RECENT ADVANCES IN SCIENCE 13 



algebraic systems, it is of interest that Robinson (Amer. Journ. 

 Math. 191 7, 39, 95-112) has constructed a canonical form 

 which has no exceptional cases and will apply equally to a 

 differential system or a system of polynomials. 



Geometry. — R. L. Moore {Bull. Amer. Math. Soc. 191 7, 23, 

 233-6) gives a proof of the simple fact in analysis situs that 

 every two points of a continuous curve are the extremities of at 

 least one simple continuous arc that lies entirely on that curve. 

 The theorem can be almost at once applied to a curve in a space 

 of any number of dimensions. 



E. K. Wakeford (Proc. Lond. Math. Soc. 1916, 15, 340-2) 

 deduces a proof of the theorem of the double six of lines in space 

 from a projective form of Miquel's theorem on the form of five 

 parabolas, each of which touches four out of five straight lines 

 in a plane. 



J. Hodgkmson(ibid. 343-53) investigates the interdependence 

 of the nine double points which are sufficient to determine 

 uniquely a plane sextic curve. 



Miss Hilda P. Hudson (ibid. 385) discusses the Cremona 

 transformations of a plane sextic with ten double points. 



H. Hilton and Miss R. E. Colomb (Amer. Journ. Math. 191 7, 

 39, 86-94) investigate the nature of the " orthoptic " locus (the 

 locus of the intersection of two perpendicular tangents) of a 

 given real plane algebraic curve. 



L. C. Cox (ibid. 59-74) establishes a method which enables 

 us to determine the Cremona transformations with seven funda- 

 mental points which correspond to a given linear transformation 

 of the quartic curve. 



L. P. Eisenhart (Trans. Amer. Math. Soc. 1917, 18, 97-124) 

 develops the theory of certain transformations of conjugate 

 systems of curves on a surface. 



A. E.Young (Amer. Journ. Math. 191 7, 39, 75-85) discusses 

 the problem of determining all surfaces having lines of curvature 

 which are either what Bianchi has named " isotherm-conjugate " 

 or associate isotherm-conjugate. 



ASTRONOMY. By H. Spencer Jones, M.A., B.Sc, Royal Observatory, 

 Greenwich. 



Stellar Evolution. — Much valuable work has been done recently 

 by Mr. J. H. Jeans on the important subjects of cosmogony 

 and stellar dynamics. For these investigations Mr. Jeans has 



