414 SCIENTIFIC RECORD FOR 1885. 



and making six* of each, which was universally admitted to be a 

 " perfect " number. Curious variations in the brightness of the new 

 satellite were noticed by Cassini, and his observations have been co'n- 

 firmed by subsequent observers. The explanation seems to be that o))- 

 I)Osite sides of the satellite have different reflecting powers, and that 

 the satellite, in revolving arouud Saturn, keeps the same face always 

 turned towards the planet. In this latter respect we have an analogous 

 case in our moon. Professor Pickering gives the magnitude of lapetus, 

 from photometric measures, 11-82, and the mean diameter 486 miles. 



The observations now published were, for the most part, made by Pro- 

 fessor Hall himself with the 26-iuch equatorial of the Naval Observa- 

 tory, in the years 1875-'84; a few were made by Professor ISTewcomb in 

 1874. In regard to the examination of the observations for large re- 

 siduals. Professor Hall remarks : " In this work no observation has been 

 rej»Kted. When observations have been honestly made, I dislike to 

 enter on the process of culling them. By rejecting the large residuals 

 the work is made to appear more accurate than it really is, and thus 

 we fail to get the right estimate of its quality." 



The adopted mean distance of lapetus from Saturn, determined by two 

 different methods of observing, (one by differences of right ascension and 

 declination and the other by angles of position and distances,) which 

 give very accordant results, is SlS-^olOS ± 0-"02645 ; and the time for 

 one revolution around the planet seventy-nine days, seven hours, tifty- 

 six minutes, forty seconds. From this periodic time of the satellite 

 and its mean distance, the mass of Saturn expressed as a fraction of 

 the sun's mass is rAi? or about 93-2 times the mass of the earth. Pro- 

 fessor Hall's paper concludes with some useful tables of the satellite's 

 motion. 



Uranus : The satellites of Uranus. — In Appendix i to the Washington 

 Observations for 1881 Prof. Asaph Hall has published the results of 

 his investigations of the orbits of Uranus, " Oheron " and " Titania.''^ 

 " The satellites of Uranus were amongst the first objects observed with 

 the 20 inch refractor of the Naval Observatory, after it was mounted in 

 November. 1873. The first series during the oppositions of 1874 and 

 1875 were discussed by Professor Newcomb, with the view to the de- 

 termination of the mass of the planet, and the foruiation of tables of 

 the motions of the satellites, which were published in the Washington 

 Observations for 1873. Remarking that as the earth would be nearly 

 in the plane of the orbits in the year 1882, and observations made about 



* Professor Hall has called my attention to a sliglii; error in Grant's rendering of 

 Huyghens' remark (History of Physical Astronomy, p. 268). The discovery of Titan 

 made the number of phiDcts and satellites, each equal to sis, and six (not twelve, as 

 Grant puts it) was regarded as a "'perfect" number : " - - - utriqiie illo, quem 

 perfectum dicimus, numero continentur - - - " Huygenii Opera Varia, vol. 2, p. 

 530), a perfect number being one that is equal to the sum of all its divisors including 

 unity. 



