NOTES. 



433 



any other curved line. When the axis is perpendicular to the base, the 

 solid is a right cone. If a right cone with a circular base be cut at right 

 angles to the base by a plane passing through the apex, the section will 

 be a triangle. If the cone be cut through both sides by a plane parallel 

 to the base, the section will be a circle. If the cone be cut slanting quite 

 through both sides, the section will be an ellipse, fig. 6. If the cone be 

 cut parallel to one of the sloping sides as A B, the section will be a para. 



Fig. 7. 



bola, fig. 7. And if the plane cut only one side of the cone, and be not 

 parallel to the other, the section will be a hyperbola, fig. 8. Thus there 

 are five conic sections. 



NOTE 23, p. 5. Inverse square of distance. The attraction of one 

 body for another at the distance of two miles is four times less than at 

 the distance of one mile ; at three miles, it is nine times less than at one ; 

 at four miles, it is sixteen times less, and so on. That is, the gravitating 

 force decreases in intensity as the squares of the distance increase. 



NOTE 24, p. 5. Ellipse. One of the conic sections, fig. 6. An 

 ellipse may be drawn by fixing the ends of a string to two points, S and F, 

 in a sheet of paper, and then carrying the point of a pencil round in the 

 loop of the string kept stretched, the length of the string being greater 

 than the distance between the two points. The points S and F are called 

 the foci, C the centre, SC or CF the excentricity, AP the major axis, 

 Q D the minor axis, and P S the focal distance. It is evident that, the 

 less the excentricity C S, the "nearer does the ellipse approach to a circle ; 

 and from the construction it is clear that the length of the string S m F is 

 equal to the major axis PA. If T t be a tangent to the ellipse at m, then 

 the angle T m S is equal to the angle t m F ; and, as this is true for every 

 point in the ellipse, it follows that, in an elliptical reflecting surface, rays 

 of light or sound coming from one focus S will be reflected by the surface 

 to the other focus F, since the angle of incidence is equal to the angle of 

 reflection by the theories of light and sound. 



NOTE 25, p. 5. Periodic time. The time in which a planet or comet 

 performs a revolution round the sun, or a satellite about its planet. 



U 



