RECENT ADVANCES IN SCIENCE 271 



R. L. Hippisley described linkages illustrating the cubic trans- 

 formation of elliptic functions. 



Gabriel M. Green (Amer. Journ. Math. 191 5, 37, 215) gives 

 the introductory part of an investigation of the projective 

 differential geometry of one-parameter families of space curves, 

 such a family being regarded as a component family of a 

 conjugate net on a curved surface. Indeed, the author makes 

 use of the fact that, in studying a geometric configuration, it 

 is often convenient to study the configuration as part of another 

 which is characterised by some peculiar geometric property. 

 In the same number of the same journal (ibid. 281) R. D. Beetle 

 considers some congruences associated with a one-parameter 

 family of curves, which are other than the congruence formed 

 by the tangents to the curves. 



The classification by invariants of plane cubic curves modulo 

 2 is dealt with by L. E. Dickson (ibid. 107), and he points out 

 that the methods employed are applicable to other problems 

 of the same nature and that they indicate the decided advantage 

 to be gained in the theory of modular invariants from modular 

 geometry as developed by himself, Bussey and Veblen, and 

 Coble. 



L. P. Eisenhart (ibid. 1 79) develops the equations of a surface 

 from the point of view of regarding a surface as the locus of a 

 one-parameter family of curves C, using for moving axes the 

 principal directions of the curves C. The fundamental equa- 

 tions of condition to be satisfied by a set of functions determining 

 a surface are established. 



In 1855 Hesse pointed out the connection of the plane 

 quartic curve with the figure of the general net of quadrics in 

 space; J. R. Conner (ibid. 1916, 38, 155) investigates, by 

 almost exclusively geometrical methods, the correspondences 

 determined by the bitangents of a quartic ; the intimate 

 connection between the plane and space figures makes intuitive 

 many geometrical relations in ' both which might otherwise 

 be difficult to prove. 



E. B. Wilson and C. L. E. Moore (Proc. Nat. Acad. Sci., 

 Washington, D.C., 191 6, 2, No. 5) develop a theory of two- 

 dimensional surfaces in w-dimensional space by the method of 

 analysis outlined by Ricci in his absolute differential calculus. 

 This work continues the work of Kommerell, E. Levi, and 

 Segre. 



