1923] Proceedings of the Elisha Mitchell Society 35 



the question arises as to whether ability in recognizing facial ex- 

 pressions is an inherited or an acquired capacity. An experimental 

 study by the writer, in which an expression-naming test was given 

 both before and after study of the chart mentioned above showed a 

 correlation between original scoire and gain through study of — .86. 

 This seems to indicate that the ability to identify emotional expres- 

 sions is an acquired rather than an inherited ability. Finally, the 

 problem as to the exact factors in development of this ability is a 

 complex one, probably involving fine discernment, intelligence, op- 

 portunity, and an objective attitude toward the world. 



262nd Meeting — January 9, 1923 

 J. W. Lasley — A Frohlem in Projective Differential Geometry. 



In a former paper it has been pointed out that Klein's classifi- 

 cation of geometry from the standpoint of groups leads, among others, 

 to a kind of geometry called projective, characterized by the invari- 

 ance of such things as the order and class of a curve, collinearity and 

 coplanarity of points, coplanarity and concurrence of lines, etc. Pro- 

 jective geometry, on the other hand, leads to sub-classification called 

 differential and integral, depending respectively upon whether a lim- 

 ited portion or the entirety of a geometric configuration is to be 

 considered. 



The present paper concerns itself with some of the results ob- 

 tained from considering a problem in the field of projective differ- 

 ential geometry. A tangent plane meets a surface in a curve which 

 has a double point at the point of contact. Double points which are 

 also points of inflection are called flecnodes, a name due to Cayley. 

 The tangents at such double points are asympytotic tangents. For 

 a ruled surface there are ordinarily two such points on each gen- 

 erator. One of the asymptotic tangents is a generator of the ruled 

 surface. The other generates a ruled surface which is called the 

 fleenode surface. It is a surface of two sheets, though not necessarily 

 bipartite. These sheets are called the first and minus first fleenode 

 transforms of the original ruled surface. • Wilczynski has shown that 

 the minus first transform of the first transform is the original sur- 

 face. The first transform of the first transform ordinarily leads to 

 a new surface. Continuing in this way we have a suite of ruled sur- 

 faces which is called the fleenode suite. Questions arise as to whether 



