September 27, 1895.] 



SGIENGE. 



397 



plane, viz., conies having double contact 

 with two fixed conies, etc., and in space, of 

 conies touching six fixed planes, conies hav- 

 ing double contact with three quadrics in- 

 scribed in the same developable, circles hav- 

 ing double contact with two confocal quad- 

 rics, etc. These results are principally de- 

 duced by means of elliptic integrals and the 

 first-class of hyper-elliptic integrals, and 

 from them flow certain theorems concerning 

 doublj^ infinite porisms of curvilinear poly- 

 gons. This paper will be published in the 

 Bulletin of the American Mathematical Society. 



Professor Taber's paper related to the 

 orthogonal transformations which leave a 

 bilinear form unaltered, and their genera- 

 tion by means of infinitesimal transforma- 

 tions. It has been contributed to the Quar- 

 terly Journal of Pure and Applied Mathematics. 



In Professor Hathawaj^'s paper the proof 

 consists in identifying, by means of ele- 

 mentary geometry, the product of several 

 versors with the composition of a set of ro- 

 tations through angles double those of the 

 corresponding versors. The obvious asso- 

 ciative principle of the composition of the 

 rotations proves the corresponding associa- 

 tive principle of multiplication of versors. 

 This paper will appear in the Bulletin of the 

 American Mathematical Society. It was pre- 

 sented to the Society by Professor Shaw. 



Professor Maschke's paper contains a 

 very elegant application of elliptic functions 

 to curves drawn on the surface of a circular 

 ring. This paper will also appear in the 

 Bulletin of the American Mathematical Society. 

 It was presented to the Society by Professor 

 Morley. 



At the afternoon session, August 28th, 

 two topics were presented to the Society 

 for general discussion: 



(1) 'A general subject catalogue or index 

 of mathematical literature.' 



(2) ' The mathematical cun-iculum of 

 the college and scientific school.' 



The first discussion was opened by the 



Secretary, who gave a brief account of the 

 ' Repertoire hihliocjraphique des sciences mathe- 

 7natiques,' in course of publication by the 

 Mathematical Society of France. The dis- 

 cussion was continued by Professors Morley, 

 Woodward and McMahon. On motion by 

 Professor McMahon, it was resolved that the 

 Council be requested to consider the desira- 

 bility of ofieringto the Mathematical Society 

 of France the cooperation of this Society and 

 of drawing up a plan for such cooperation. 



The second discussion was opened by 

 Professor Shaw, who presented a table of 

 statistics showing the character of the 

 mathematical instruction in 101 represen- 

 tative colleges and scientific schools. The 

 discussion was continued by Professors 

 White, Morley, Van Vleck, Doolittle, 

 Chandler, Pupin and Woodward. It seemed 

 to be generally held that the work of the 

 preparatory schools as a whole is not sufiB- 

 ciently thorough to serve as a satisfactory 

 basis for collegiate courses; that a greater pro- 

 portion of the students' time should be given 

 to mathematical study; that greater stress 

 should be laid on the fundamental subjects; 

 that elementary portions of applied mathe- 

 matics should be earlier introduced and 

 more extensively taught, and that spherical 

 trigonometry should be in great part, or 

 altogether, dropped from the required cur- 

 riculum. 



At the close of the discussion the thanks 

 of the Society were tendered to the Spring- 

 field Local Committee for the accommoda- 

 tions and hospitality which the Society had 

 enjoyed, and the meeting was adjourned. 



Thomas S. Fiske. 

 Columbia College. 



THE SPRINGFIELD MEETING OF THE AMERI- 

 CAN ASSOCIATION FOR THE ADVANCE- 

 MENT OF SCIENCE. 



SECTION A. MATHEMATICS AND ASTRONOMY. 



In section A, Mathematics and As- 

 tronomj', the following papers were read : 



