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quent. If we excite a wave above that will float over an increased 

 amount of water, the nodes will move down till the wave has 

 passed away, when they suddenly come back into place. When 

 we cause these waves to follow in rapid succession, we have, in 

 the descent and return of the nodes, a perfect miniature of the 

 vibrating sheet, — the same effect is often produced by the fric- 

 tion of the water over the obstruction. 



The letter was acompanied by sketches representing the nodes 

 from an obstruction in the bed of the stream, and from a dam, — 

 the latter in the vertical sheet, across which they extended, being 

 o and 5, the number being governed by the depth of the water 

 at the dam. 



To produce a vibrating sheet, these nodes must first be set in 

 motion, which is done by the waves caused by the friction of the 

 water on the dam. If we count these waves as they pass the 

 edge of the dam, and the vibrations of buildings in the vicinity, 

 they are found always to correspond. With 10 inches of water 

 flowing over the dam, we have 3 nodes on the sheet, and 280 

 vibrations per minute ; with 8 inches, 4 nodes and 300 vibra- 

 tions ; with 7 inches, 5 nodes and 335 vibrations ; with 5 inches, 

 8 nodes and over 400 vibrations. 



The appearance of a vibrating sheet is very changeable under 

 different reflections of light. At one time the downward motion 

 is alone visible, giving the impression that the nodes are con- 

 stantly forming and falling ; a few hours after, the upward mo- 

 tion only is seen, indicating that the agitation of the sheet proceeds 

 from the bottom ; at other times the descent and return of the 

 nodes are alike visible. 



The vibrations of buildings near the dam often cease by a want 

 of synchronous action of the whole sheet, or by heavy waves from 

 above the dam. After the freshet in June, 1858, the water was 

 of a dark greenish yellow color, and deposited a thick coating of 

 slimy matter upon the edge of the dam, which prevented any 

 friction ; consequently all vibrations ceased for several weeks, 

 notwithstanding the water passed the most favorable points for 

 producing them. 



A series of long-continued and careful experiments has con- 

 vinced him that the sheet is of the concavo-convex form. This 

 may be demonstrated by viewing the sheet from both sides, or by 



