E. Loomis on vibrating Water-falls, ; 365 
and that the descending sheet serves merely as a load, to retard 
the velocity of these vibrations. 
This theory will be fully established or disproved, when we 
are able to compute the effect produced upon: the vibrations of 
a column of air, by a descending sheet of water of given dimen- 
sions. 
Why are not these vibrations noticed wherever water pours over 
a dam? 
It is believed that most water-falls exhibit some degree of 
vibratory motion at certain stages of water; but in order that 
these vibrations may be powerful and long-continued, the edge 
of the dam must be horizontal, and quite smooth; otherwise 
the thickness of the descending sheet will not be uniform; and 
the sheet will swell into ridges in some places, while other parts 
come thin. The sheet will divide in some places before 
reaching the bottom of the fall, and this leaves an opening in 
the enclosure which contains the column of vibrating air. 
This is probably the reason why many water-falls never ex- 
hibit this phenomenon in a palpable manner; and why in only a 
few cases is the vibration so powerful as to cause any annoyance, 
hy ts a particular height of water requisite to produce these 
vibrations 
The descending sheet of water must have a thickness of several 
inches; otherwise it is divided by the action of the air, and 
the column of air ceases to be enclosed on all sides. With a fall 
of nine feet, as at South Natick, a thickness of 4 or 5 inches is 
Tequisite; and with a fall of 30 feet, as at Holyoke, a thickness 
of nearly a foot is requisite. At Lawrence, with a fall of 34 feet, 
the vibrations are not noticed when the depth of water is much 
less than 3 feet; but this seems to be owing to the inequalities 
on the top of the dam, resulting from the iron bars being bent 
over by the spring freshets, and confining some of the flash 
boards to the top of the dam. | 
The vibrations cease almost entirely when the water exceeds 
a certain height, because the thickness of the sheet becomes too 
great in comparison with its height, and there being some cohe- 
Sion between the particles of the liquid, the sheet partakes some- 
what of the rigidity of a solid body. In order to*produce a 
Strong effect, the thickness of the sheet must not exceed about 
one-sixth or one-eighth of the height of the fall. At South 
atick, with a fall of 9 feet, which is somewhat diminished by 
the back water at the time of a freshet, the vibrations cease when 
the depth of water much exceeds ten inches. At Holyoke, with 
a fall of 80 feet, which is also diminished by the back water at 
the time of a freshet, the vibrations cease when the depth of 
water much exceeds 5 feet. At Lawrence also, where the fall 
is a little greater than at Holyoke, the vibrations cease when the 
depth of water on the crest of the dam much exceeds five feet. 
