LECTURE. 



ON PLANETAEY DISTUEBANCES 



BY PROF. E. S. SNELL, 



or AMHERST COLLEOE, M ASSAOHnBETTS. 



The laws offeree and motion are everywhere the same. Whether a 

 pehhlehe thrownhythe hand of a child, or a world be launched into space 

 by the will of the Creator, the same laws will forever govern the move- 

 ments of the two bodies, and the same principles will be employed to 

 c^ilculate their paths. If no second force operates to disturb them, 

 they will pursue a straight course, and at a uniform rate for endless 

 ages. But should a second impulse be applied to the moving body, 

 and in some other direction, it will follow neither its original track 

 nor that of the neiu force, but will describe a line between the two, 

 which can be precisely determined, both in direction and velocity, 

 from the magnitude and direction of the two forces. And this inter- 

 mediate line will be as exactly straight, and described with a velocity 

 as perfectly uniform, as though but one force had originated the 

 motion. This is denominated compound motion ; but it is the force 

 which is compound, not the motion. 



If the body, which has commenced its rectilinear path, should be 

 subject to an attractive force urging it towards some centre, and in- 

 creasing as the square of the distance diminishes, and vice versa, then 

 it will move in an orbit about that centre ; and this orbit will inevi- 

 tably be one of the figures called the conic sections, in the focus of 

 which the attracting body resides. The stone thrown by the hand, 

 and describing a path bent towards the earth, has in fact begun to 

 move in such an orbit ; and if the earth could attract it by the usual 

 law of gravity, and at the same time present no obstruction to its 

 course, the stone would descend with increasing velocity, pass around 

 the centre within the distance of a few feet, and with a speed of many 

 thousands of miles per second, then ascend more and more slowly to 

 its place of departure, and thus, after the lapse of a few minutes from 

 the time it was thrown, be ready to begin the same journey anew ; 

 and this elliptical circulation would be continued forever, if no new 

 force should come in to prevent. The path of a projectile near the 

 earth is usually called a parabola ; and for all the purposes of calcu- 

 lation it is sufficiently near the truth ; for the extremity of so eccentric 

 an ellipse is infinitely near to a parabola, and this curve is much 

 more simple than the ellipse. So the upright corners of a building 

 are considered parallel lines, though in fact they converge towards the 

 earth's centre. 



The same principles which determine for us the resultant movement 

 under the action of tioo forces will also enable us to find it, when three. 



