516 



BRIDGE. 



p 



I XXXI. 

 Fig. 7. 



Theory, each particle on the plane AB is diminished in the 

 proportion cf the sine of its incidence EFB; and the 

 action on the face being given, the effect of it in the 

 direction BD, or parallel to the axis, will be found 

 by still further diminishing it, in the ratio of the sine 

 of obliquity. In the common case then, when the 

 length of the pier is in the line of the stream, the re- 

 sistance of the pier will be as the square of the sine 

 of incidence, or it will be inversely as the square of 

 the length of the face AB of the pier, that being a 

 straight line. Otherwise, if EF represent the abso- 

 lute force of any particle, draw the perpendiculars 

 FG, EG, and GH, then FG exhibits the impulse 

 perpendicular to the force AB, and FH the effect of 

 that impulse in the direction of the axis BD ; where, 

 by the way, it may be observed, that if the angles 

 DAB and DBA be equal, that is, if ABC be a 

 right angle, then are FG and GE equal, also FH 

 and HE ; so that the absolute impulse on the sides 

 of a rectangular wedge is just half the impulse on its 

 base. We might pursue this mode of reasoning 

 much further. We should find among other things, 

 that the absolute impulse on right lined triangles, is 

 less than on any curvilineal figure ; that the impulse 

 on cylinders, or the front of half cylinders, is just 

 two thirds of the direct impulse on the base ; that 

 in all other curves, the nearer they approach to the 

 right lined triangle, the less is the impulse upon 

 them ; and it is sufficiently evident, that the impulse 

 will be always the less the more acute we make the 

 vertex of that triangle, that is, the greater projection, 

 and the sharper a point we give to the pier. 



This is the way in which De la Hire, Emerson, 

 and other writers, have treated the subject. They give 

 equations expressing the properties of different forms 

 of sterlings ; the whole being derived from the common 

 theories of the resistance of flu'ds, conceiving the 

 impulsion 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 fur- 

 ther. We are convinced that it is founded altogether 

 upon an improper assumption ; and, at any rate, it is 

 of small importance 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 en- 

 quire after that which guides with most effect the wa- 

 ter under the arches, and prevents the dangerous ac- 

 tion on the foundation? 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 employed 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 subject more at length. 

 See HYDRODYNAMICS. 



We shall, therefore, at present, only exhibit, in a 

 familiar 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 concep- 

 tions of the actions against which he is to provide. 

 LXXXI. Let a b BA, Fig. 9. and erf DC, Fig. 10. be a thin 

 Fig. 9, 10. film of water, which has advanced against the flat 



end AB, CD of the pier, and whether the first la- ' 

 mina of particles act by impulsion or not, for this " 

 is not a place for metaphysical discussion, let ano- 

 ther and another succeed, until at length they con- 

 stitute a plate or film ab BA, or cd DC, 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 sup- 

 pose it, for a moment, to be stationary. The second 

 film now comes on, and being hindered from passing 

 up to the pier by the first film, ab BA, can produce 

 nothing like impulsion upon the pier, but it will pro- 

 pagate its force through the fluid film, in the way in 

 which only a force is propagated through fluids ; 

 that is in every direction. The pier, therefore, will 

 receive the impression of the second film unimpaired, 

 but in the way of a pressure only, not as an impul- 

 sion. 



In the mean time, the first film which is com- 

 pressed between the pier, and the second film ad- 

 vancing, and the waters of which cannot as yet move 

 off sidewise, being opposed by the other parts of the 

 stream, hitherto supposed to be at the same level, 

 must obey the hydrostatical law, and yield to the 

 impression received, by its waters rising upwards, 

 the only way in which they are free to move. There 

 will be an accumulation C ef immediately before the 

 pier. The second film will 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 waters of 

 this accumulation being so much higher than the rest 

 of the stream, must tend to slide off on all sides. This 

 sliding off will cast them down in inclination towards 

 the edges, and of course the greatest elevation will 

 be just in the middle between A and B. At the same 

 time, the same pressure which produces this accumu- 

 lation, or, if it may be so considered, the very accu- 

 mulation itself will propagate, in every direction, 

 through that film, a corresponding 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 accumula- 

 tion 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 be- 

 ing reflected as in the collision of bodies in free spuce, 

 cannot be entertained. Speculations founded upo 

 that principle leave out the most remarkable feature 

 of the case, viz. the fluidity of the water. Yet a trif- 

 ling attention to that circumstance, renders the no- 

 tions throughout the whole process much more fa- 

 miliar. We have established the fact of the accu- 

 mulation of the fluid immediately in front of the pier. 

 It is evident that no force whatever can be propaga- 

 ted through the fluid, without such an accumula- 

 tion ; we may therefore consider at once the accumu- 

 lation as the cause, mark, and measure of every sub- 

 sequent modification of the passing stream, and we 

 will find it fully equal to the explanation of all the 

 phenomena. 



Of the film of water in the immediate neighbour- 

 hood of the pier, every part is urged laterally with 

 the same force, viz. the excess cf pressure produced 



