354 SCIENCE PROGRESS 



singular correspondences ; he limits himself to curves of genus 

 two and to the symmetrical case, showing that we may regard 

 the correspondence as having two real positive valencies. 



J. de Vries [Proc. Amst. Acad., 23, 1921, 462, 466) considers 

 the involutory transformation of the lines of space which is 

 defined from two involutions on two straight lines, in which 

 P, P' are corresponding points on the first line, and Q, Q' 

 corresponding points on the second, by associating the lines 

 PQ, P'Q'. 



A bilinear equation Xcnp/is = O {r, s = i — 6) between the 

 co-ordinates of two lines is said to define a bilinear connex of 

 pairs of lines, the conjugate lines of a given line forming in 

 general a linear complex. The equation may also be inter- 

 preted as a reciprocity between pairs of points on a quadric 

 variety in space of five dimensions. C. Segre {Rend. Palermo, 

 44, 1920, 139) examines the case in which c„ + Cj, = O, when 

 the connex is said to be " alternate." 



Segre {Rend. Lincei, 30 (i), 1921 200, 227) also has a couple 

 of notes on the surface of Veronese, which is of the fourth order 

 and of two dimensions in space of five dimensions, and can be 

 represented point for point on a plane. 



S. Carrus {C.R., 173, 1921, 69, 219, 437) and A. Demoulin 

 {Mem. de la Soc. Roy. de Liege, 11, 1921, i) deal with triply- 

 orthogonal systems of surfaces. 



A rectilinear congruence for which the asymptotic lines on 

 the two focal surfaces correspond is called, after Weingarten, 

 a W-congruence. Papers on these congruences have been 

 published by L. P. Eisenhart {Annals of Math., 22, 1921, 161), 

 G.Fuhim {Rend. Lincei, ZO {i), I g2 1, 2yT, ; 30(2), 1921,22), and 

 P. Tortorici {Math. Zs., 10, 1921, 255). 



E. P. Lane {Amer. Journ. Math., 43, 1921, 52) continues the 

 work of Wilczynski on the general theory of congruences in 

 connection with a completely integrable system of partial dif- 

 ferential equations. 



J. K. Whittemore {Annals of Math., 22, 192 1, 217) deter- 

 mines minimal surfaces which contain straight lines ; and A, 

 Demoulin {Bull, de I' Acad. Roy. de Belgique, 7, 192 1, 293) in- 

 vestigates geodesies on Enneper's minimal surface. 



Extensions of minimal surfaces to higher space are given by 

 C. L. E. Moore {Bull. Amer. Math. Soc, 27, 1921, 211) and A. 

 Palatini {Annali di mat., 29, 1921, 191). 



ASTBONOMY. By H. Spencer Jones, M.A., B.Sc, Chief Assistant, 

 Royal Observatory, Greenwich. 



The Age of the Earth.' — At the meeting of the British Association 

 in Edinburgh in September last a joint discussion on the age 

 of the earth took place under the auspices of the sections for 



