COMET OF 1889-1896-1903. 291 



can be shown that there was a strong intermediate disturbance 

 by Saturn. 



44. In 42 it was shown that if the periodic time of Comet 

 Brooks in 1883 had been sHghtly larger than that indicated by 

 the definitive elements, then the comet and Jupiter would have 

 had an extremely close appulse in 1827. In fact had the 

 period of the comet previous to 1883 been 29.6 years, then two 

 periods of the comet would have been exactly equal to five of 

 Jupiter and the two bodies would have been together in 1827. 

 This period, 29.6 years, differs only four tenths of a year from 

 the period indicated by the definitive elements and it is not at 

 all impossible that the definitive period may be in error by that 

 amount. In 39 it was shown that the perturbations due to 

 the figure of Jupiter made nearly two and one quarter years 

 difference in the period ; that the period, derived by omitting 

 these perturbations, was 31.5 years. Hence if the numerical 

 values of the perturbations due to the figure of Jupiter, as found 

 in 34, are some 18 percent, too large, then the periodic time 

 of the comet previous to 1883 would have been just 29.6 years. 

 As these perturbations vary inversely as to the fourth power of 

 the distance of the comet from Jupiter, a change of some 5 per 

 cent, or 4,000 miles, in the peri-jovian distance of the comet 

 would fully account for the necessary change in these pertur- 

 bations. In other words, if the comet passed Jupiter, at the 

 time of closest approach, some 4,000 miles, or one tenth radius 

 of the planet, further from the planet than is indicated by the 

 definitive elements, then two periods of the comet previous to 

 1883 were equal to five of Jupiter and the two bodies were in 

 close approach in 1827. 



45. By making various suppositions as to the period between 

 1827 and 1883 we can give to the appulse to Jupiter in 1827 

 any character that we desire. It is worthy of note, however, 

 that for the definitive period of 29.2 years and for any period 

 between that and 29.6 years, the perturbations of it in 1827 

 were of a character such as to increase the periodic time of the 

 comet ; that is, previous to 1827 the periodic time of the comet 

 would have been smaller than it was after that date. If this 



