Mabch 23, 1906.] 



SCIENCE. 



461 



University. This address has already been 

 published in Science for January 12 of 

 the current year. 



At the regular program meeting of the 

 section, held on the morning of December 

 30, the following papers were presented: 



On the groups of Order p^"^q having 

 Ahelian Subgroups H mn of Type {n, n, 

 ■■■, n) : Dr. 0. F. Glenn, Drury College, 

 Springfield, Mo. 



This paper is supplementary to one pre- 

 sented by the author at the Philadelphia 

 meeting of the association, in which the 

 case n^^l was discussed. The defining 

 relations of all groups described in the 

 title are tabulated, and their properties 

 discussed in relation to the properties of 

 the Galois field (?i^[p"™] determined by 

 the automorph of the subgroup H. It is 

 found that all of the groups in question 

 are members of a general family and have 

 one general set of defining relations. 



A New Straight in no'ii-Euclidean Geom- 

 etry: Professor G. B. Halstbd, Kenyon 

 College, Gambler, 0. 

 The paper sets forth the discovery that, 

 in Riemannean non-Euclidean geometry, 

 the six mid-points of the parts of the six 

 rays from the vertices of any triangle ob- 

 tained by prolonging the sides, are co- 

 straight. This is a new and noteworthy 

 straight associated with every triangle. 



The theorem is demonstrated, and then 

 interpreted in ordinary Euclidean space. 



A Chapter in the Present State of Develop- 

 ment of the Elliptic Functions : Professor 

 Harris Hancock, University of Cincin- 

 nati, Cincinnati, 0. 



The paper is an attempt to show that 

 practically all (American and European) 

 writers on the elliptic functions have been 

 giving too much emphasis to certain parts 

 of Weierstrass 's theory, while they have 

 neglected many of the lines of thought 



which Weierstrass himself considered 

 fundamental. 



It is shown that the so-called Weier- 

 strassean normal-form is not due to Weier- 

 strass. The introduction of new functions 

 gives a different aspect to the presentation 

 of the elliptic functions, although little that 

 is new has been added thereby to the theory 

 itself. Weierstrass 's great work lies in a 

 somewhat different direction; with him 

 the problem of determining all analytical 

 functions which have algebraic addition- 

 theorems is the leading idea. 



The paper also brings into evidence sev- 

 eral fundamental theorems of Hermite and 

 shows some of the characteristics of Rie- 

 mann's theory. 



A Catalogue of 1,607 Zodiacal Stars for the 

 Epochs 1900 and 1920, Reduced to an 

 Absolute System: Mr. H. B. Hbdrick, 

 U. S. Naval Observatory, Washington, 

 D. C. 



This catalogue was prepared by the 

 writer, in the Nautical Almanac Office, in 

 order to fill the widely felt need of more 

 fundamental positions of stars within the 

 zodiac. 



In its construction fifty-two observa- 

 tional catalogues were used. Systematic 

 corrections were applied to each catalogue 

 to reduce it to the same absolute system as 

 that of the 'Catalogue of Fundamental 

 Stars,' by Professor Simon Newcomb, pub- 

 lished in the 'Astronomical Papers of the 

 American Ephemeris,' Volume 8, Part 2. 

 Definitive positions were obtained by 

 least square solutions of all the observations 

 of each star. Right ascensions, declinations, 

 variations and proper motions are given for 

 two epochs, 1900 and 1920. Other fea- 

 tures are the reference numbers to well- 

 known catalogues, the Besselian star con- 

 stants for 1910 for each star, and an index 

 of stars by letter and constellation or by a 

 special name. 



