COMET OF 1889-1896-1903. 289 



approximately computed. The changes for the elements n and 

 L were alone considered and intervals of 200 and 400 days 

 were used in the computations. The total perturbations during 

 this interval were found to be small, the integrated values for 

 Feb. 1.5 1 83 1 being, 



A,u = — c/'.4763 



AZ =— 41' 30^^ 



And the resulting elements of the comet for this epoch are, 



IS3I.0 



The closest approach of the comet to Jupiter occurred in the 

 latter part of 1828, but at no time did the comet approach 

 Jupiter closer than six times the radius of the latter's sphere of 

 activity. Hence the resulting perturbations were too small to 

 cause any decided change in the orbit of the comet. 



Thus the definite elements do not indicate any close approach 

 of the comet to either Jupiter or Saturn during the interval be- 

 tween 1779 ^^^ 1886. 



43. There is another method by which the question of iden- 

 tity may be investigated, and that is, by means of the criterion 

 formulated by Tisserand. By an investigation of the path of a 

 comet through the planet's sphere of activity Tisserand de- 

 rived a function, ;/, of the comet's elements, which remains prac- 

 tically unaltered however great the change in the separate ele- 

 ments. This function is given by the formula,' 



Where a, p, and i are respectively the semi-axis major, the 

 parameter and the inclination of the comet's orbit, and A and R, 

 the semi-axis major and the radius vector of the disturbing 

 i Mecanique Celeste, Vol. IV, p. 203. 



