Olbers on Cornels 



h 8. 



According to this notation, we 'may easily express the four 

 equations in question. The condition that the tliree places of 

 the comet must be in a plane, passing through the sun, affords 

 us the equation 



y" z — y' z" _ y'" z' — y'z'" 

 x" y' — x'y" oc'" y' — x'y'" ' 

 which is already sufficiently simple, but which may be made 

 considerably more so, when the values of the quantities con- 

 cerned in it are substituted. 



[Note 2. The lines joining any successive places of the 

 comet must necessarily pass through the intersection of its or- 

 bit with the ecliptic ; consequently, the points in which these 

 lines meet the plane of the ecliptic must be situated in the line 

 of the nodes, and the place of the node may be computed 

 from either of them, since the tangent of its longitude will be 

 -, takmg X and y for the ordinates determining its situation in 

 the plane of the ecliptic. For the first pair of observations we 



shall obviously have a; = x'-|- , „ (a:" — a;'), and y zzy' 



^ _^ „ (y' — y'), which are to each other as x' (z' — z") + z' 



