12 SCIENCE PROGRESS 



(Bull. Amer. Math. Soc. 191 8, 24, 207-10) of F. Gomes Teixeira's 

 Problemes celebres de la Geometrie elementaire (see Science 

 Progress, 191 7, 12, 160). 



H. L. Smith (Annals of Math. 191 7, 19, 137-41) proves in 

 a simple manner, by using a theorem of Schoenflies, the funda- 

 mental lemma of H. Tietze in his proof (1914) that every one- 

 to-one continuous representation of a square upon itself which 

 preserves sense is a deformation ; that is, it may be regarded 

 as a member of a continuous one-parameter family of such 

 representations which contains the identity. 



Mary Gertrude Haseman (Trans. Roy. Soc. Edinburgh, 191 8, 

 52, 235-55), continuing the work of Listing (1874) and Tait 

 (1876-86), studies those knots in particular which exhibit a 

 special kind of symmetry — the " amphicheiral " knots — and 

 gives a census of the amphicheirals with twelve crossings. 



F. Irwin and H. N. Wright (Annals of Math. 1917, 19, 152-8) 

 study what they call " polynomial " curves, y = F(x), where 

 F (x) is a polynomial in x alone, which do not seem to have 

 been thoroughly treated up to the present time. Some applica- 

 tions of the theory are also given. 



Algebraic curves form the subject of work by G. Rosati 

 (Ann. di Mat. 1916, 25, 1-32), L. Brusotti (ibid. 99-128), 

 A. M. Harding (Giorn. di Mat. 1916, 54, 185-222), C. Burali- 

 Forti (ibid. 249-78), A. L. Nelson (Rend, del Circ. mat. di 

 Palermo, 1916, 41, 238-62), and J. de Vries (Versl. Kon. Akad. 

 van Wet. Amsterdam, 25, 954-60) ; and curves of the fourth 

 order in space by L. Vietoris (Sitzungsber. der K. Akad. der 

 Wiss. in Wien, 1916, 125 [Haj, 259-83). 



J. M. Stetson (Annals of Math. 191 7, 19, 106-26) studies 

 the relations between the radial transformation and some of 

 the other simple transformations of general conjugate systems 

 of curves on a surface, and these results are applied to the 

 surfaces both of whose Laplace transforms are lines of curva- 

 ture. 



On solid geometry in general we may notice the late G. 

 Darboux's Principes de geometrie analytique (Paris, 191 7 ; Rev. 

 sem. 191 7, 25 [2], 58), and C. Cailler's three articles (Arch, de 

 Geneve, 191 6, 42). Geodesies on quadrics are discussed by 

 A. Arwin (Arkiv for Mat. 1916, 11, No. 9). On algebraic sur- 

 faces see K. W. Rutgers (Nieuw Archief voor Wiskunde, 191 7, 

 12, 109-34), C. H. van Os (ibid. 169-87, and Versl. Kon. Akad. 



