234 MACHINERY IN CONNECTION WITH WATER. 



breadth of tlie wave, that is, the distance from crest to 

 crest, or from hollow to hollow. 



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 al- 

 ways 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 J inches 

 long beats once in each second, and a wave whose breadth 

 is 39J inches travels that breadth in one second. The' 

 length of a pendulum must be increased 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 traveling their breadth in one second ; and thus 

 their breadth, and consequently their speed, increases as 

 the square of the time. Large waves, therefore, roll on- 

 ward with far greater velocity than small ones. If only 

 thirty-nine inches wide, they move about two and a quar- 

 ter miles an hour, and pass once each second ; if 



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



53 do. do. 9 do. do. 4 do. 



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



836 do. do. 36 do. do. 16 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 falling or sub- 

 siding, and it then rolls onward with a real progressive 

 motion from the momentum it has acquired, breaks into 

 foam, and lashes the earth and rocks. The sea billows 

 are sometimes twenty-five feet in elevation,* and when 

 these advance upon a stranded ship on a lee shore, with 



* No authentic measnreracnt gives the perpendicular height of waves 

 more tliau twenty-flve feet. 



