1 82 SCIENCE PROGRESS 



L. P. Eisenhart (Bull. Amer. Math. Soc. 191 8, 24, 227-37) 

 gives an excellent account of Darboux's contribution to geo- 

 metry, and a long and thorough review (ibid. 394-403) of 

 Darboux's last work, the Principes de Geometrie analytique 

 (Paris, 191 7). 



H. S. White (Bull. Amer. Math. Soc. 191 8, 24, 238-43) gives 

 an account of the first two volumes of Cremona's Opere mate- 

 matiche. 



J. R. Kline (Annals of Math. 191 8, 19, 185-200) gives a 

 non-intuitional definition of the notion of " sameness of sense " 

 on closed curves in non-metrical plane analysis situs. All his 

 theorems are proved on the basis of R. L. Moore's (191 6) 

 system of axioms (cf. Science Progress, 191 6, 11, 270 ; 191 7, 

 12, 194; 191 8, 12, 548). 



C. L. E. Moore (Annals of Math. 191 8, 19, 176-84) studies 

 motions in hyperspace by a method making use of Lie's in- 

 finitesimal transformations. 



J. Eiesland (Amer. Journ. Math. 191 8, 40, 1-46) continues 

 his work on flat-sphere geometry. 



J. V. De Porte (ibid. 47-68) writes on irrational involutions 

 on algebraic curves. 



J. R. Musselman (ibid. 69-86) writes on the set of eight 

 self-associated points in space. 



C. L. E. Moore (Amer. Math. Monthly, 191 7, 24, 456-62) 

 gives a substitute for Dapin's indicatrix for the study of sur- 

 faces, which has the advantage that it can be easily generalised. 



L. P. Eisenhart (Annals of Math. 191 8, 19, 217-30) dis- 

 cusses some types of surfaces which can be generated in more 

 than one way by the motion of an invariable curve, when the 

 types are not so very simple or well known as, for instance, 

 ruled surfaces and surfaces of revolution. 



J. K. Whittemore (Amer. Journ. Math. 1916, 40, 87-96) 

 discusses associate minimal surfaces. 



APPLIED MATHEMATICS. By S. Brodetsky, M.A., Ph.D., 



A. F.Ac. S., University, Bristol. 



It is necessary first to define the sense in which the term Applied 

 Mathematics is to be used here. Whilst all would agree that 

 certain subjects must be classed under Physics and others 

 under Astronomy, there is in reality no sharp line of demarca- 

 tion between Applied Mathematics and Physics on the one 



