314 REPORT — 1844. 



out of its course. In like manner the observer near the shore perceives that 

 pieces of wood, or any floating bodies immersed in the water near its surface, 

 and the water in their vicinity, are not carried towards the shore with the ra- 

 pidity of the wave, but are left nearly in the same place after the wave has 

 passed them, as before. Nay, if the tide be ebbing, the waves may even be ob- 

 served coming with considerable velocity towards the shore, while the body of 

 water is actually receding, and any object floating in it is carried in the opposite 

 direction to the waves, out to sea. Thus it is that we are impressed with the 

 idea, that the motion of a wave may be different from t}ie motion of the water 

 in which it moves ; that the water may move in one direction and the wave 

 in another ; that water may transmit a wave while itself may remain in the 

 same place. 



If then we have learned that a water wave is not what it seems, a heap of 

 water moving along the surface of the sea with a velocity visible to the eye, 

 it is natural to inquire what a wave really is ; tvhat is wave-motion as distinct 

 from water-motion ? 



For the purpose of this inquiry let us take a simple example. I have a 

 long narrow trough or channel of water, filled to the depth of my finger 

 length. I place my hand in the water, and for a second of time push forward 

 along the channel the water which my hand touches, and instantly cease from 

 further motion. The immediate result is easily conceived ; I have simply 

 pushed forward the particles of water which I touched, out of their former 

 place to another place further on in the channel, and they repose in their new 

 place at rest as at first. Here is a final effect, and here my agency has ceased 

 — not so the motion of the water ; I pushed forward a given mass out of its 

 place into another, but that other place was formerly occui^ied by a mass of 

 water equal to that which I have forcibly intruded into its place ; what then 

 has become of the displaced occupant ? it has been forced into the place of 

 that immediately before it, and the occupant which it has dislodged is again 

 pushed forward on the occupant of the next place, and thus in succession 

 volume after volume continues to carry on a process of disjslaceraent which 

 only ends with the termination of the channel, or with the exhaustion of the 

 displacing force originally impressed by my hand, and communicated from 

 one to another successive mas^ of the water. This process continues without 

 the continuance of the original disturbing agency, and is prolonged often to 

 great distances and through long periods of time. The continuation of this 

 motion is therefore independent of the volition which caused it. It is a pro- 

 cess carried on by the particles of water themselves obeying two forces, the 

 original force of disturbance and the force of gravity. It is therefore a hy- 

 drodynamical phasnomenon conformable to fixed law. I have now ceased 

 to exercise any control over the phaenomenon, but as I attentively watch 

 the processes I have set a-going, I observe each successive portion of water in 

 the act of being displaced by one moving mass of water, and in the act of 

 displacing its successor. As the water particles crowd upon one another in 

 the act of going out of their old places into the new, the crowd forms a tem- 

 porary heap visible on the surface of the fluid, and as each successive mass is 

 displacing it? successor, there is always one such heap, and this heap travels 

 apparently along the channel at that point where the process of displacement 

 is going on, and although there may be only one crowd, yet it consists suc- 

 cessively of always another and another set of migrating particles. 



This visible moving heap of crmvdiny particles is a true ivave, the rapidity 

 with which the displacement of one outgoing mass by that which takes its 

 place, goes forward, determines the velocity with which the heap appears to 

 move, and is called the velocity of transmissio7i of the wave. The shape which 



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