184 Prof. Magnus's Hydraulic Researches. 



this direction in passing through the orifice, and thus the re- 

 sistance experienced by the particles coming from the prominent 

 corners, produces that greater change of form akeady described. 



73. The pecuhar form of the upper part, xyoozz,, fig. 19, of 

 the jet from a square aperture is also explained by the influence 

 of pressure, as above elucidated (§§ 65 to 68). 



The particles of water coming from the corners of the square 

 exert a greater pressure on the sections immediately beneath the 

 aperture than the others ; hence the corners arc blunted, as is 

 seen in the section a. In passing from this to the following- 

 section, the blunt corners exert a greater pressure than the sides 

 of the square. For this reason the corners become more and 

 more blunt in the lower sections, and the sides of the square 

 become smaller. Hence on the jet are formed the triangular 

 siu'faccs X1/0, fig. 19, which are sometimes vertical; but some- 

 times, when a greater pressure is exerted by the blunt corners 

 on the interior of the jet, appear pressed outwards, so that the 

 point is more prominent than the side of the apertui'C above it. 

 With a regular efflux, however, the four points o lie in the same 

 horizontal plane. The section in this plane is almost square, 

 although its sides are generally bent inwards ; the edges o cor- 

 respond, however, to the centres of the sides of the aperture, a 

 phfenomenon which has been frequently observed, but never before 

 explained. The somewhat curved surfaces xoo, yoo, &c. are con- 

 tinued to zz,. By the pressure which is exerted in these on the 

 interior of the jet, the masses of water which form the surfaces 

 opq, OiPiqi, &c. are forced out, and the same action is produced 

 as with a cruciform aperture, § 61, or as if four jets coming from 

 the corners of the square were to move towards each other, 



74. If the motion of the several particles of water be consi- 

 dered, it follows directly from the explanation of the origin of 

 the jet just given, § 65 et seq., that scarcely one of them moves 

 in a vertical plane. It is manifest that in that part of the jet 

 where the various surfaces opq, o^p^q^, &c. are situated, the par- 

 ticles do not remain in the same vertical plane. But even in 

 that part of the jet above the first system of these surfaces, xyoo^zs^, 

 they do not remain in the same vertical plane, with the exception 

 of those particles which come from the middle of the sides of the 

 square; for the parts coming from the prominent places of the 

 aperture press aside those particles opposing resistance to them. 

 This lateral motion may be clearly perceived in the surfaces yoo^z, 

 for the particles are seen moving from y, and from the places 

 situated under y in the line yz above oo^, towards o and o^. 

 Similarly it is evident, that in the surfaces xyo the particles con- 

 verge towards o. These converging and diverging motions of 

 the particles have already been observed by Poncelet and Les- 



