MECHANICS 73 



movements must be relatively complex. Nevertheless 

 the motions of liquids have the same basis and obey the 

 fundamental laws of the movements of solid bodies. 



We have seen that, abstracting the action of the 

 atmosphere, all bodies which fall from the same height 

 fall simultaneously and attain the same velocity at each 

 stage of their descent. We have also seen* that the 

 velocities they require are as the square roots of the 

 heights through which they fall, so that an object must 

 be four times higher than another if we desire that it 

 should attain twice the velocity of the latter. 



Let us suppose that we have two vessels before us, each 

 containing a depth of four feet of water, but that 

 one vessel is six feet in diameter, while the other has 

 but a breadth of one foot. Further let us suppose 

 that a similarly sized hole be made in each vessel 

 six inches from the bottom. It might be thought 

 that the stream issuing forth from the larger vessel 

 will be projected much further than that from the 

 smaller one. Such, however, is not the fact ; they 

 will be projected equally far. Not only is this the 

 case, but it will be the same if the two liquids are of 

 different densities. Mercury will be projected as far, 

 and no further than, water, if they both issue from 

 similar orifices, placed at the same depth beneath the 

 surfaces of the two liquids. Here, as -with solids, if we 

 wish to double the velocity we must raise the surface of 

 the fluid fourfold, and to make it four times as great 

 we must raise it sixteenfold and so on and the greater 

 the velocity, the further outwards will the jet of 

 discharge extend. This jet, in falling, always describes 

 a parabola, i.e., falls in a parabolic curve. The particles 



* See ante, p. 60, 



