i8o SCIENCE PROGRESS 



G. Herglotz {Leipzig Ber., 73, 192 1, 215-25), G. Fubini 

 {Math. Ann., 85, 1922, 213-21), J. A. Schouten {Math. Zs., 

 13, 1922, 56-81) and A. Finzi {Rend. Lincei, 31, 1922, 8-12) 

 write on differential geometry in n dimensions. 



J. Lipka {Rend. Lincei, 31, 1922, 353-6) and A. Myller 

 {C.R., 174, 1922, 997-9) use Levi-Civita's theory of parallelism 

 respectively to define geodesic curvature and to obtain pro- 

 perties of ruled surfaces. 



Sophus Lie showed how to determine all translation-surfaces 

 in three-dimensional space ; B. Gambler {C.R., 174, 1922, 

 98-100) points out that his method does not give all possible 

 surfaces of this kind in space of more dimensions. 



H. Liebmann {Sitz. Heidelberg, 1921, Abh. 5 ; Math. Zs., 

 13, 1922, 10-17) discusses surfaces of constant curvature. 



E. J. Wilczynski {Math. Ann., 85, 1922, 208-12) gives an 

 account of the work of G. M. Green and himself on the geo- 

 metrical significance of isothermal conjugacy of a net of 

 curves on a surface. 



B. Gambler {C.R., 174, 1922, 523, 661, 1613) considers 

 point transformations between two surfaces connected with 

 their fundamental quadratic forms ; e.g. such that conjugate 

 nets on one become orthogonal nets on the other. 



He also investigates {C.R., 174, 1922, 921-4) isothermal 

 surfaces of which the spherical representation is isothermal. 



H. Jonas {Math. Ann., 86, 1922, 78-98) considers the 

 deformation of line congruences. 



Beginning in 191 6, a series of memoirs have appeared, 

 first in the Leipzig Berichte, and then in the Mathematische 

 Zeitschrift and the Abhandlungen of the recently founded 

 mathematical Seminar at Hamburg, bearing the general 

 title of : " tjber affine Geometric." They deal with properties 

 which are invariant under the group of affine transformations 

 of determinant unity ; the inspirer of the series, W. Blaschke, 

 promises a connected account of the subject in the second 

 volume of his Vorlesungen uber Differentialgeometrie, of which 

 the first has recently appeared. The latest memoirs are by 

 W. Blaschke {Math. Zs., 12, 1922, 262-73 ; Hamburg Seminar, 

 1, 1922, 1 5 1-6) on the analogues in affine geometry to minimal 

 surfaces and the non-deformability of the sphere ; by A. 

 Winternitz {ibid., 99-101) and by K. Reidemeister {ibid., 

 127-39). 



APPLIED MATHEMATICS. By S. Brodetsky, M.A.. Ph.D., F.Inst.P., 

 D.Sc, University, Leeds. 



Henri Poincare died in 191 2, leaving behind a legacy of 

 scientific achievement of remarkable extent and versatility. 

 The pure mathematician, the applied mathematician, the 



