134 



W. Kapteyn: "On some integral equations", p. 286. 



H. G. VAN DE Sande Bakuuyzen, N. WiLDEBOEii and J. W. DiEi'ERiNii: "Cumpaiison of 

 the measuring bar used in the base-measurement at Stroe with tht; Dutch IMetre No. 27", 

 p. 300. 



H. G. VAN DE Sande Bakuuyzen: "Comparison of the Duteli platinum-iridium JSIetre No. 27 

 with the international Metre M, as derived from the measurements by the Dutch Metre- 

 Commission in 1879 and 1880, and a preliminary determination of the lengtli of the 

 measuring-bar of the French base-apparatus in international Metros", ]). ;}11. 



L. K. Wolff : ''On the formation of antibodies after injection of sensitized antigens". 11. 

 (Communicated by Trof. C. Eykman), p. 318. 



F. M. Jaeger: ''The ITemperature-coefficients of the free Surface-energy of Liquids at Tem- 

 peratures from —80" to 1650" C. 1. INIethods and Apparatus. (Communicated by Trof. 

 P. VAN Romburgh). vWith two plates), p. 3*29. 



F. M. Jaeger and M. J. Smit: Ibid II. "Measurements of some Aliphatic Derivatives," ]>. 365. 

 Ibid III. "Measurements of some Aromatic Derivatives." ^Communicated by I'rof. P. van 



ROMBURGII;, p. 386. 



F. M. Jaeger and Jul. Kahn: Ibid IV. "Measurements of some Aliphatic and Aromatic 



Ethers". (Communicated by Pi of. P. van Romburgh), p. 395. 

 F. ^I. Jaeger: Ibid V. "Measurements of homologous Aromatic Hydrocarbons and some of 



their Ilalogenderivatives", p. 405. Ibid VI. "General Remarks '. (Communicated by Prof. 



P. v.AN Romburgh), p. 410. 

 H. Haga and F. M. Jaeger: "On the real Syiiimetry of Cordierite and Apoi)hyllite". (With 



two plates), p. 430. 

 P. Zeeman: "Fresnel's coefficient for light of difterent colours". (First part). (With one plate), 



p. 445. 

 J. J. VAN Laar: ''A new relation between the critical quantities, and on the unity of all 



substances in their thermic bohavionr". (Conclusion). (Communicated by Prof. H. A. 



LORENTZ), p. 451. 



Mathematics. — "A triple involution of the third chins." By 

 Professor Jan de Vries. 



(Communicated in tlie meeting of May 30, 1914). 



1. I consider the projective nets of conies represented by 



;.%-^ + X'aJ' + ra^'" = and Xb/- + AV + A' 6^"^ = . (1) 

 The points of intersection of corresponding conies form a quadruple 



invohition ^). 



On the straight line YZ, which we may represent by x^ = Qt/k + 



-j- ozk, the two nets determine the pairs of points, indicated by 

 2:?. {Q'ay'-]-2oaa^a,^o\i,') — and -2";. {Q%f--\-2(iabyb, + o"-b,') = 0. 



3 3 



These equations produce the same pair of points, as soon as the 

 relations 



2}My' = t2: xb,,\ ::£Xaya~ = t:e ib,jb,, ^;.a/ ^r^: kb~\ 



3 3 3 3 3 3 



are satisfied. 



By elimination of A, A', V' we find from this system the relation 



I «/ — tby-, ttyci- — rbfibzi Oz' — "^b-- ,| = . . . . (2) 



1) This involution is an intersection of the linear congruence of elliptic twisted 

 quartics, which I have considered in my communication in vol. XIV, p. 1127 of 

 these Proceedings. 



