part of segment is found to be: 



V:j a" sin (f cos cf y' R^ — «^^ + ^/s -^^ tan~^ ( tail (f — J — 



— a sin q) {R~ — ^/-^ a~ sin^ (p) tan~^ . 



a cos (p 



If we now first perform the integration with respect to between 

 the limits and öj, where 0-^ is given by the circumstance that the 

 centre C of the third sphere cannot lie within the two spheres A 

 and B (see fig. on page 142), we have to integrate: 



I |(/i + acosdf 



10, 



') The angle AMG indicated as C by Prof. v. d. Waals has here been called u~, 

 whilst the angle indicated as <p has here been called 5. 



