( 7«7 ) 



line /,, or wlicn liaxing taken one of llioso three lines in that manner 

 we choose the other two in snch a way that they both cut this 

 new line. So there is only one solution, in which the four lines 

 /j, /,, /,, /, cross each other. 



From the ahove consideration which can easily be confirmed 

 analytically ensues (hat the supposition of four planes «, given arbi- 

 trarily and of four \ertices Oi i;i\en arl)itrarily dominates the case 

 of four projecti\e pencils of rays with merely hyperboloidic cjua- 

 druplets to such an extent that the projective cori-espondence is (i.xcd 

 by the condition of the hyperbohtidic position. This now again includes 

 that the case of the three quadruplets with hyperboloidic i>osition, 

 treated above in details, cannot present itself if the planes «,■ and 

 the points 0; haxe been taken arbitrarily. For these three quadruplets 

 must also put in an appearance if we wish all quadruplets to have 

 hyperboloidic position, and they delerinine the |)rojective relation 

 uneqiuvocally, i.e. three hyperl)ol(iidic (juadruplets lead here to pure 

 hyperboloidic quadruplets. 



Not to get too redundant, we put aside (he examination of the 

 less remarkable series of quadratic surfaces, answering to this most 

 general case of four peneils of rays with merely hyperboloidic 

 quadruple(s. 



Astronomy. — "On the orhiUil plam's of Jupiter a satellites'. By 

 Dr. W. DK SiTTi'.K. (Communicated by Prof. J. C. K.\pteyx). 



The following pages contain a condensed summary of the results 

 of an investigation, which will soon be published in detail in the 

 "Annals of the Royal Observatory at the Cape of Good Hope". 

 The material on which this investigation is based consists entirely 

 of observations made at the Cape Observatory, viz. : 



1. Heliometer-observations made in 1891 by Gii.i, and Finlay, 

 discussed by me and published in my inaugural dissertation. ') 



2. Photographic plates taken at the Cape Observatory in 1891, 

 measured and discussed by me. 



3. Heliometer-observations made in 19(J1 and 1902 by Cookson, 

 discussed by himself and published in Monthly Notices, June 

 1904 p. 728—747. 



4. Photographic plates taken in 1903 and 1904, measured and 

 discussed bv me, 



^} Discussion of rieliomelei'-Obsci'vations of Jupiter's Satellites, Groningen J. B. 



WOLTERS 1901. 



