Prof. Magnus's Hydraulic Researches. 193 



longation of the jet. It is generally so moved that it has no 

 determinate axis of rotation. The cavity just formed is seen to 

 move with the water from its place of formation, so that it is 

 observed on the surface at the same time that it swims in the 

 water. This phfenomenon is particularly seen when the water 

 is only a few inches deep. 



If the water be moved quite irregularly, the cavity is seldom 

 produced. 



105. It is easy to see how a screw-formed cavity is produced 

 by a rotation of the water. In consequence of the centrifugal 

 force, the particles move away from the axis of rotation in all 

 directions; but they experience a gi'eater resistance in the deeper 

 strata, where the pressure of the water is greater. Hence their 

 distance from the axis of rotation is less in the lower strata, and 

 diminishes with the depth. In this manner a funnel-shaped 

 space is formed, in which the centrifugal force acts in an oppo- 

 site direction to the hydrostatic pressure. But since, in the dif- 

 ferent strata, the rotation does not take place readily about the 

 same axis and with the same velocity, the cavity assumes a screw 

 shape. 



106. If water which does not rotate, but is quite tranquil, is 

 met by a jet, it produces, as was mentioned, § 100, a rotation 

 after some time. This is not produced as long as the jet is quite 

 regular, not even if a jet from a square or other polygonal orifice 

 be used. But the slightest irregularity in the jet, and this is 

 much more the case in jets from angular than from circular 

 apertui'es, sets the water near the place where the jet meets it 

 in irregular motion. The resultants of the motions of the indi- 

 vidual parts do not go through the same point, and hence a 

 rotation commences which rapidly increases when it has once 

 begun. It is scarcely necessary to mention how easily such an 

 irregularity occurs in circular jets, or rather how difficult it is to 

 avoid them. Any motion communicated either to the vessel from 

 which the water flows, or to that into which it flows, is sufficient 

 to produce it, for the motions produced are easily communicated 

 from the one to the other. 



107. If the jet meets the spiral-shaped windings of such a 

 cavity, which is changed by a motion of the surrounding water, 

 the wall of the cavity is hit by the jet, air is enclosed and carried 

 dowxa with the water which streams in. The same occurs if the 

 cavity changes its form or position by an alteration in the nature 

 of the jet. 



108. If the water which supplies the jet be set in vibra- 

 tions, the jet assumes, even if it comes from a circular aperture, 

 the round form mentioned, § 80, and then air-bubbles penetrate 

 into the water very easily. The force with which this happens 



