( 110 ) 



„iv 



V -' -2' z^ 3 z^^» ^ 3 ^V 



1 

 As — , /) and the 3 heliocentric distances r are known, è"^, z 

 a 



and z^^^ can be computed for each of the 3 points P^, P^ and P^. 



For a circular orbit all the derivatives of z are equal to zero 



sin X \/z 

 and the function U becomes . According to the preceding 



development we obtain for an elliptic orbit the following approxi- 

 mate formula for U, which still contains the 6^^ power of the 

 interval : 



sin X V/z x" / r r)\ 



U = J^4__.W9_4 5L , . . (VIII) 



By means of the values which take U^^, U^ and U^ for the 

 values Tj, Tj and x^ of the argument x, we obtain foi* n.^ and 

 /Zj values containing the terms of the 5"^^^ order with respect to the 

 intervals ; while the approximation may be extended to the 6"^^^ order, 

 if we add to the above mentioned expression for Ü -. 



z^ (— ;. — 120fi + 170;.^ + 340;i,a — 1020^/-^). 



5040 

 where ). and ft denote 



;. = - f 9 — 4 - — 5 ^^ 



,= 3/2- 1- ^ 



V a r 



Astrononiy. — ''Supplement to the account of the deter inination 

 of the longitude of St. Denis {Island of Reunion), executed 

 in 1874, containing also a general account of the observation 

 of the transit of Venus", ^y Prof. J. A. C. Oudejians. 



When I set about to correct the imperfections left in my first 

 communication, 1 began by calculating foi- the times of observation 

 of the occultations the correction of Newcomb's parallactic correction, 

 mentioned on p. 603 of my previous paper; as said there this 

 correction amounts to 



+ 0"67 sin D -f 0"05 sin {D - g) — 0"09 sin {D -f g% 



where D stands for the mean elongation of the moon from the sun, 

 g for the moon's mean anomaly, and g' for that of the sun. 



