VECTOR METHOD IN THE DETERMINATION OF ORBITS. 151 



of the ecliptic, which would make (C^.^P), (@ 2 -?), (@ 3 -^) vanish, 

 except for exceedingly minute quantities depending on the latitude of 

 the sun and the geocentric coordinates of the observatories, if these 

 are included in @j, @ 2 , @ 3 . 



The equations (a), (6), (c), which are together equivalent to (7), I 

 would solve as follows, almost in the same way as Fabritius, but 

 relying a little more on interpolation, and less on the convergence of 

 which he speaks, which in special cases may more or less fail. 



Setting r = r 2 and r 3 = r 2 in (a), which thus modified I shall call (a'), 

 and solving this (a') by " trial and error," using p z as the independent 

 variable, as soon as I have a value of p 2 which I think will give a 

 residual of (a') of the same order of smallness as the effect of changing 



5 and 5 into =, I determine from this value by (b) and (c), r* and 



M *> M O /y> O / N ' N ' * 



r 3 , and then find the residual of (a), using the values of r 1? r 2 , r 3 

 derived all from the same assumed p 2 . Now using the last value of 



A in my previous calculations on (a') which indeed applies 



only roughly to the (a), I would get a value p 2 which I would use for 

 the second "hypothesis" in (a). This will give a second residual in 

 (a), which will enable me to make a more satisfactory interpolation. 

 As many more interpolations may be made as shall be found necessary. 



Some such method, which should perhaps be called the method of 

 Fabritius, would, I think, in most cases probably be the best for 

 solution of equation (7). 



Of course I am quite aware that the merit of my paper, if any, lies 

 principally in the fundamental approximation (1). I will add a few 

 words on this subject. 



The equation may be written more symmetrically 



/ 2 _i_ 2 Q 2\ / 2 i 2 Q 2\ 



It might be made entirely symmetrical by writing T 2 for T 2 . 



If an expression ending with t s had been used, we could still have 

 satisfied two of the conditions relating to acceleration, and should 

 have obtained 



' =0, Ila 





or 



