288 POOR. 



Thus in longitude 298° there could be no possible approach ; 

 Saturn being- in a widely different part of its orbit when the 

 comet reached this point. On the other hand when the comet 

 reached longitude 79°, Saturn was only about 30° from the 

 same point. This, however, made the distance between the 

 two bodies so great that the resulting perturbations were inap- 

 preciable. It will be noted, however, that if the average period 

 of the comet previous to 1881 had been 28.5 years then the 

 comet and Saturn would have both reached the common point 

 of their orbits at nearly the same time in 1 796 ; and if the 

 period had been 27.9 years there would have been a close ap- 

 pulse of the two bodies in 1825. Such approaches are not 

 indicated by the definitive elements, the smallest value for the 

 period being 29.2 years. Unless, therefore, during the interval 

 between 1825 and 188 1 there were other perturbations suffi- 

 cient to appreciably change the orbit of the comet, there could 

 have been no close approach to Saturn. This fact, that there 

 could have been no large disturbance by Saturn, is of special 

 importance, as we shall see hereafter. 



42. Approaches to Jupiter. The definitive set of elements 

 shows that the period of the comet previous to 1883 was 29.2 

 years, while that of Jupiter is 1 1.86 years. These two periods 

 are incommensurable, but are somewhat in the ratio of 5 to 2 : 

 five periods of Jupiter being equal to 59.3 years, whilst two 

 periods of the comet are equal to 58.4 years. Thus the mean 

 set of elements would indicate that the comet passed perihelion 

 in longitude 188° in February 1828 whilst Jupiter passed the 

 same point about ten months previously. The comet, being at 

 perihelion, was moving more rapidly than Jupiter and gained 

 upon that planet. In the years, 1829 and 1830, therefore, the 

 planet and comet were sufficiently close together for the latter 

 to cause appreciable perturbations. Had the periodic time of 

 the comet been slightly larger than that indicated by the defini- 

 tive elements, this appulse of the comet and Jupiter in 1828 

 would have been extremely close. 



In order to form some idea as to the character of this appulse 

 the perturbations for the interval between 1883 and 1830 were 



