368 SCIENCE PROGRESS 



L. L. Dines, Trans. Amer. Math. Soc, xx (1919), pp. 45—65, 

 discusses projective transformations in function space ; the 

 transformations are extensions to infinitely many variables of 

 the general projective transformation of n variables. 



F. R. Sharpe and V. Snyder, Trans. Amer. Math. Soc, xx 

 (1919), pp. 185-202, discuss various types of involutorial space 

 transformations ; the only type which has been systematically 

 investigated hitherto is the monoidal type, by Montesano, 1st. 

 Lombardi Rend., (2), xxi (1888). 



A memoir by the late G. M. Green (dec. January 24, 1919, 

 ait. 27) is published in the Trails. Amer. Math. Soc, xx (191 9), 

 pp. 79-153, on the general theory of surfaces and rectilinear 

 congruences ; among the many advances made by the author 

 in the theory of the differential geometry of surfaces from the 

 projective aspect may be mentioned his discussion of the pro- 

 jective substitute for the normal to a surface. 



L. E. J. Brouwer, Comptes Rendus, 168 (1919), pp. 677-678, 

 enumerates regular Riemann surfaces of genus unity. In a 

 subsequent communication (ibid., pp. 845-848) he enumerates 

 the finite groups of topological transformations of the anchor 

 ring. A paper to be associated with the latter appears on 

 pp. 1042-1044. 



R. L. Hippisley, Proc. London Math. Soc, (2), xviii (1919), 

 pp. 136-140, gives a new method of describing a three-bar curve, 

 based on the theorem that the pedal triangle of a point on a 

 three-bar curve, with reference to the triangle of foci, has the 

 property that its vertices are at fixed distances from a variable 

 point. 



T. C. Lewis, Messenger, xlviii (191 8), pp. 1 13-128, continues 

 his researches on pentaspherical co-ordinates. 



C. H. Sisam, Quarterly Journal, xlviii (191 8), pp. 104-112, 

 discusses the locus formed by the point of concurrence of three 

 tangents (with collinear points of contact) to a given algebraic 

 curve ; and also the envelope derived from the reciprocal con- 

 struction. 



C. H. Sisam, Amer. Journ. of Math., xli (1919), pp. 212-224, 

 investigates surfaces containing two pencils of cubic curves. 

 The paper is a continuation of a former paper (ibid., pp. 49- 

 59) on surfaces generated by an algebraic s}^stem of cubic 

 curves not forming a pencil. 



B. Gambier, Comptes Rendus, 168 (1919), pp. 674-677, 

 examines surfaces applicable to a paraboloid of revolution. 



T. Cohen, Amer. Journ. of Math., xli (1919), pp. 191-211, 

 gives a number of properties of the plane quartic and various 

 derived curves. 



R. Goormaghtigh, Nouv. Ann. de Math., (4), xix, pp. 93- 

 iii, investigates a family of plane curves, denned by a some- 



