( ÖÖ ) 



pass five Q 3 cutting b and c. From this is evident that a, b and c are 

 fivefold right lines. 



With a right line m through O k the scroll («, ft y) has thirteen 

 points lying in Ok m common, so its image m' (right line through 

 Ok) cuts ip 30 likewise in 13 points lying outside 0&. We conclude 

 from this that the four points are seven teenfold on ip 30 . 



So the right lines OkOi lie on this surface; that they are fourfold 

 right lines can be shown in this manner. 



As Ok and Oi are ninefold on («, ,?, y) the right line OkOi is cut 

 outside those points by 22 — 18=4 transversals of the curves a, 0, y; 

 the images of these right lines are conies through Ok and Oi resting 

 on m 0n, b, c and d and forming with O m O n a q 3 of the system. 



The section of if? 30 with O x % O t can consist outside the three 

 fourfold right lines only of, conies; these are easy to indicate. In the 

 first place we can bring through O lt O t ,O t a conic cutting b and c; 

 it is completed to a (> 3 by each of the two right lines out of 4 

 resting on the conic and on d. Then the sections of d and of the 

 transversal with 4 to b and c with 0^0^,0^ determine a conic 

 forming with the indicated transversal a q 3 . So we have in lf t ,0 t 

 three double and three simple conies ; with the three fourfold right 

 lines they form a section of order 30. 



On tp 30 lie therefore 4 seven teen fold points, 3 fivefold, 6 fourfold 

 and 36 simple right lines, 12 double conies and 36 simple conies. 



Astronomy. — ''■Contributions to the determination of geographical 

 positions on the West coast of Africa. III." By C. Sanders. 

 (Communicated by E. F. van de Sande Bakhuyzen). 



(Communicated in the meeting of May 30, 1908). 



I. Introduction. 



After a stay in Europe during the winter 1902 — 1903 I returned 

 to Portuguese West Africa and remained there until the autumn 

 1906 when I again went to Europe for some time. 



During this period 1903 — 1906 I have once more tried to contri- 

 bute to the determination of geographical positions in these parts as 

 much as time and circumstances allowed. Circumstances, however, 

 were often unfavourable to my observations, and hence the results 

 obtained are less than I had desired and expected at first. 



The results obtained may be ranged under three heads. 



1. New determinations at Chiloango. In November and December 



