January 13, 1899.] 



SCIENCE. 



57 



searches may continue. There remains much 

 to be done and a part of this collection of 

 exhibits has very nearly attained the object 

 proposed." 



Among the specific conclusions are these: 



Smoke cannot be suppressed without considerable 

 excess of cost. 



Special fuels, as anthracite, coke, fuel-gas and 

 mineral oils, may be resorted to, and with success, 

 where cost is not objectionable. 



The chimney-top should be visible to the man at 

 the furnace. 



Prolonged trials should supplement such investiga- 

 tions as those prosecuted by this Commission, to as- 

 certain the durability of the apparatus and of its effi- 

 ciency. 



Existing legislation, well enforced, is advised, 

 rather than any specific new legislation. 



The appendix to the report is an elaborate 

 presentation of the logs, tables and draw- 

 ings of the apparatus of the trials described 

 in the text. The whole constitutes a very 

 valuable contribution to the literature of 

 the subject, in the department of applied 

 science, and deserves to be permanently 

 preserved in every library of applied science, 

 beside the reports of the Franklin Institute 

 discussion. 



R. H. Thueston. 



A3IERICAN MATHEMATICAL SOCIETY. 

 The fifth annual meeting of the American 

 Mathematical Society was held in Fayer- 

 weather Hall of Columbia University, on 

 AVednesday, December 28, 1898. On the 

 two following days the Chicago Section of 

 the Society held its fourth regular meeting 

 in the Ryerson Physical Labratory of the 

 University of Chicago. At the election 

 held at the annual meeting the following 

 officers and members of the Council were 

 chosen : President, R. S. Woodward ; First 

 Vice-President, E. H. Moore ; Second Vice- 

 President, T. S. Fiske; Secretary, F. N. 

 Cole ; Treasurer, Harold Jacoby ; Librarian, 

 Pomeroy Ladue ; Committee of Publication, 

 T. S. Fiske, F. IST. Cole, Alexander Ziwet ; 



members of the Council to serve for three 

 years, Maxime Bocher, James Pierpont, 

 Charlotte Angas Scott. 



The Society has now completed its tenth 

 year of continuous existence, having been 

 organized as the New York Mathematical 

 Society in November, 1888, and reorganized 

 under its present title in July, 1894. The 

 Bulletin is now in its eighth annual volume ; 

 the first number appeared in October, 1891. 

 The present membership of the Society is 315. 

 About ninety papers have been presented at 

 its meetings during the past year. The 

 Chicago Section was organized in April, 

 1897, and has proved from the beginning a 

 valued addition to the Society's strength. 



At the annual meeting the following 

 papers were read : 



(1) Peofessoe M. I. PuPiN : 'On multiple reso- 

 nance. ' 



(2) De. a. S. CnESSiN" : ' On the development of the 

 perturbative function in terms of the eccentric 

 anomalies.' 



(3) De. a. S. Chessin : 'On some points of the the- 

 ory of functions.' 



(4) Peofessoe E. 0. Lovett : 'On the transforma- 

 tion of straight lines into spheres.' 



(5) Dk. E. J. WiLCZYNSKi : ' A generalization of 

 Appell's factorial functions.' 



(6) Peofessoe Oemond Stone : 'On the solution 

 of Delaunay's canonical system of equations.' 



(7) De. Viegil Snydee : 'Asymptotic lines on 

 ruled surfaces having two rectilinear generators.' 



(8) Dr. G. A. MiLLEE : 'On a memoir on the sub- 

 stitution groups whose degree is less than nine.' 



(9) De. W. Schulz : 'On the partial differential 

 equation 



3% 3'it . „ 



and its connection with Diriohlet's principle.' 



The following is a list of the papers read 

 before the Chicago Section : 



(1) De. L. E. Dickson: 'The determination of the 

 structure of all linear homogeneous groups in a 

 Galoi.s field which possess a quadratic invariant, 

 with the announcement of two new systems of 

 simple groups.' 



(2) Mr. Gael C. Engbeeg : 'The Cartesian oval 

 and the auxiliary parabola. ' 



