This is the way in which De la Hire, Emerson, and other writers, have treated the sweet They give equations expressing the properties of different forms of sterlings ; the whole being derived front the common theories of the resistance of fluids, conceiving the im pulsion of the particles of the fluid to be the same as in the collision of hard bodies in free space.
But it is needless to follow this theory much further. AVe are convinced that it is founded altogether upon an improper assumption ; and, at any rate, it is of small im portance to the point in question. We think it may even reasonably be doubted, whether the best form of the sterling be merely that which gives least resistance to the stream. Should we not rather enqulre after that which guides with most effect the water under the arches, and prevents the dangerous action tin the foun dation ? At all events, we cannot concede, that the mode of action of the particles of water is the same which the above theory supposes, and which is commonly employ ed by writers on this subject. It would lead us into too wide a digression, to state the reasons which may be given against this doctrine of impulsion ; besides, we shall have another opportunity of considering the sub ject more at length. See HYDRODYNAMICS.
We shall, therefore, at present, only exhibit, in a fa miliar way, the notion we have of the real action of a fluid in motion, which, although it may be more difficult to adapt to the precision of mathematical reasoning, will, we are convinced, be of more value to the practical builder, in giving him clear conceptions of the actions against which he is to provide. Let abBA, Plate LX XXI, Fig. 9, and cc/DC, Fig. 10, be a thin film of water, which has advanced against the flat end Alt, CD of the pier, and whether the first lamina of particles act by impulsion or not,—for this is not a place for meta physical discussion,—let another and another succeed, until at length they constitute a plate or film abBA, or edDC, possessed of the properties of a fluid. This film will have had its direct motion destroyed by collision with the flat end of the pier. It cannot flow back, for it is stopped by the adjoining and following waters. Let us suppose it for a moment, to be stationary. The se cond film now co.nes on, and being hindered from pass ing up to the pier by the first film, abBA, can produce nothing like impulsion upon the pier, but it will propa gate its force through the fluid film, in the way in which only a force is propagated through fluids; that is in eve ry direction. The pier, therefore, will receive the im
pression of the second film unimpaired, but in the way of a pressure only, not as an impulsion.
In the mean time, the first film which is compressed between the pier, and the second film advancing, and the waters of whiAcannot as yet move off sidewise, be ing opposed by the other parts of the stream, hitherto supposed to be at the same level, must obey the hydro statical law, and yield to the impression received, by its waters rising upwards, the only way in wluch they arc free to move. There will be an accumulation Ctfimme diately before the pier. The second film wilt also be raised upon the same principle, but not so much ; the third will be somewhat less than the second, and so on.
Now it is evident, that the superficial of this accumulation being so much higher than the r, • of the stream, must tend to slide of on all sides. , s'ding off will cast them down in inclination towards c iges, and of course the greatest elevation will be jut at the middle between A and B. At the same time, the same pressure witch produces this accumulation, or, if it may be so considered, the very accumulation itself will propagate, in every direction, through that film, a cor responding pressure. This will enable the waters of the film to escape at each side, by pressing transversely on the passing current. No water could so escape without such an accumulation as we speak of; for the passing stream, being otherwise at the same level, would reacT with an equal pressure.
The notion, therefore, of the particles of water being reflected as in the collision of bodies in free space, can not be entertained. Speculations founded upon that principle leave out the most remarkable feature of the case, viz, the fluidity of the water. Yet a trifling atten tion to that circumstance, renders the notions through out the whole much more familiar. We have established the fact of the accumulation of the fluid im mediately in front of the pier. It is evident that no force whatever can be propagated through the fluid, without such an accumulation; we may therefore consider at once the accumulation as the cause, mark, and measure of every subsequent modification of the passing stream, and we will find it fully equal to the explanation of all the phenomena.