[Illustration:  Fig. 16.]

Sec. 11. Application of the Wave-theory to the Phenomena of
Diffraction.

Of these and of a multitude of similar effects the Emission Theory is incompetent to offer any satisfactory explanation.  Let us see how they are accounted for by the Theory of Undulation.

And here, with the view of reaching absolute clearness, I must make an appeal to that faculty the importance of which I have dwelt upon so earnestly here and elsewhere—­the faculty of imagination.  Figure yourself upon the sea-shore, with a well-formed wave advancing.  Take a line of particles along the front of the wave, all at the same distance below the crest; they are all rising in the same manner and at the same rate.  Take a similar line of particles on the back of the wave, they are all falling in the same manner and at the same rate.  Take a line of particles along the crest, they are all in the same condition as regards the motion of the wave.  The same is true for a line of particles along the furrow of the wave.

The particles referred to in each of these cases respectively, being in the same condition as regards the motion of the wave, are said to be in the same phase of vibration.  But if you compare a particle on the front of the wave with one at the back; or, more generally, if you compare together any two particles not occupying the same position in the wave, their conditions of motion not being the same, they are said to be in different phases of vibration.  If one of the particles lie upon the crest, and the other on the furrow of the wave, then, as one is about to rise and the other about to fall, they are said to be in opposite phases of vibration.

There is still another point to be cleared up—­and it is one of the utmost importance as regards our present subject.  Let O (fig. 17) be a spot in still water which, when disturbed, produces a series of circular waves:  the disturbance necessary to produce these waves is simply an oscillation up and down of the water at O. Let m n be the position of the ridge of one of the waves at any moment, and m’ n’ its position a second or two afterwards.  Now every particle of water, as the wave passes it, oscillates, as we have learned, up and down.  If, then, this oscillation be a sufficient origin of wave-motion, each distinct particle of the wave m n ought to give birth, to a series of circular waves.  This is the important point up to which I wish to lead you.  Every particle of the wave m n does act in this way.  Taking each particle as a centre, and surrounding it by a circular wave with a radius equal to the distance between m n and m’ n’, the coalescence of all these little waves would build up the large ridge m’ n’ exactly as we find it built up in nature.  Here, in fact, we resolve the wave-motion into its elements, and having succeeded in doing this we shall have no great difficulty in applying our knowledge to optical phenomena.