396 



SCIENCE. 



[N. S. Vol. XIV. No. 350. 



taken as element, a theory results which is 

 in its analytical aspect identical with the 

 Pliicker line theory of the lineoid, while 

 the two theories are geometrically dispa- 

 rate. It is seen that, while neither of these 

 geometries has a correlate in its own do- 

 main, each is in the domain of 4- space the 

 perfect correlative of the other. Natu- 

 rally, therefore, in the geometry of 4-space, 

 whether it be the point-lineoid theory or 

 the line- plane theory, the two doctrines in 

 question play indispensable and precisely 

 coordinate roles. The subject is treated 

 under the following six headings : Intro- 

 ductory considerations, concerning certain 

 metric relationships, homogeneous coordi- 

 nates of the plane, the linear complex plane, 

 linear congruences of planes, projective 

 transformations by means of complexes. 



' The Next Opposition of Eros ' : Pro- 

 fessor H. A. Howe and Miss M. C. Traylgr. 



The planet Eros, to which astronomers 

 have recently given so much attention, is 

 now too near the sun for observation. As 

 it is evident that the observatories near the 

 equator will have a better chance to redis- 

 cover the planet than those in the United 

 States, computations have been made for 

 Manila, where the Jesuit Fathers have a 

 large telescope, and for Arequipa, Peru, 

 where the Bruce 24-inch star camera is 

 stationed. To represent the United States 

 Denver has been chosen, its latitude being 

 39° 41'. For each of the three dates. May 

 1, June 1 and July 1 of 1902 have been 

 computed the times of sunrise, of the be- 

 ginning of the morning twilight, and of 

 the rising of Eros. From these computa- 

 tions it appears that the conditions for early 

 rediscovery are most favorable at Arequipa, 

 excellent at Manila, and unpropitious at 

 Denver. But before July 1 it should cer- 

 tainly have been observed in the United 

 States. 



In order to have a secure basis for a 

 theory about the causes of the planet's 



variability, it is suggested that a table of 

 standard magnitudes be computed for the 

 entire period of visibility (May, 1902- 

 October, 1903), on the assumption that the 

 changes of brightness depend only on the 

 relative positions of the sun, the earth and 

 Eros. A comparison of the measured 

 magnitudes with these will give data for 

 theorizing. 



A chart giving the path of Eros through 

 the sky was exhibited, and also a paste- 

 board model of the orbits of the earth and 

 the planet, showing their positions at favor- 

 able oppositions. This paper will appear 

 in Popular Astronomy. 



' On the Dimensions, Masses and Densi- 

 ties of the Satellites ' : Professor T. J. J. 

 See, U. S. ISTaval Observatory. 



The author points out the difficulty of 

 measuring the angular diameters of very 

 small bodies, on account of the tremors of 

 the atmosphere, and then takes up the 

 densities of the great planets as found in 

 his recent investigations. He concludes 

 that the average density of the four inner 

 planets is 4.25, that of the outer planets 

 1.50. It is mentioned that the smaller 

 inner planets have less density than the 

 larger because the matter is less compressed 

 by the action of gravity. 



He then considers the diameters of the 

 four large satellities of Jupiter ; and, after 

 analyzing the masses found by various in- 

 vestigators since the days of Laplace, 

 adopts finally the masses used by Professor 

 J. C. Adams. These masses, with the 

 author's diameters, lead to the following 

 densities for the several satellites : 



( Water = 1.) 



An investigation of Titan, the largest 

 satellite of Saturn, shows its probable mass 

 to be ^yVt *^^* of Saturn, and the density 

 2.03. Thus Titan appears to be solid, and 



