COMETS. 



the motion of the comet proceeding from m' through p towards A, 

 and will continue to do so until the line of direction becomes- 

 perpendicular to that of the comet's motion, after which it will 

 accelerate it. 



It appears, therefore, that during the period of the comet, 

 the disturbing action of tSe planet is subject to several changes- 

 of direction, owing partly to the change of position of the comet 

 and partly to that of the planet ; and the total effect of the dis- 

 turbing action of the planet on the comet's period is found by 

 taking the difference between the total amount of all the accele- 

 rating and all the retarding actions. 



In the case of the planet Jupiter and Halley's comet, the 

 former makes nearly seven complete revolutions in a single period 

 of the comet ; and consequently its disturbing action is not only 

 subject to several changes of direction, but also to continual vari- 

 ation of intensity, owing to its change of distance from the comet. 



Small as the arc m' p m of the comet's path is which is included 

 within the orbit of Jupiter, the fraction of the period in which 

 this arc is traversed by the comet is much smaller, as will be 

 apparent by considering the application of the principle of equable 

 areas * to this case. The time taken by the comet to move over 

 the arc m' p m is in the same proportion to its entire period, as the 

 area included between the arc m' P m and the lines m 1 s and m s- 

 is to the entire area of the ellipse A r. 



To simplify the explanation the orbit of the comet has here 

 been supposed to be in the plane of that of the disturbing planet. 

 If it be not, the disturbing action will have another component 

 at right angles to the plane of the comet's orbit, the effect of 

 which will be a tendency to vary the inclination. 



60. The result of the investigation by Clairaut showed, that the 

 total effect of the disturbing action of Jupiter and Saturn on 

 Halley's comet between its perihelions in 1682 and in 1759, was- 

 to increase its period by 618 days as compared with the time of 

 its preceding revolution, of which increase, 100 days were due to 

 the action of Saturn, and 518 to that of Jupiter. 



Clairaut did not take into account the disturbing action of the 

 earth, which was not altogether inconsiderable, and could not 

 allow for those of the undiscovered planets, Uranus and Neptune. 

 The effects of the action of the other planets, Mars, Yenus, Mer- 

 cury, and the planetoids, are in these cases insignificant. 



61. In the interval of three quarters of a century which pre- 

 ceded the next re-appearance of this comet, science continued to 

 progress, and instruments of observation and principles and 



* See "Handbook of Astronomy," chap. xii. 2599. 

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