RECENT ADVANCES IN SCIENCE 199 



that the series in question are always convergent. It thus 

 follows that the equality of the absolute invariants is a sufficient 

 as well as a necessary condition for the equivalence of two pairs 

 of curves. The method used is one impossible in the conformal 

 theory, and is to reduce the question to one in differential 

 equations and then to apply certain existence theorems, due 

 to Briot and Bouquet, for solutions at a singular point. 



A. L. Miller (ibid. 292) obtains the theorem, analogous to 

 Pascal's theorem, that if a decagon be doubly inscribed in a 

 cubic the remaining ten intersections of the odd sides with the 

 even ones lie on a conic. 



L. P. Eisenhart (Rend, del Circ. mat. di Palermo, 191 6, 41, 

 94-102) shows that right conoids and cylinders are the only 

 surfaces which can be generated by the motion of an invariable 

 curve whose points describe straight lines. 



M. H. Sznyter (Amer. Math. Monthly, 191 7, 24, 11 3-9) 

 establishes for the pentahedroid in a four-dimensional space 

 metrical theorems similar to those found in ordinary solid 

 geometry dealing with the tetrahedron. 



In connection with papers of some years ago on the pro- 

 jective differential geometry of curved surfaces by E. J. Wil- 

 czynski, F.M.Morrison (Amer. Journ. Math. 1917,39, 199-220) 

 has a paper on the relation between some important notions 

 of projective and metrical geometry. He studies metrically 

 for the first time certain configurations associated with a point 

 on a surface which had been defined and investigated by 

 Wilczynski from a projective point of view. By means of 

 these configurations Morrison defines some new classes of 

 special points on a surface and some new kinds of surfaces, and 

 applies these notions to the minimal surface of Enneper. 



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



Greenwich. 



Solar Prominences. — The publication of an important memoir 

 by Mr. and Mrs. John Evershed dealing with solar prominences 

 (Results of Prominence Observations, Memoirs of the Kodai- 

 kanal Observatory, vol. 1, pt. ii. pp. iv. + 72, with 11 dia- 

 grams and 12 plates) provides a convenient opportunity to 

 review briefly our present knowledge of solar prominences, the 

 more so as much of that knowledge is due to the observations 

 of Mr. Evershed, first in his private observatory at Kenley 



