COMET OF 18S9-1896-1903 265 



traversing its relative orbit about the planet. It will become 

 more effective, if we merely use the idea of the "sphere" as 

 defining approximately the point, at which we may conveniently 

 transpose the sun and the planet, as disturbing and central 

 bodies ; and after the transformation has been made, we may 

 treat the sun and the comet as bodies revolving about the 

 planet as central body ; the sun acting as a disturbing body 

 upon the comet. The perturbations of the comet by the sun 

 may be computed in a manner entirely similar to the usual 

 methods. The exact point in the comet's orbit, at which the 

 transformation is made, is of no great importance, provided the 

 perturbations be carefully computed both before and after ; and 

 this fact furnishes us with the desired, and an absolute, control. 



As the comet approaches Jupiter in its orbit about the sun, 

 compute carefully the planetary perturbations, thus deriving 

 the osculating elliptic elements of the comet for two dates, t 

 and f , one of which, /, is that upon which the comet enters the 

 so called " sphere," the other, /', being ten days or two weeks 

 later, or after the comet is well within the sphere. From the 

 osculating elements of date / compute the heliocentric coordi- 

 nates and their derivatives for that date, thence find the coor- 

 dinates and velocities relative to Jupiter, and thence by the 

 transformation-formulas the osculating hyperbola about Jupiter ; 

 with these hyperbolic elements compute the solar perturbations 

 for the interval f — /, apply them and thus derive the oscu- 

 lating hyperbola for the date /'. With these elements we may 

 readily compute the coordinates, x' , y' , z' , of the comet referred 

 to Jupiter for the date /'. 



Then with the osculating elliptic elements of the comet about 

 the sun, as already derived for the date, /', we compute first 

 the heliocentric coordinates of the comet and thence derive 

 the coordinates, x" , y" , c" , of the comet referred to Jupiter for 

 the date /'. If all formulas and computations are correct, we 

 shall have absolutely, 



x^=x" yf=^y" z'^z" > 



and a perfect control is secured. 



