MECHANICS 65 



Another, and a most noteworthy, conic section* 

 is one formed by cutting across a cone in any place, 

 not at right angles to its base. It may be drawn 

 in the following simple way : If two ends of a thread 

 be attached to two points of a horizontal surface 

 the thread being much longer than the distance 

 between such two points and if a pencil be so placed 

 as to stretch the thread outwards as much as pos- 

 sible, and then be carried round (always so stretching 

 the thread) till it describes a closed curve, such a figure 

 will be an ellipse. The two points of attachment of the 

 thread, form what are called the Joci of the ellipse, and 

 the more these are approximated the more circular the 

 ellipse will become ; and it becomes transformed into a 

 circle as soon as they coincide. 



Now if a body were projected horizontally from a 

 point external to the earth's surface with sufficient 

 velocity, it would be carried in a certain time to a much 

 greater distance than gravity would make it fall during 

 that same time, and then (if there were no air) it would 

 never fall to that surface, but would continually go 

 round the earth in an ellipse the precise form of which 

 would depend on the exact velocity and direction given 

 to the body. 



Every stone flung into the air describes a little bit 

 of an ellipse round the centre of the earth, which it 

 would complete but for the overpowering attraction 

 of the earth. 



It has been ascertained that such a body, whatever 

 the amount of its divergence from a circle i.e., what- 

 ever the eccentricity of the ellipse in which it migh 

 move would be subject to the following law : 



* See ante, p. 37. 



