BREADTH AND VELOCITY OP WAVES. 207 



tion, is called breadth of the wave, that is, the distance 

 from crest to crest or from hollow to lioUow. 



There is a striking similarity between the rising and 

 falling of waves and the vibrations of a pendulum, and 

 it is a very interesting and remarkable fact that a wave 

 always travels its own breadth in precisely the same 

 time that a pendulum whose length is equal to that 

 breadth performs one vibration. Thus, a pendulum 

 39^ inches long beats once in each second, and a wave 

 whose breadth is 39^ inches travels that breadth in 

 one second. The length of a pendulum must be in- 

 creased as the square of the time for its vibrations ; 

 that is, to beat but once in two seconds, it must be 

 four times as long as for one second ; to beat once in 

 three seconds, it must be nine times as long, and so on. 

 In the same way, waves which travel their breadth in 

 two seconds are four times as wide as those travehng 

 their breadth in one second ; and thus their breadth, 

 and consequently their speed, increases as the square 

 of the time. Large waves, therefore, roll onward with 

 far greater velocity than small ones. If only thirty- 

 nine inches wide, they move about two and a quarter 

 miles an hour, and pass once each second ; if 



13 feet wide, they move 4^ miles an hour, passing once in 2 seconds. 



52 do. do. 9 do. do. 4 do'. 



209 do. do. 18 do. do. 8 do. 



836 do. do. 3G do. do. IG do. 



Although the water itself does not advance where 

 there is much depth, yet when it reaches a shore or 

 beach, the hard and shallow bottom prevents it from 

 falhng or subsiding, and it then rolls onward with a 

 real progressive motion by the momentum it has ac- 



