374 Vibrating Dams. 
able to compute these effects rigorously for the Cuyahoga Falls 
dam, but presume that they nearly balance each other. 'The 
number of vibrations thus computed, on the supposition of three 
vibrating segments, corresponds very closely with the estimate on 
p. 365; it is hence inferred that this was the common, perhaps 
the only mode of vibration of this dam. I much regret that I 
had not the opportunity of measuring accurately the number of 
vibrations, and of obtaining some direct evidence of the number 
of nodes. At Springfield it appears pretty clear that there are 
two and a half vibrating segments, the half segment at the north 
end vibrating as if that extremity were entirely free. With a 
rod of uniform size and elasticity the first two segments would 
be of one hundred and eighty feet each, and the remaining half 
segment ninety feet. Ina dam, these conditions of perfectly 
uniform thickness and elasticity could not be expected, and the 
segments may be considerably unequal. A prismatic beam of oak 
one hundred and eighty feet long and twenty two inches thick, 
would make one vibration per second. It is remarkable that the 
vibrations of the three segments appear not to be synchronous, 
but succeed each other at intervals of about a quarter of a second. 
If this observation was made while standing at the north end of 
the dam, a part of the retardation might be ascribed to the velo- 
city of sound, which travels one hundred and eighty feet in about 
the sixth part of a second. It would seem that the intervals 
should be different when observed from one end of the dam, and 
from a station thirty rods below, though no mention is made of 
any such difference. ‘This point deserves further examination. 
The dam at Scantic is one hundred feet long, and makes five 
vibrations per second. It may hence be conjectured to vibrate 
in two segments. No direct evidence of this fact is furnished by 
the preceding statement. It is not improbable however that pe- 
culiarities may be detected in the falling sheet, similar to those at 
Springfield, which would indicate the position of the nodes. 
4. Why ts the effect of the vibrations impaired by dividing the 
sheet of water ?—The facts stated on pp. 366, 370, may seem in- 
consistent with the idea that the dam is itself the original vibra- 
ting body. ‘These facts do indeed indicate that the descending 
sheet of water has an important office to perform. This office I 
conceive to be that of a membrane vibrating in unison with the 
dam and reinforcing the sound. \ Behind this sheet, is a confined 
