The moment selected for the figure is that in which the first of the series, a,, is on the point of

Fig. 12

moving vertically upwards out of the initial line, i.e. when the front of a wave of the form in question has just reached the point a. Since the second particle started one-sixteenth of a second after the first, its position in the figure will be below the initial line at a,' making the line a, a,' equal to the line 015 in Fig. 11. The next particle, which is two-sixteenths of a second behind a, in its path, will be at a making a, a, equal to 014 in the same figure. In this way the positions of all the points a, a, a,, &c., in Fig. 12 are determined from Fig. 11. They give us, at once, a general idea of the form of the resulting wave. By laying down more points along the line AB in Fig. 11, we can get as many more points on the wave as we please, and should

thus ultimately arrive at a continuous curved line. This is the wave-form resulting from the given vibration-mode with which we started, and, since only one wave-form can be obtained from it, we infer that each different mode of particle-vibration gives rise to a different form of wave.

13. It has now been demonstrated that when a wave is produced by particles vibrating in a plane passing through its line of advance, and in paths perpendicular to that line, the amplitude of the wave is equal to the extent of particle-vibration and the length and form of the wave are determined by the rate and mode of vibration respectively. These relations were also shown to hold conversely.

We will next consider a type of oscillatory movement which is important from its similarity to that to which the transmission of Sound is due.

14. Anyone who has looked down from a slight elevation upon a field of standing corn on a gusty day, must have frequently observed a kind of thrill running along its surface, As each ear of corn is capable of only a slight swaying movement, we have here necessarily an instance of wave-motion, the earvibrations corresponding to the particle-vibrations in the cases already examined. There is, however, this important peculiarity in the instance now before us, that the ears' movements are mainly horizontal,

i.e. executed in the line of the wave's advance. The wave, therefore, no longer presents itself to the eye as exclusively a condition of alternate protuberance of outline in opposite directions, but mainly as a state of more tightly, or less tightly, packed ears. The

annexed figure gives a rough idea how this takes place. The wind is supposed to be moving from left to right and to have just reached the ear A. Its neighbours to the right are still undisturbed. The stalk of C has just swung back into its erect position. The ears about B are closer to, and those about C further apart from, each other than is the case with those on which the wind has not yet acted.

After this illustration, it will be easy to conceive a kind of wave-motion in which there is no longer any movement transverse to the direction in which the wave is advancing.

15. Let a series of particles, originally at rest in equidistant positions along a straight line, as in that at the head of Fig. 14, be executing equal

periodic vibrations in that line, in such a manner that each is the same fixed amount further back in

its path than is its neighbour to the left, and therefore exactly as much more forward than is its neighbour to the right.

(0) shows the condition of the row of particles at the moment when that on the extreme left is beginning its swing from left to right, which, in accordance with the direction of the wave's advance as indicated by an arrow in the figure, we may call its forward swing. The equidistant vertical straight lines fix the extent of vibration for each separate particle. The constant amount of relative backwardness, or 'retardation' as it is technically called, between successive particles is, as in Figs. 5 and 7, one-eighth of the period of a complete vibration. Thus, proceeding from left to right along the line (0), we have the first particle beginning a forward swing, the second, third, fourth and fifth particles entering respectively on the fourth, third, second and first quarters of a backward swing, and the sixth, seventh, eighth and ninth particles on the fourth, third, second, and first quarters of a forward swing.

Since the ninth particle is just beginning a forward swing, its situation is exactly the same as that of the first. Beyond this point, therefore, we have only repetition of the state of things between the first and ninth particles. The row (0) is therefore made up of a series of groups, or cycles, of the same number of particles arranged in the same manner throughout. Two such cycles, included by