136 



SCIENCE. 



[N. S. Vol. XVI. No. 395. 



Second Report on Recent Progress in the 

 Theory of Groups of Finite Order: Pro- 

 fessor G. A. Miller, Stanford Univer- 

 sity. 

 In the absence of Professor Miller this 



report was presented in abstract by Dr. W. 



B. Fite, of Cornell University. It will be 



published in the Bulletin of the American 



ilathematical Society. 



Displacements Polygons: Professor J. 



BuRKiTT Webb, Stevens Institute of 



Technology. 



Owing to the absence of Professor "Webb 

 at the time this paper was called for it was 

 read by title. 



Some Theorems on Ordinary Continued 

 Fractions: Professor Thomas E. McKin- 

 NEY, Marietta College. 

 Let D be any positive integer not a per- 

 fect square, and let its square root be repre- 

 sented by an ordinary continued frac- 

 tion. This paper determines the form of D 

 so that the continued fraction representing 

 its square root may have a period with one, 

 two,- three or four elements, and applies 

 the results to the determination of the num- 

 ber of reduced forms in the class to which 

 the indefinite quadratic form (1, 0, D) 

 belongs. 



On the Forms of Sextic Scrolls of Genus 

 One: Dr. Virgil Snyder, Cornell Univer- 

 sity. 



In his classification of sextic scrolls of 

 genus 1, Dr. Snyder employed the method 

 of point correspondence between two plane 

 sections and made use of the following 

 theorems which were proved in one of his 

 former papers: (1) The nodal curve (sim- 

 ple or composite) is of order 9: (2) every 

 generator cuts four others, and (3) any 

 non-reducible plane curve lying on the sur- 

 face is of genus 1. 



Thirty-three types are found, ten of 

 whicli have a multiple conic. It will be 



published in the American Journal of 

 Mathematics. 



Transformation of the Hypergeometric 

 Series: Professor Edgar Frisby, U. S. 

 Naval Observatory. 

 If in the differential equation of the 



second order connecting the elements of the 



hypergeometric series 



= 1 + 



aB „/3(a + l)(/3 + l) 



i-2-r.(>'+i) 

 a;'^P' be substituted for P, new relations 

 are obtained in which P' takes the place of 

 P, and the new elements are functions of 

 the original elements. p. is determined 

 from the condition that the new series 

 must be of the same general form as the 

 old. If, in addition, x be replaced by 1/x 

 another series is obtained. From these two 

 new series, by proper substitution of the 

 new derived elements, are obtained almost 

 by inspection, the twenty different series 

 ordinarily given in works on differential 

 equations. 



Edwin S. Crawley, 



Secretary. 



SECTION G, BOTANY. 



Section G of the American Association 

 met in the Botanical Hall of Phipps Con- 

 servatory on the mornings of June 30 and 

 July 3, 1902. In the absence of Professor 

 D. H. Campbell, Stanford University, Pro- 

 fessor C. E. Bessey, of the University of 

 Nebraska, was elected acting Vice-Presi- 

 dent. 



The abstracts of papers presented are as 

 follows : 



The Prevalence of Alternaria in Nebraska 

 and Colorado During the Drought of 

 1901 : George Grant Hedgcock, Lincoln, 

 Nebr. 



This paper gives a brief synopsis of 

 observations made in various sections of 

 Nebraska and Colorado during the severe 

 period of drought in July and August of 



