148 ANNUAL OF SCIENTIFIC DISCOVERT. 



Professor Loomis, on the vibrations of a dam at South Natick, Mass. 

 These resulted in ascertaining that the time of a vibration, according 

 to the depth of water on the edge of the dam, was a little less than the 

 time in which a solid body would fall through a space equal to the 

 depth of the water. Thus, when the depth of water was 5.06 inches, 

 the time of one vibration was 0.138 of a second, while the time of a 

 solid body falling through that depth was 0.162 of a second. 



The dam across the Connecticut River, at Holyoke, Mass., is 1017 

 feet long, and 30 feet high. It is formed of square timbers inclined 22 

 degrees to the horizon. From the crest of the dam, the water descends 

 along an apron about four feet in length, sloping downward at an angle 

 of 22 degrees. The sheet of water falling over this dam exhibits three 

 different rates of vibration, namely, about 256, 135, and 81 vibrations per 

 minute, corresponding to depths of 16, 28, and 56 inches of water on 

 the dam. The change from the first to the second rate of vibration 

 takes place when the depth of water is from 23 to 26 inches ; and the 

 change from the second rate to the third takes place when the depth is 

 from 35 to 4 7 inches. The vibrations are not noticed when the depth 

 of water is less than about 1 2 inches, and they also disappear when the 

 depth is as great as 80 inches. 



At Lawrence, Mass., Mr. B. Coolidge, engineer, made a series of ob- 

 servations, as also did Prof. Loomis. In all these, the time of the vibra- 

 tions was taken, and compared with the time which a solid body would 

 occupy in falling from the same height ; and the number of vibrations 

 of a column of air of the depth behind the sheet of falling water has 

 been calculated. Now, as to the conclusions, Prof. Loomis says, " I 

 do not know of any theory which will enable us to compute the precise 

 influence of a sheet of water of given dimensions ; but at present, it 

 seems probable that the vibratory motion originates in the column of 

 air behind the sheet of water, and that the descending sheet serves 

 merely as a load to retard the velocity of these vibrations." When the 

 edge of the dam is uneven, and when the sheet of water is very thin, 

 an opening will be left for the column of air behind the sheet, and no 

 vibrations are produced. In reference to this point, Prof. Loomis 

 says, " It is believed that most waterfalls exhibit some decree of vi- 



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bratory 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 become 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 vibrat- 

 ing air. This is probably the reason why many waterfalls 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." 



The answer to the question, Why the vibrations vary or disappear 

 with variations in the height of the water is given as follows : " The 

 descending sheet of water must have a thickness of several inches ; oth- 

 erwise, 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 four or five inches is requisite ; and with a fall 

 of thirty feet, as at Holyoke, a thickness of nearly a foot is requisite. 



