LESSONS IN PHYSICS. 47 



illustrated by swinging a pail partly filled with water over the 

 head or in any direction; the centrifugal force so overcomes the 

 force of gravity that not a drop of water falls. Race tracks and 

 railroad tracks are raised on the outside of a curve to prevent 

 overturning from the centrifugal force exerted when -passing the 

 ciirve. 



The ball from the bat, the arrow from the bow, the bullet from 

 the gun, are projectiles, and all move in curved lines. An impul- 

 sive force in each case gives the body motion, which would be in a 

 straight line but for the action of the constant force of gravity. 

 The range of a projectile is the horizontal distance through which 

 it moves. This distance depends upon the energy of the impulsive 

 force, the angle at which the body starts and on the resistance of 

 the air. Theoretically an angle of 45 degrees would give the 

 greatest range ; but in practice an angle of about 30 degrees is 

 found to be best for a bullet, and about 35 degrees for an arrow. 



Motions in liquids may be waves caused by winds; may be 

 tidal waves caused by the attraction of the sun and moon; may 

 be currents caused by gravity, by winds or unequal heating; or 

 they may be vibrations arising from an endless variety of causes. 

 In either case the motions vary greatly, and are useful and in- 

 teresting in various ways. Examples of these motions and their 

 effects are so common and well known that they need only be 

 mentioned here. But wa,ter is often conveyed from reservoirs 

 through pipes for use in various ways, and it is interesting to 

 notice that the results in practice differ so widely from theoret- 

 ical deductions that most calculations are made from arbitrary 

 rules. If we examine a. jet of water flowing from an orifice in a 

 vessel we shall see that it grows rapidly smaller, so that at a 

 little distance its size is only about two-thirds as great as at the 

 orifice. Beyond this point the contraction of the jet is gradual . The 

 rapid contraction near the orifice is due to cross currents, caused 

 by the water flowing toward the orifice from different directions. 

 The effect of these cross currents can be diminished somewhat by 

 the use of short tubes; but when all is done scarcely more than 

 80 per cent, of theoretical flow can be secured. The flow of water 



