Prof. Magnus's Hydraulic Researches. 97 



prevented by their connexion with this surface. The continual 

 contraciion of the intermediate surface deflects the jets from 

 their direction, but the former thereby becomes thinner and is 

 ultimately ruptured. The jets then continue to move onwards 

 in the same direction as the one they had when they separated 

 from the surface. 



22. If the force with which the jets move is not sufficient to 

 rupture the surface, either because the angle between them or 

 their velocity is too small, or because only a small portion of 

 them pursues the same path, the greater having served to form 

 the water surface, the jets are continually brought nearer to one 

 another by the force of cohesion, and the water surface appears 

 unbroken, as shown by bcdc^, in fig. 7. 



But inasmuch as the axes of the jets before contact were not 

 in one plane, they do not meet one another now; that which 

 was before on one side, e. g. the right or above, lies on the other 

 side, the left or below, at the next contact. Tor if we imagine 

 a plane parallel to the axes of botlf jets immediately before con- 

 tact and equally distant from both, the force with which the 

 homologous points of both jets seek to approach one another 

 may be divided into two equal parts, of which the one acts in the 

 above plane, the other perpendicular to it. The latter causes 

 the two corresponding points of the jets in this plane to approach 

 one anothei*, and therefore moves both in opposite directions. 

 Hence the jets arrive in the above plane, but in consequence of 

 their inertia they pass beyond it ; and thus the jet which for- 

 merly lay on one side of the plane now lies on the other, and 

 vice versa. This process is repeated, and thus the closed sur- 

 faces bed and dc^ef, fig. 8, are produced. 



23. When the jets encounter merely at their edges, only a 

 small part of them is employed to form the water surface. The 

 greater part continues its path, and consequently remains almost 

 entirely in the plane which is parallel to the axes of the jets before 

 contact, fig. 7. 



For the same reason, the second and third water surfaces, when 

 they exist, also remain nearly parallel to this plane. 



24. When, however, a more complete contact between the 

 jets takes place, the position of the surface changes ; for the im- 

 pinging masses would form a surface perpendicular to the plane 

 parallel to both jets before contact, were they not connected with 

 the parts of the jets which continue their journey in this plane. 

 It is evident, however, that if the masses of these parts of the 

 jets are small in comparison to the mass of the water surface, the 

 direction of the latter will determine that of the jets themselves. 

 And as this surface, if unconnected with the jets, would be per- 

 pendicular to the plane passing through the axes, it is evident 



