180 Prof. Magnuses Hydraulic Researches. 



The water which falls from the three arms ocij, xy^, xyn forms, 

 as in a former case, § 61, thick edges, ye, y^^e^p which encounter 

 centrally. Thereby result the two surfaces 7-j)q and riPiQi, which 

 bisect the angle made by the edgesyeand yuC,!, as well as that by the 

 edges yi,ei, and y^e^ and which have the position xp and xpp fig. 18. 

 But by the central encounter of the edges 7/e and y,ei a third surface, 

 iczv, is formed, which bisects the angle of these edges, or is at right 

 angles to yxy,, and consequently falls in the prolongation of the 

 TplanexyiiCi. It extends itself onlytowards the side?/;^,and isscarcely 

 perceptible on the other side, whei'e it is met by the edge y^ye^^. 

 The edges of the surfaces rpq and riPiCji form by their encounter 

 a new surface inn, which falls in the same plane with 7vzv. There 

 are formed, however, by the encounter of the surfaces rpq, TiPffi 

 with the surface tozv, two new surfaces, hik and A^ijA;^. A second 

 system of surfaces is not perceptible in this jet, because by the 

 encounter of surfaces of unequal mass the motion is too irregular, 

 and hence the connexion between the particles of water is too 

 much disturbed. 



Jets from a square orifice. 



64. When the water issues from a square orifice, and when 

 no hindrance, rotation, or other disturbing motion is present in 

 the vessel, a jet is obtained whose form is similar to that shown 

 in fig. 19, when viewed from a position perpendicularly opposite 

 one of the sides of the square. 



Below the place of greatest contraction, ooo, four surfaces, opq, 

 Sec, are seen whose productions pass perpendicularly through 

 the centres of the sides of the aperture. Below this system of 

 surfaces is a second and similar one, which also contains four 

 surfaces, uvw, &c. These latter bisect the angles of the first 

 system, and consequently coincide in direction with the diagonals 

 of the square aperture. To understand this better, a, /S, y, B repre- 

 sent the horizontal sections of the jet at those places where the 

 dotted lines ««,, /3/3,, 7-/;, SS^ cut the jet. Below the second 

 there is a third system of surfaces, which again is similarly 

 situated to the first ; and below that a fourth, whose surfaces 

 are parallel with the second, and so on. I have often observed 

 nine such sharply-defined surfaces below each other, and below 

 these a considerable number which were not so sharply defined. 

 After what has been said before, § 61, about the origin of such 

 surfaces from a cruciform aperture, no further explanation is 

 needed to show how the second system of surfaces is produced 

 from the first, and from the second the following ones. But it 

 is not so easy to explain how the first system of surfaces is 

 formed, or how the peculiar form is produced, which the jet 

 shows previous to the commencement of the first system. I will 

 endeavour to explain the origin of this form. 



