64 ELEMENTS OF SCIENCE 



pendulum in its oscillation, varies as the square root of 

 its length, thus four pendulums, the relative lengths of 

 which may be represented by the numbers i, 4, 9, and 

 1 6, will oscillate in periods represented by i, 2, 3, 

 and 4. 



All that has been said with respect to uniformly 

 accelerated motion applies equally to uniformly retarded 

 motion. Thus when any body is projected straight 

 upwards from the earth's surface, it rises 32 feet less 

 during each succeeding second, till its velocity (which is 

 decreased during the ascent as it increases during a 

 descent) is exhausted. Thus it must pass each successive 

 point as it descends again, with the same velocity as that 

 it possessed as it passed each such point during its 

 ascent. 



But we have constantly to consider the joint effects 

 of a body with uniform motion and a uniformly accele- 

 rated motion as, for example, when a shot is fired 

 from a cannon. Such a body is impressed with the 

 uniform motion imparted by the explosion and with the 

 uniformly accelerated motion due to the force of gravity. 

 Putting entirely aside the action of friction and atmo- 

 spheric resistance, we find that there is an exact compo- 

 sition of forces. Thus at any moment the cannon ball 

 will be at the spot it would have reached had it been 

 carried, in a straight line, to the elevation it would have 

 attained by the force of projection acting alone, during 

 the time elapsed, and then fallen thence in an exactly 

 similar time. The junction of all these points of coinci- 

 dence i.e., the path followed by the projectile always 

 forms a peculiar curved line called a parabola a curve 

 such as would be produced by the margin of a section of 

 a circular cone cut through parallel to any part of its 

 slanting surface. 



