COMETS. 



comet would follow while visible as determined by the following 

 data : 



Longitude Longitude of Perihelion 



Inclination. ofiiode,, perihelion. distance. Direction. 



1 7 3?' 53 5' 33 10/ 'S8 retrograde. 







57. In announcing his prediction Clairaut stated, that the 

 time assigned for the approaching perihelion might vary from the 

 actual time to the extent of a month ; for that independently of 

 any error either in the methods or process of calculation, the 

 event might deviate more or less from its predicted occurrence, 

 by reason of the attraction of an undiscovered planet of our 

 system revolving beyond the orbit of Saturn. In twenty-two 

 years after this time this conjecture was realised, by the dis- 

 covery of the planet Uranus, by the late Sir William Herschel, 

 revolving round the sun one thousand millions of miles beyond 

 the orbit of Saturn ! 



58. The comet, in fine, appeared in December 1758, and followed 

 the path predicted by Clairaut, which diifered but little from that 

 which it had pursued on former appearances. It passed through 

 perihelion on the 13th of March, within twenty-two days of 

 time, and within the limit of the possible errors assigned by 

 Clairaut. 



59. The general effects of a planet in accelerating or retarding 

 the motion of a comet are easily explained, although the exact 

 details of the disturbances are too complicated to admit of any 

 exposition here. 



Let P, fig. 3, represent the place of the disturbing planet, and 

 c that of the comet. The attraction of the planet on the comet 

 will then be a force directed from c 

 towards P, and by the principle of the 

 composition of forces is equivalent to 

 two components, one c m in the direc- 

 tion of the comet's path, and the other 

 c n perpendicular to that path. If the 

 motion of the comet be directed from c 

 towards m, it will be accelerated ; and 

 if it be directed from c towards m', it 

 will be retarded by that component of 

 the planet's attraction which is directed from c to m. The other 

 component c n being at right angles to the comet's motion, will 

 have no direct effect either in accelerating or retarding it. 



It appears, therefore, in general that, if the direction of the 

 comet's motion c m make an acute angle with the line c P drawn 

 to the planet, the planet's attraction will accelerate it ; and if 

 180 



