Vibrating Dams. 373 
very annoying. But after the dam was loaded with two hundred 
and fifty additional tons of stone, all other circumstances remain- 
ing the same, the vibrations ceased. Moreover, direct evidence 
of the vibration of the dam is afforded at Scantic, (p. 367,) and at 
Northampton, (p. 370,) by the tremulous motion of the water ex- 
tending a short distance back of the edge of the dam. The fact 
mentioned at Springfield, (p. 368,) of the apparent vibrations of 
the dam, is probably to be explained in the same way. Although 
refraction through the undulating surface of the water would give 
an apparent motion to the timbers of the dam, yet this undula- 
ting surface itself indicates real vibrations in the dam. 
2. These vibrations are excited in the dam by the friction of 
the running water.—Vibrations of the dam must be communica- 
ted to surrounding objects, the air, water, earth, etc. In which 
of these are the vibrations first excited? Does the air communi- 
cate vibrations to the dam, or the dam to the air? ‘This question 
is answered by the experiment at Cuyahoga Falls. When the 
dam is so loaded that it cannot vibrate, the phenomenon ceases 
entirely. Hence it is clear that the dam is the original vibrating 
body; and those who have observed the vibrations excited in 
elastic rods and plates by a bow, will probably have little hesita- 
tion in admitting that the running water performs the oflice of a 
bow. We may easily estimate the velocity requisite to produce 
the greatest effect. The depth of water at the time of the great- 
est vibrations is estimated at five or six inches for Cuyahoga 
Falls; four or five inches at Scantic; a little less than eight inch- 
es at Springfield; and at Gardiner, for a-stone dam, about six feet. 
That is, a wooden dam requires a velocity of five or six feet per 
second, and a stone dam about twenty feet. The ordinary ve- 
locity of the bow upon a bass viol is perhaps one foot per second. 
3. The time of a vibration may be computed when we know 
the dimensions of the dam.—F rom some experiments made with 
the largest beams I have been able to command, it is inferred that 
a single beam of white oak two feet thick and ninety feet long, vi- 
brating as a whole, would make 1.5 single vibrations per second. 
Vibrating in two segments, it would make 6.0 vibrations, and in 
three segments 13.8 vibrations per second. The time of vibra- 
_tion is independent of the width when the beam is free ; but if one 
edge of a long plank be confined, its number of vibrations is in- 
creased, while by loading it the number is diminished. I am un- 
