164 



SCIENCE 



[N. S. Vol. XXVII. No. 683 



8. In July, October and November when 

 there was no direct sunlight shining on the 

 ring the entire ring was distinctly visible 

 with the 40-inch telescope of the Yerkes 

 Observatory. 



On July 2 there were two luminous con- 

 spicuous masses or condensations visible on 

 the ansse, both preceding and following. 

 As the visible surface of the ring and the 

 condensations were on the shadow side of 

 the ring where no direct sunlight could 

 fall, the natural coneliision would be that 

 the rings must be self-luminous. But this, 

 from the nature of the constitution of the 

 rings, is shown to be impossible. 



The explanation given for this phe- 

 nomenon is that the sunlight sifts through 

 among the particles composing the rings, 

 and by diffusion, or scattering and reflec- 

 tion, the dark side becomes luminous. 

 Micrometer measures show that the conden- 

 sations fall on the bright outer portion of 

 the inner bright ring and on its projection 

 near the planet. It is believed that the 

 greater density of this part of the ring 

 makes it more luminous when seen from 

 underneath— just as it appears when the 

 direct sunlight falls on it. In reality what 

 we have seen, therefore, is the surface of 

 the ring seen at a very oblique angle, where 

 it is less than 1" of arc in width, illumi- 

 nated by the sunlight percolating through 

 the rings, similar to the sunlit view that we 

 get of the ring-s, but far more feebly illumi- 

 nated. That these bright places are not 

 real elevations above the surface of the 

 ring is shown by the fact that they dis- 

 appeared when the edge of the ring was 

 toward us, at which time they should have 

 been better seen if they were masses on the 

 ring. The eye was simply deceived by 

 their greater brightness, which gave them 

 the appearance of being masses on the ring. 



9. Professor Frost gave a description of 

 a solar spectrograph recently mounted in 

 the Snow building of the Yerkes Observa- 



tory and explained some preliminary re- 

 sults obtained by means of this instrument. 



10. The new method here presented by 

 Professor Laves rests on the geometric ft 

 properties of the hodogi'aphic circle. It " 

 shows that from the observed maximum 



and minimum velocities we can determine 

 K and Ke cos w where K is the radius of 

 the hodographic circle, e the eccentricity of 

 the orbit and o> the longitude of the peri- 

 astron. By Schwarzschild 's proceeding the 

 time of periastron-passage is determined 

 from the course of velocities. The velocity 

 at periastron derived from the same curve 

 furnishes two points in the hodograph of 

 which the one of the two is the periastron. 

 The diameter through this point cuts the 

 chord of central distance Ee cos w in the 

 focus. The values of e and <» are read off 

 by a finely graduated scale. 



11. Professor Schlesinger's tables for h 

 and c are based on a previous transforma- : 

 tion of the equatorial coordinates a, 8 of a 

 star into A, fi, its ecliptical coordinates. 

 The present tables do away with this trans- 

 formation and furnish at once the right 

 ascension A and declination D of the apex 

 of the earth's motion. The correction x is 

 brought upon the following form : 

 x^V } sin S sin D -h cos 8 cos D eos (a — A)}. 



The quantities V sin D, V cos D and A are 

 tabulated for every other degree of the cir- 

 cumference. Tables of difference for 1' 

 change in each one of these tabulated 

 quantities are added to facilitate the cal- 

 culation. This paper will be published in 

 the Astrophysical Journal. 



12. The paper by Professor Cairns is 

 devoted to a generalization of the Hilbert 

 theory of a quadratic form in an infinite 

 number of variables. It embodies the re- 

 sults reached in work carried out as part 

 of the requirement for the degree of doctor 

 of philosophy at Gottingen. The investi- 

 gation ai'ose in seeking to adapt the method 



