424 NATURAL SCIENCE. June. 



mud-particles. When the water is disturbed by the passage of waves, 

 the sphere becomes an ellipsoid, but it does not viix with the surrounding 

 water. The longest axis of the ellipsoid is vertical when the mass is 

 under (or within) the crest of a wave, and its shortest axis is hori- 

 zontal and parallel to the direction in which the waves are travelling 

 — this direction we will call longitudinal. The transverse axis of 

 the ellipsoid, that is, the axis parallel to the crest of the wave, 

 remains unchanged throughout, and therefore equal to the diameter 

 of the spherical mass we started with. As this remains unaltered, we 

 may leave it out from further consideration. 



As the mass we are considering falls into the trough behind, that 

 is, as the wave recedes from it, it comes to be elongated in a series of 

 new directions. At first sight, the mass appears to rotate in the direc- 

 tion in which each of its parts revolves, so that the upper end of the long 

 axis comes to be inclined forwards till when the bottom of the trough 

 is reached this long axis is horizontal and longitudinal. The mass, 

 however, does not really rotate : the point which was uppermost when 

 the mass was at the crest of the wave is uppermost still when in the 

 trough. The foym of the ellipsoid rotates, while its substance does 

 not. The long axis is vertical every time the mass is at the crest of 

 a wave. In passing from one wave-crest to the next the form (not the 

 substance) rotates through half a revolution. During the same period 

 each particle performs a complete circular journey. The relative move- 

 ment of any two particles in the mass is one of oscillation. Take, for 

 instance, the uppermost and the lowermost particles of the spherical 

 mass with which we started. When the water is still, one is vertically 

 above the other. During the movement the upper one (A) moves in 

 a circle, and the lower one (B) moves in a smaller circle. A is there- 

 fore above B when both are under the crest, and again when botli are 

 under the bottom of the trough. At every moment A and B are 

 moving in the same direction, but A always faster than B. At the 

 crest both are moving forwards, A therefore comes to be slightly in 

 front of B, but as both turn to move backwards, A comes to be above 

 B again in the trough and then comes to be behind it. If we take 

 two other particles a similar result is reached, but with a difference. 

 If the two particles are not in the same vertical transverse plane when 

 at rest, then they will not at any moment be moving in the same 

 direction. Suppose C and D be particles at the two ends of the 

 "longitudinal" diameter of the sphere in still water, C being in front, 

 D behind. Then as the waves advance D will always move some- 

 what before C, so that when the middle of the mass is under the crest 

 D will already have begun to move downwards, while C is still 

 moving upwards. At this stage C and D will also be nearer together 

 than at any other. In tlie trough these will be further apart than at 

 any other stage, and while both are moving backwards D will already 

 be moving backwards and upwards, while C is still moving backwards 

 and downwards. 



