This is a subject which has endangered many an animated discussion among men of science, millwrights, and others, and it seems to be still a mooted question. It has been noticed that natural waterfalls, however great, seldom produce any vibrations in their imme-iiate neighborhoods, while some artificial dams jarr the buildings in their vicinity for several miles around. The cause of this phenomena is worthy of investigation, for it is desirable to build dams that will produce no vibrations. To an inquiry made of us a few weeks since, by a correspondent in Vermont, we gave an answer which has called forth some important information on the subject. In a letter received from R. Fitzgerald, of New Haven, Conn., he takes the ground that the jarring effect produced by some dams is caused by compressed air, under the smooth sheet of water, and not by the falling of the water. He states that, "forty years ago, there was a dam across the Salmon river, at Malone, Franklin county, N. Y., which had a smooth sheet of water passing over it, and the windows of the houses in the village were kept constantly vibrating by it, until a tree drifted down the river and lodged in the central part of the dam in such a position as to break the sheet of water, when the j arring of the windows ceased." This he attributed to the tree allowing the confined air to escape. Since that period, he ha~s witnessed many similar cases. Our correspondent has formed his opinion without positive proof as to the cause ; he may be right, but our opinion differs from his. In our last number, we intended to publish his letter (but were unable to do so), with the following answer:—"It appears to us that air should act as an elastic cushion to prevent, and not cause, vibrations in waterfalls. Any obstruction which breaks a sheet of falling water prevents the regularity of its vibrations, and stops or modifies jarring sensations, upon the same principle that a body of soldiers walking at random over a suspension bridge prevents it vibrating, whereas, if they keep in regular marching order, they will cause it to oscillate violently, as was done near Manchester, England, in 1831, by which a bridge fell down." Since we penned the foregoing, we have received a copy of the transactions of the American Academy of Sciences, just published, giving an account of the meeting held at Boston in September last, at which there was a paper read on this very subject, by Charles Stodder, in relation to the dam at Hadley Falls, on the Connecticut River. It seems that the vibrations of this dam are extensive in their influence, and, in fact, are a subject of wonder, being felt at Springfield, seven miles distant, and at Amherst, distant fourteen miles. In his paper, Mr. Stodder states that the only cause he " has seen assigned for this phenomenon is the agitation of the air behind the falling sheet of water"—the same cause as that described by our correspondent, Mr. Fitzgerald. Mr. Stodder, however, entertains a different opinion, and states that such a theory is entirely disproved by a dam at Lewiston, where the water falls over an inclined plane, leaving no space for air under it, and yet the vibrations are very decided. The dam at Hadley is 1,000 feet long, and it has a vertical fall of 32 feet. The water does not fall in an even stream from the summit of the dam to the surface of the water below, but the upper surface in section presents to the eye a waved outline. This ap--pearance Mr. Stodder has noticed at Hadley, Nashua, Lawrence, and other vertical falls. What is the cause of this ? The following is the answer of Mr. Stodder:—" The phenomena is caused by that property of falling fluids by which they assume the globular form, which may be seen at the Kauterskill Falls on the Catskill Mountains, where the whole body of the falling water is broken into drops. Applying this principle to the fall over an artificial dam, the water at the very ' commencement of its descent begins to assume ihat form, and the further it descends the learer it approaches to it. In passing over a lam like that at Hadley, the water presents % uniform depth throughout the whole length Df the dam, and if we imagine the current of water to be an infinitude of small streams of miform depth in contact with one another, 3ach having the same tendency, the result cnust be to produce swellings and contractions throughout the whole extent of the dam. When iach of these waves strikes the bottom, it gives i blow proportioned in force to the body of water falling from the hight of the dam. Every variation in the depth of the water causes a variation in the size and distance of ihe waves, each of these causes a concussion Ln proportionate intensity to the weight of water in it, and in rapidity to their distance ipart. These effects of falling water should be expected in general only on artificial falls, such as mill dams." Respecting natural falls, tie says :—"As their faces are rarely vertical, but are broken with angular rocks, causing various depths of water on them, and as every variety of depth alters the -Conditions to form the concussive pulsations, there is no coinci-lence among them, so that the waves of one part strike- the bottom in the invervals of those )f aother part, and thus the concussion of me neutralizes the other. At Hadley, the lam is one right line from bank to bank, the bed of the river is solid rock, and the top of the dam is level. The waves or pulsations of "ailing water are uniform, and strike the bottom with sychronous concussion from one end of the dam to the other. It is not surprising that the earth should be felt to vibrate at Springfield and Amherst." We have presented a similar idea to this in the case of a body of soldiers marching over a suspension bridge. At the close of the reading of Mr. Stodder's paper, Dr. C. T. Jackson, to controvert the opinions advanced in it, stated that vibrations were noticed at the dam in Nashua, N. H., " only when the wind is in such a direction as to break the fall and permit the air to escape, which is evidently confined behind the*sheet of water." The two opinions here set forth are all that we have ever heard advanced as to the cause of vibrations in dams. We must say that we cannot see how air can cause such vibrations, and the circumstance stated by Dr. Jackson, as an argument against Mr. Stodder's opinion, is one we would construe in favor of it. As the vibrations of the dam at Nashua are only felt when the wind is in a certain direction, in all likelihood it produces the synchronous pulsations of the falling water just in the same manner that it causes suspension bridges to oscillate, and by which peculiar undulations it has caused a number of them to fall. The tree which stuck in the center ol the dam over Salmon river may have disturbed the regular undulations of the water, and thus have stopped the vibrations. But, be that as it may, it appears to be a fact which engineers will do well to investigafe, as it maj afford important information in relation tc dams, whereby they may be constructed so as not to produce vibrations.