Prof. Magnus's Hydraulic Researches. 1 85 



bros*, who, however^ as observed above, have not stated how 

 these motions of the particles arise. The explanation given of 

 the origin of the jet proves their necessity, so that these motions 

 may be taken as a proof of the correctness of the explanation. 



75. The forms of jets from triangular, pentagonal, hexagonal, 

 and all other regular polygonal apertures, may be explained in 

 an exactly similar manner to those from a quadratic aperture. 

 The form of a triangular jet is given in fig. 21. The surfaces of 

 the first system, opq, &c., are also in this at right angles to the 

 sides of the aperture xy, &c., and the form of the part between 

 the aperture and this first system is intelligible enough after 

 what has been said, §. 73 et seq., of a quadratic aperture. 



In pentagonal and hexagonal apertures the several surfaces 

 opq are still distinctly perceptible. With all these apertures, a 

 second and third system of surfaces, and often more, arc visible. 

 The surfaces of each system bisect, as in the triangular and 

 quadratic apertures, the angles between the surfaces of the pre- 

 ceding system ; but the more corners the aperture has, the less 

 prominent are the surfaces. If the number of the corners is 

 great, the surfaces of a system lie very near each other, and 

 they then appear like a dilatation of the jet uniformly disposed 

 around it. 



Jet from a circular aperture. 



7Q. Circrdar jets deport themselves difi'erently to those coming 

 from angular apertures. After what has been published by 

 Savart, it might have been supposed that the dilatations just 

 mentioned, which the surfaces belonging to a system in a poly- 

 gonal jet form, would also occur in circular jets. But this 

 is not the case. For such a jet exhibits no dilatations if it 

 issues from perfectly circular apertures ; if all hindrances in 

 the interior of the vessel are avoided, if no rotatory or other 

 motion occurs, there is formed under these circumstances a con- 

 nected mass of considerable length, without any, or at all events 

 with so inconsiderable dilatations, that they are scarcely per- 

 ceptible. From an aperture 13 millims. in diameter, and with 

 a pressure of 0'^-25, I have obtained a jet which fell vei-tically 

 2'"'5 without any dilatations. It would doubtless have re- 

 tained its connectedness to a still greater depth had it been pos- 

 sible to fix the vessel firmly enough at a greater height. The 

 depth to which the jet remains continuous, is changed as well by 

 the pressure as by the diameter of the aperture. The smaller 

 this is, the smaller is the distance to which the jet retains its 

 continuity ; and this distance is also smaller the less the pres- 

 sure under which the efflux takes place. 



* Experiences HydrauUques, p. 151. 



Phil. Mag. S. 4. Vol. 11. No. 71. March 1856. 



