ON WAVES. 315 



the crowding of the particles gives to the surface of the water constitutes the 

 form of the loave. The distance (in the direction of the transmission) along 

 which the crowd extends, is called the length or amplitude of the wave. The 

 number of particles which at any one time are out of their place, constitute 

 the volume of the wave ; the time which must elapse befoi-e particles can effect 

 their translation from their old places to the new, may be termed the period 

 of the wave. The height of the ivave is to be reckoned from the highest point 

 or crest to the surface of the fluid when in repose. 



Such is the wave motion — very different is the ivater motion. Let us 

 select from the crowd of water particles an individual and watch its behaviour 

 during the migration. The progressive agitation first reaches it while still in 

 perfect repose ; the crowd behind it push it forward and new particles take 

 its place. One particle is urged forward on that before it, and being still 

 urged on from behind by the crowd still swelling and increasing, it is raised 

 out of its place and carried forward with the velocity of the surrounding par- 

 ticles ; it is urged still on until the particles which displaced it have made 

 room for themselves behind it, and then the power diminishes. Having now 

 in its turn pushed the particles before it along out of their place, and crowded 

 them together on their antecedents, it is gradully left behind and finally settles 

 quietly down in its new place. Thus then the motion of migration of an in- 

 dividual particle of water is very different from the motion of transmission of 

 the wave. 



The wave goes still forward along through the channel, but each individual 

 water particle remains behind. The wave passes on with a continuous un- 

 interrupted motion. The water particle is at rest, starts, rises, is accelerated, 

 is slowly retarded, and finally stops still. The range of the particle's motion 

 is short ; its translation is interrupted and final. Its vertical range and hori- 

 zontal range are finite. It describes an orbit or path during the transit of the 

 wave over it, and remains for ever after at rest, unless when a second wave 

 happens immediately to follow the first, when it will describe a second time 

 its path of translation, passing through a series of new positions or phases 

 during the period of the wave. The motion of the particle is not therefore 

 like the apparent motion of the wave, either uniform or continuous. The 

 motion of the water particles is a true motion of translation of matter from 

 one place to another, with the velocity and range which the senses observe. 

 But the wave motion is an ideal individuality attributed by the mind of the 

 observer to a process of changes of relative position or of absolute place, which 

 at no two instants belongs to the same particles in the same place. The 

 water does not travel, the visible heap at no two successive instants is the 

 same. It is the motion of particles which goes on, now at this place, now at 

 that, having passed all the intermediate points. It is the crowding motion 

 alone which is transmitted. This crowding motion transmitted along the 

 water idealised and individualised is a true wave. 



Wave propagation therefore consists in the transmission fromoneclassof par- 

 ticles to another, of a motion differing in kind from the motion of transmission. 

 Wavemotion is therefore transcendental motion ; motion in the second degree ; 

 the motion of motion — the transference of motion without the transference 

 of the matter, of form without the substance, of force without the agent. 



It is essential to the accurate conception and examination of waves, that 

 this distinction between the toave motion and the water motion be clearly con- 

 ceived. It has been well illustrated by the agitations of a crowd of people, 

 and of a field of standing corn waving with the wind. If we stand on an 

 eminence, we notice that each gust as it passes along the field bending and 

 crowding the stalks, marks its course by the motion it gives to the grain, and 



