preponderance of direct over retrograde motion that only two have 

 their motion retrograde, viz., Halley's comet and the comet associated 

 with the great Leonid swarm of meteors. 



Professor Newton succeeded in explaining this remarkable differ- 

 ence in behaviour of the two classes of comets. He shows that the 

 preponderance of small inclinations and the preponderance of direct 

 over retrograde motions would inevitably establish themselves amongst 

 comets of short period, on the supposition that each of these is a 

 comet of the other class which has at some time passed so close to a 

 planet that it was drawn aside from its original orbit. 



Laplace had shown that if a comet passes close to a planet the 

 influence of the planet upon it may be found to a first approximation 

 by drawing a sphere of a certain size round the planet, and suppos- 

 ing that the comet has moved in a parabola round the sun, undis- 

 turbed by the planet, until it passes inside the sphere ; and that 

 while inside the sphere it moves in a hyperbola relatively to the 

 planet, attracted by the planet alone and unperturbed by the sun. 

 This is equivalent to supposing that as a first approximation we may 

 neglect the small difference between the direction and amount of 

 the sun's attraction upon the comet and planet while the former is 

 traversing the sphere from the point of its entrance into the sphere 

 to its point of exit. 



Professor Newton points out that if the comet passes in front of 

 the planet as the planet advances along its orbit, then it will neces- 

 sarily accelerate the planet and thereby increase the planet's kinetic 

 energy. An equal amount of energy must be lost by the comet, of 

 which therefore the speed relatively to the sun decreases ; and there- 

 fore, if the orbit round the sun was a parabola before it entered the 

 sphere of the planet's influence, it will start along an ellipse after 

 emerging from that sphere. It thus becomes a member of the solar 

 system. On the other hand, if the comet pass behind the planet the 

 opposite effect is produced. The planet loses kinetic energy which 

 the comet gains, so that the comet when it extricates itself from the 

 sphere of the planet's influence, proceeds to move in a hyperbolic 

 orbit round the sun, past which it can make but one sweep, and will 

 then finally quit the solar system unless it encounter some other 

 planet. 



Professor Newton deals specially with the planet Jupiter. It is 

 manifest that the only parabolic orbits which approach that planet 

 are to be found amongst those of which the perihelion lies as near 

 to the sun or nearer than the orbit of Jupiter. Professor Newton 

 shows that out of 1,000,000,000 comets traversing the solar system 

 in such orbits, about 839* -will have their orbits changed by that 



* From this number a small deduction, perhaps of some dozen or so, has 

 to be made, to allow for those comets which actually collide with the planet. 



