round die circular base of the vein in 



the resisted surface. 



M. Du Buat next proceeds to ascertain the amount 



f ^ e resistance, when an imnioveable surface U placed 

 bs*> bed in a current of indefinite extent. The instrument 

 in > ciutem which be used for this purpose was a box of white iron, 



HYDRODYNAMICS. 



contact with 



545 



of Fluid*, 



UK di- 



presenting a surface of one square foot. It had a 

 thickness of nearly four lines, and was shut on all sides 

 except a small opening in its posterior surface, into 

 which was soldered the horizontal branch of a rectangu- 

 lar tin tube 16 lines in diameter, which received a float 

 that indicated the height to which the water rose 

 within the tube. By means of a bar of iron of about 10 

 feet long, which could be attached to the back of the 

 box, the box could be fixed at any distance below the 

 surface of the current. Five holes, each about a line 

 in diameter, were perforated in the anterior side of the 

 tin box. The first was in the middle, the second equi- 

 distant, in a horizontal line, from the middle and the 

 edge, and the third in the same horizontal line, but only 

 10 lines distant from the edge; the fourth was quite 

 close to the edge ; and the fifth in the lower angle of 

 the square. When the box was fixed, and the current 

 of water was allowed to enter one or more of these holes, 

 the fluid rose in the rectangular tin tube to a height 

 due to the- pressure of the current. In this way Du 

 Buat made several experiments, which gave very singu- 

 lar results. The pressure was not only found to dimi- 

 nish from the centre of the surface to the edge or mar- 

 gin, but it became nothing at a certain di-tance from 

 the centre, and afterwards negative at the margin. 

 That is, when the water entered through the central 

 ho'f, it rose to a certain height in the tin tube above 

 the level of the stream. ThU In- Jit diminished when 

 the water entered at a hole nearer the margin, the 

 height became nothing at a certain distance, and still 

 nearer the margin the fluid was actually depressed in 

 the tin tube below the surface of the current. Du 

 Boat explains this remarkable fact by saying, that the 

 real pressure against any part of the surface is only the 

 difference of the pressure against that part considered 

 separately from the rest of the surface, and the height 

 due to the variable velocity with which the water 

 move* along the surface which is .-truck ; that is, the 

 water in escaping along the surface always diminishes 

 the real pressure of the current ; but towards the edges 

 it becomes more powerful than the real current, and 

 therefore that part is less pressed than if the fluid were 



ovcable, and will therefore link in the tin tube. 

 In order to ascertain the mean pressure upon the 

 whole surface, Du Buat shut up the holes already men- 

 tipped, and perforated the same surface with <ri3 holes, 

 disposed symmetrically, with 25 on each side. By expo- 

 sing this surface to the current, it appeared that the 

 height of the water in the tube was 2.1 } lines, when 

 the mean velocity wa 36 inches per second, which is 

 due to a height of 21 J lines. Hence the height due to 

 the mean resistance U equal to 1.186 times the height 

 due to the velocity. 



By a similar contrivance Du Buat measured the di- 

 minution of presanre, or the non-prttturr as be calls 

 it, experienced by the posterior part of a body fixed in 

 a current. He found, I </, That the diminution of pres- 

 sure increased considerably by lengthening the body ; 

 2</, That it increased a little from the circumference of 

 the body to its centre ; and, 3<//y, That the diminution 

 of pressure U proportional to die area of the surface 

 that U submerged. 



VOL. XI. PART II. 



It had hitherto been supposed by all authors, that HcsUi 

 the resistance experienced by a surface at rest from a ^ '""^ ', 

 fluid in motion-, was exactly equal to the resistance of t j^, v e ,7. 

 the same surface when it moved in stagnant water, with s j$ tan ce to 

 a velocity equal to that of the current. M. Du Buat bodies mo- 

 resolved to examine this point experimentally, and ng in 

 from a variety of experiments made on the river ^*? r a 

 Hayne, between Mons and Conde, he concluded, 1st, 

 That the phenomena are by no means the same when 

 the body is at rest as when it is in motion, id, That 

 in the latter case, the pressure does not diminish st> 

 sensibly from the centre to the circumference, and in- 

 stead of a negative pressure towards the sides, that tho 

 pressure is then so great, as to be measured by the 

 third of the height due to the velocity, which shew 

 that the water runs along the anterior surface with k - 

 velocity, or with more uniformity. 3d, That the pres- 

 sures diminish in a less ratio than the sauare of the 

 velocity, when the velocities are less than three or four 

 feet per second. 4//i, That the mean pressures are mea- 

 sured by the exact height due to the velocity, instead 

 of 1 . 1 N(J limes the height, as before : And, 5i/i/y, That 

 the diminution of pressure diminishes little from the 

 centre to the circumference in the same order as the 

 jirc.-iMirc-s. 



The next object of M. Du Buat is to determine the RUnce 

 quantity of fluid which globes and plane surfaces drag * r "' 

 along with them, when oscillating in a fluid. The ; 

 globe* were of wood, lead and glass. They oscillated 

 in a vessel 51 inches long, 1 ~ inches wide, and 1 4- inch- 

 es deep : They were entirely immersed about three 

 inches below the surface, and the wire which suspend- 

 ed them was as delicate as their weight would permit. 

 The general result of these experiments is, that a globe 

 ' oscillating in water drag* along with it, both before and 

 behind, a portion of fluid whose volume exceeds a little 



I 



its own volume, or nearly of its own volume. 



1UH) 



Similar experiments were made with various plane 

 surfaces of white iron, cylinders oscillating in the plane 

 of their axes, quadrangular prisms oscillating in the 

 plane of their axes, triangular prisms oscillating in the 

 plane of their axes, cube* oscillating directly, cubes 

 oscillating by the common section of two of their 

 bounding planes, cube* oscillating by a solid angle, 

 quadrangular prism* oscillating by the common sec- 

 tion of two oblique face*, cylinders oscillating in the 

 direction of their diameter*, and cones, pyramids and 

 mixed bodies oscillating in the plane of their axes; but 

 our limits will not permit us to give any account of 

 these experiment*, which will be found in Part III. 

 sect. 1 . chap. viii. of Du Buat'* Principe* D'Hyilrau- 

 liijHf, torn. ii. 



The attention of Du Buat is next directed to the ira- Retkunct 

 port ant subject of the resistance opposed to vessels in at vencU in 

 narrow canals. From a comparison of several cxperi- nnw w- 

 ments, he has deduced the following formula: 



8.46 

 or R = -= 



nab. 



P K 



n r- 



c 



T+ 2 T+ 2 ' 



in which C is the area of the section of the canal, 6 the 

 area of the section of the vessel, and R the resistance ; 

 the resistance in a fluid of indefinite extent being = 1. 

 In order to compare this formula with experiments, 

 Du Buat employed five kinds of prismatic boats, se- 

 veral feet in length, and terminated both before and 

 behind by a plane surface. The boat 

 32 



