MATHEMATICS 179 



{Math. Ann., 85, 1922, i-io) and A. M. Bedarida {Rend. 

 Lincei, 31, 1922, 5-8). 



Geometry. — H. Liebmann {Math. Ann., 85, 1922, 172-6) 

 proves that besides displacements there are no projective 

 transformations of the hyperboUc plane which transform 

 proper points into proper points. 



H. Mohrmann {ibid., 177-83) gives examples of non- 

 Desarguesian geometry in the plane ; and M. Dehn {ibid., 

 1 84-94) writes on the principle of duality in non-Archimedean 

 geometry. 



C. M. Sparrow {Amer. Journ. Math., 43, 1921, 222-5) 

 discusses the Fermat and Hessian points of the non-euclidean 

 triangle ; C. Servais {Bull. d. Belgique, 7, 1921, 641-52 ; 

 8, 1922, 62, 103) writes on the' geometry of the tetrahedron ; 

 and F. Schottky {Sitz. Berlin, 1922, 173-81) gives theorems about 

 points on an ellipse which include Graves's and MacCullagh's. 



F. Schilling {Math. Ann., 85, 1922, 200-7) gives a space 

 generalisation of the Peaucellier cell, and F. H. Murray {C.R., 

 174, 1922, 1399) describes an instrument of manageable size 

 by means of which arcs of very large circles may be drawn 

 accurately. 



F. Enriques {Math. Ann., 85, 1922, 195-9) shows how 

 results in the geometry on an algebraic curve may be obtained 

 from consideration of the degenerate case in which the curve 

 is rational. 



H. Hilton {Proc. L.M.S., 21, 1922, 1-13) discusses plane 

 curves of degree 2n with tangents having bi-w-point contact ; 

 F. V. Morley {ibid., 140-60) gives an analytical treatment of 

 the 3-bar curve; and W. P. Milne {ibid., 134-9) proves a 

 theorem of Morley's on apolarity by means of cubic surfaces. 



M. Castellani {Rend. Lincei, 31, 1922, 347-50), defining the 

 osculating space of a surface as the least space which contains 

 the osculating planes of all curves through the point, investi- 

 gates surfaces whose osculating spaces are bi-osculating. 



D. Montesano {Rend. Napoli, 27, 192 1, 116, 164) and L. 

 Godeaux {Mem. d. Belgique, 6, 1922, fasc. 12) discuss birational 

 transformations in space. 



F. Sibirani {Rend. Lombardo, 54, 1922, 404-13) writes on 

 hue congruences of equal slope ; and E. Veneroni {ibid., 383-94) 

 on congruences of conies. 



E. Study {Math. Ann., 86, 1922, 40-77)> in his usual pole- 

 mical style, sets out to reduce to order Lie's sphere geometry. 



E. Vessiot {C.R., 174, 1922, 989-91) studies properties of 

 systems of circles which are not altered by conformal trans- 

 formations. 



E. H. Neville {Proc. Camb. Phil. S., 21, 1922, 97-107) 

 improves de la Vallee Poussin's definition of an envelope. 



