150 VECTOR METHOD IN THE DETERMINATION OF ORBITS. 



which would serve the purpose, and then to find better values of 

 p 2 , r 2 by setting in equation second of (2) 



the expressions in brackets denoting numbers derived from the 

 approximate values already found. This is similar to or identical with 

 the method of Fabritius, except that he combines with it the principle 

 of interpolation (for the first value in the third "hypothesis"). As 

 I found the approximation by this method sometimes slow or failing, 

 notably in the case of Swift's comet, 1880 V, I tried the method 

 published in my paper. Indeed, it may be said that the method of 

 my paper was constructed to meet the exigencies of the case of the 

 comet, 1880 V. 



In ordinary cases I think that the method of Fabritius may very 

 likely be better than that which I published. The equations are very 

 simply and perspicuously represented in vector notations. I shall use 

 the notations of my paper, writing E, F, etc., for German letters.* To 

 eliminate p l and p B from equation (7) in my paper, multiply directly 

 by gj X g 3 . This gives 



3 



(a) 



To eliminate p 3 and r 3 , multiply by ( 3 xS 3 which gives 



- i -ic&HAfoWJ-o. (6) 



'2 ' 



When we have found p lt r lt p z , r 2 it is not necessary to eliminate 

 any of them, and to save labor in forming the equation for p s , r s , I 

 should be inclined to take the components in (7) in the direction of 

 one of the coordinate axes, choosing that one which is most nearly 

 directed towards the third observed position. However, I will write 



where ty may represent an axis of coordinates, or ((^xSi) which 

 would give Fabritius' equation. It might be directed towards the pole 



* [In the remainder of the letter as here printed German capitals have been substituted 

 for the E, f\ P, etc. of the original, thus making the notation uniform with that of 

 the paper referred to.] 



