76 ELEMENTS OF SCIENCE 



breadth of a wave is measured between particles which 

 are in similar position, e.g., from those at the greatest 

 depression in front of and behind the wave. This 

 dimension, like the length of a pendulum, varies as the 

 square of the time of oscillation and the velocity of a wave 

 varies as the square root of its breadth. Thus if a boat 

 be noticed on one day to rise and fall twice as often as it 

 did on the previous day, then the waves which pass 

 under it must have become four times as broad, while 

 moving with only double velocity. 



The laws of hydrodynamics have led to the construc- 

 tion of aquatic machines for raising water. It would 

 be quite beyond the purpose of this work to describe 

 such in detail, but we must briefly refer to the screw 

 of Archimedes, water-rams, and water-wheels. 



The first may be either a flexible tube open at both 

 ends and wound spirally on the exterior surface of a 

 cylinder, or it may be a plate of metal coiled spirally 

 about an axis enclosed within a hollow cylinder. The 

 machine is fixed in an inclined position, with its 

 lower extremity immersed in the water which is to 

 be raised. 



While it is at rest, the water occupies the lower part 

 between two of the bends of the spiral. When turned, 

 the machine is rotated on its axis, and the part contain- 

 ing the liquid being thus elevated, the water will be 

 caused, by gravity, to descend into the lower part 

 between the next bends of the spiral, and so, in reality, 

 it rises with respect to its former position in the rotating 

 spiral coil within which it is confined. Thus the water 

 continually proceeds towards the upper part of the 

 machine from whence it is discharged. 



A water-ram is a machine by which the action of 

 gravity on falling water is utilised by a succession of 



