io SCIENCE PROGRESS 



geometrica delle equazioni e delle funzioni algebriche. A. Emch 

 (Amer. Math. Monthly, 1919, 26, 63-5) develops a theorem of 

 Appell (191 8) into a known (Steiner, 1828) theorem of closure 

 on an equilateral hyperbola. A. Lodge (Math. Gaz. 19 19, 9, 

 322-6) calls attention to some simple means of interpolating 

 points in a cubic graph, and of indicating gradients without 

 actual calculation. 



A. E. Jolliffe (Proc. Lond. Math. Soc. 191 8, 17, 184-94) 

 proves that any cross-ratio of the pencil formed by the four 

 tangents from any point to a nodal cubic is connected by a 

 rational algebraic equation with the corresponding cross-ratio 

 of the pencil formed by joining the points of contact to the 

 node ; and discusses some properties of the quadrangle formed 

 by the points of contact of these tangents. W. P. Milne (ibid. 

 237-40) obtains, in connection with a previous paper published 

 by him in the same Proceedings, a symmetrical condition for 

 co-apolar triads on a cubic curve. Milne also (Proc. Edinburgh 

 Math. Soc. 191 8, 36, 84-90) writes on the apolar locus of two 

 tetrads of points on a conic. W. R. W. Roberts (Proc. Roy. 

 Irish Acad. 191 9, A. 34, 62-6) discusses the equation of the 

 tangent at a given point on a uni-nodal quartic curve. 



A. M. Howe (Amer. Journ. Math. 191 9, 41, 25-48) discusses 

 all the different algebraic (1,3) point correspondences between 

 two planes. T. R. Holcroft (ibid. 5-24) gives a classification 

 of general (2, 3) point correspondences between two planes. 



V. Snyder and F. R. Sharpe (Trans. Amer. Math. Soc. 191 8, 

 19, 275-90) study the space involutions defined by a web of 

 quadrics, which have been treated synthetically by Reye in 

 1876 and 1879, but only incidentally in connection with line 

 congruences. C. H. Sisam (Amer. Journ. Math. 191 9, 41, 49- 

 59) classifies completely the types of algebraic surfaces which 

 are generated by an algebraic system of cubics that do not 

 constitute a pencil. C. V. H. Rao (Proc. Lond. Math. Soc. 191 9, 

 17, 272-305) discusses the curves which lie on the quartic 

 surface in space of four dimensions, and the corresponding 

 curves on the cubic surface and the quartic with a double conic. 



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



A.F.R.Ae.S., University, Bristol. 



There is perhaps no phase of mathematical literature that is 

 less satisfactory than that of notation. We are often told that 



