September 13, 1901.] 



SCIENCE. 



397 



less dense than the planet Mercury (3.00), 

 which is the rarest of the inner planets. 

 Professor See concludes that on the average 

 the satellites are of the density 2.36, about 

 the same as the matter which compresses 

 the crust of the earth (2.55) ; and that the 

 small satellites which cannot be measured 

 are of about the same density as those 

 which can be investigated, such as the four 

 satellites of Jupiter, and Titan, the larg- 

 est satellite of Saturn. 



' Photometric Observations of Eros ' : 

 Henry M. Parkhurst, New York City. 



These observations, extending from Sep- 

 tember 13 to March 22, comprised 382 

 double extinctions, in comparison with a 

 large number of standard stars, including 

 four other asteroids. From these observa- 

 tions the constant of brightness, reducing 

 the distances to unity, was ascertained to 

 be 9.78 mag. , and the constant factor for 

 phase angle .037. The phase correction, 

 additional to the correction for defect of il- 

 luminated surface, was found to be uniform 

 through the whole variation up to 58°. 

 The observations confirm the discovery of 

 the rapid change of brightness, undoubtedly 

 due to rotation. The author's conclusion 

 is that this change is probably due to the 

 spheroidal form of Eros, the amount of the 

 change depending upon the direction of the 

 axis of rotation with regard to the earth. 



' On the History of Several Fundamental 

 Theorems in the Theory of Groups of 

 Finite Order ' : Dr. G. A. Miller, Cornell 

 Univert^ity. 



This paper will appear in a future num- 

 ber of Science. 



' On Certain Methods in the Geometry 

 of Position ' : Professor Arnold Emch, 

 University of Colorado. 



In this paper the author attempts to out- 

 line those methods which seem to be best 

 adapted for an introductory study of pro- 

 jective geometry. Particular stress is laid 

 upon the study of homology in advanced 



plane geometry and descriptive geometry. 

 It is shown that the principles of homology 

 result naturally from the orthographic and 

 also central projection, and that their appli- 

 cation is conversely the best means for the 

 construction of projective figures. 



' The Parallaxes of 54 Piscium and Weisse 

 17^ 322 ' : Professor F. L. Chase, Yale 

 Observatory. 



This paper was supplementary to a paper 

 read by the same author before this section a 

 year ago under the title, ' The Series of Par- 

 allaxes of Large Proper Motion Stars made 

 with the Yale Heliometer, ' a research begun 

 in 1892, the observational part of which was 

 finished the present year. In that paper 

 the author had stated that the results of a 

 preliminary solution indicated two of the 

 97 stars under investigation to possess a 

 parallax of nearly 0".25, which values, if 

 confirmed by further observation, would 

 place them among the first ten or twelve 

 nearest stars so far as at present known. 

 These two stars have been further investi- 

 gated, two additional pairs of comparison 

 stars being selected for each of them, and 

 the observations with the original pairs re- 

 peated at the same time. 



Altogether there were 56 observations on 

 54 Piscium and 54 on Weisse 17", 322, dis- 

 tributed as follows : 



• 54 Piscium, Mag. 6.2. 

 Series I. 12 obs. with a & b Mags. 7.5 & 7.3 (orig.) 

 Series 11. 12 obs. with a & b (rep.) 



Series III. 16 obs. with c & d Mags. 8.7 & 8.7 

 Series IV. 16 obs. with e & f Mags. 7.5 & 5.5 



Weisse 17, 322 Mag. 8.0. 



Series I. 10 obs. with a & b Mags. 7.0 & 8.0 (orig. ) 



Series II. 12 obs. with a & b (rep.) 



Series III. 16 obs. with c & d Mags. 7.2 & 5.5 



Series IV. 16 obs. with e & f Mags. 8.6 & 7.2 



The observations treated in the customary 

 way and the equations derived therefrom 

 being solved, the following results were 

 obtained : 



