Prof. Magnus's Hydraulic Researches. 191 



of water, to see that these bubbles must be formed from a cavity 

 whose magnitude is far greater than that of tbe drops. 



94. The greater the force with which the faUing body meets 

 the water, the greater is the cavity, and hence the bubble result- 

 ing therefrom. If solid bodies, as peas or shot, fall from a few 

 inches' height into the water, very small air-bubbles are obtained ; 

 these are much larger when the bodies fall from the height of a 

 few feet. 



95. But even if the water-drops fall into the M^ater from a 

 height of many feet, the air-bubbles produced go only to a very 

 small depth, at most a few inches below the surface. Even if, 

 instead of water-drops, peas be used, the result is quite similar ; 

 there remains then a small air-bubble adhering to almost every 

 pea, which goes with it slowly to the bottom. 



96. But if leaden bullets as large as, or larger than, shot be 

 let fall into the water, the bubbles are seen to reach to a greater 

 depth. If musket-bullets be used for this experiment, and if 

 they be allowed to fall into glass vessels two or three feet deep, 

 then along the whole of the way through which the bullet passes in 

 the liquid, the air is seen to escape in bubbles, the last and largest 

 of which is separated when the bullet strikes against the bottom. 



97. Just as lead causes the penetration of air to a great depth, 

 so can this be effected by single separated masses of water when 

 they fall on the water in rapid succession ; for each successive 

 drop pushes anew, producing a stronger motion, and hence one 

 extending deeper. That is the reason why air-bubbles formed 

 by single drops of water only reach to a considerable depth when 

 they form a continuous, or almost continuous jet. 



98. For even when a jet is entirely continuous, it carries with 

 it air-bubbles downwards. In a previous treatise, " On the 

 Motion of Liquids*," I have mentioned in § 18 that a cavity 

 could be perceived when such a continuous jet fell vertically on 

 the surface of the water. The first origin of this is doubtless 

 similar to that of the falling of a solid body into water, but its 

 continuance has an entirely different reason ; for so long as the 

 cavity is there, the jet only meets the water at the deepest part 

 of it. It is there pressed towards the side; is not, however, 

 moved in a horizontal direction, but is pressed upwards by the 

 resistance which the water present ofi'ers. And since this action 

 of the resistance is repeated throughout the whole distance, the 

 motion becomes curvilinear, and there is formed a curved surface 

 or cup-shaped cavity. 



99. From this explanation, it is shown that this cup-shaped 

 cavity can only be formed under a certain velocity of the jet ; 

 for if the velocity be small, the water is moved aside with only 



* Poggendoiff's Jnnatoi, vol. Ixxx. p. 1. Phil. Mag. for January 1851. 



