268 NEWTON S PRINCIPIA. 



The fe length &quot; of a wave is the distance between two par 

 ticles in a similar state of motion. If A be this length, y 

 must be the same for x = x and x = x + A. Nowj^(*r) 

 will be a periodic function : suppose its values recur at 

 intervals of c, 



. . m A = c 9 



c 



or m = - 

 A 



and therefore, 



y = 



This is the type of a wave that travels in any one direction. 

 But it can also be demonstrated that it is the general 

 expression for all waves propagated with a uniform velocity 

 in one direction without change of form. 



There are a great variety of waves; we may have 

 waves transmitted through elastic fluids, where a state of 

 condensation travels along. We can have them propa 

 gated along the surface of an inelastic fluid, as water in 

 the form of an elevation. We can have them in solid 

 bodies, the particles of which are supposed to oscillate 

 about their mean position, and to act on each other with 

 forces different from those which would act if the body 

 had been fluid. We shall briefly consider these in turn. 

 These waves may not travel at all parts in the same direc 

 tion. They may spread themselves out from a centre. 

 In all cases a surface passing through all points in a similar 

 state of motion is called a front of the wave. The phase 

 of a wave at any point is the situation of the particle of 

 that point considered as affecting its displacement and 

 motion. Thus, two particles are in the same phase when 

 their displacements are equal, and motions the same. They 

 are in opposite phases when the displacement and motion 

 of one are equal but opposite to those of the other. 



