July 25, 1902.] 



SCIENCE. 



131 



SECTION A, MATHEMATICS AND 

 ASTRONOMY. 



The meeting of the section at Pittsburgh 

 compared favorably with former meetings 

 both in the nmnber and character of the 

 papers presented and in the attendance^ 

 The number of papers presented was 

 twenty-four, mathematical papers predomi- 

 nating somewhat over astronomical. The 

 attendance was better in the morning than 

 in the afternoon sessions, on account of the 

 large and attractive list of excursions 

 planned for the afternoons by the Local 

 Committee. The list of papers follows : 



On the Adaptability of the Glycerine Clock 

 to the Diurnal Motion of Astronomical 

 Instruments, particularly those used in 

 Photographing Solar Eclipses : Professor 

 David P. Todd, Amherst College Observa- 

 tory. 



In outline the glycerine clock is an accu- 

 rately constructed cylinder, about four 

 inches in diameter, in which travels a pis- 

 ton, the flow of the glycerine being con- 

 trolled at any required speed or rate by. 

 means of a series of needle valves. By at- 

 taching a mirror or objective to a frame, 

 equatorially mounted, the glycerine clock 

 can be set under one arm of it, at any con- 

 venient distance from the axis, and the req- 

 uisite rate for counteracting the diurnal 

 motion of the sun can be given by means 

 of the needle valves. This permits very 

 heavy weights to be thrown on the piston, 

 and therefore the vibration of the instru- 

 ments by wind can be precluded. When 

 the run of the piston is finished, the glycer- 

 ine is pumped out of the top of the cylinder 

 and forced back into the bottom, and the 

 riin is commenced over again. 



On a Convenient Type of Finder for very 

 large Equatorials: Professor David P. 

 Todd, Amherst College Observatory. 

 The object of a 'finder' is convenience. 



But in equatorials above twenty inches in 



aperture, the ordinary finder is necessarily 

 mounted so far away from the axis of the 

 great telescope that its use occasions much 

 inconvenience, simply because of the dis- 

 tance of its eyepiece from that of the great 

 tube. To obviate this difficulty, Professor 

 Todd proposes to construct the finder with 

 a pair of reflectors, either planes or prisms, 

 set at 45°, and to mount the main part of 

 its tube in rings or bearings. By turning 

 the tube in these, the flnder's eyepiece can 

 be brought as near the eyepiece of the great 

 tube as is desired, or pushed away from it 

 to admit attachment or adjustment of sub- 

 sidiary apparatus. 



Series ivhose Product is Absolutely Con- 

 vergent: Professor Floeian Cajori, 

 Colorado College. 



This paper is a continuation of the sub- 

 ject as developed by the author in his pre- 

 vious papers {Trans, of the Am. Math. Soc., 

 Vol. II.,pp. 25-36, 1901 ; Science, Vol. XIV., 

 p. 395, 1901; Bulletin of the Am. Math. 

 Soc.,'Yol. VIII., pp. 231-236, 1902) and in 

 the article of Alfred Pringsheim {Trans. 

 of the Am. Math. Soc, Vol. II., pp. 404-412, 

 1901). Some of the results previously ob- 

 tained, relating to absolutely convergent 

 products of two or more series, are general- 

 ized and the method of treatment is simpli- 

 fled. The construction of pairs of divergent 

 series with real or complex terms is given, 

 such that the product of the two series is 

 not only absolutely convergent, but equal 

 to any desired value, including zero. 



A New Treatment of Volume: Professor G. 



B. Halsted, University of Texas. 



After the establishment of a sect-calculus, 

 the area of a triangle is deflned as the pro- 

 duct of its base by half its altitude, this 

 product being proved independent of the 

 choice of base. Then the volume of a 

 tetrahedron is defined as the product of the 

 area of its base by one third its altitude, 

 this product being pi'oved independent of 



