a little way removed from the centre, the interference of the direct and reflected waves produces the magnificent chasing shown in the annexed figure.[11] The light reflected from such a surface yields a pattern of extraordinary beauty.  When the mercury is slightly struck by a needle-point in a direction concentric with the surface of the vessel, the lines of light run round in mazy coils, interlacing and unravelling themselves in a wonderful manner.  When the vessel is square, a splendid chequer-work is produced by the crossing of the direct and reflected waves.  Thus, in the case of wave-motion, the most ordinary causes give rise to most exquisite effects.  The words of Emerson are perfectly applicable here:—­

[Illustration:  Fig. 10.]

    ’Thou can’st not wave thy staff in the air,
       Or dip thy paddle in the lake,
     But it carves the brow of beauty there. 
       And the ripples in rhymes the oars forsake.’

The most impressive illustration of the action of waves on waves that I have ever seen occurs near Niagara.  For a distance of two miles, or thereabouts, below the Falls, the river Niagara flows unruffled through its excavated gorge.  The bed subsequently narrows, and the water quickens its motion.  At the place called the ‘Whirlpool Rapids,’ I estimated the width of the river at 300 feet, an estimate confirmed by the dwellers on the spot.  When it is remembered that the drainage of nearly half a continent is compressed into this space, the impetuosity of the river’s escape through this gorge may be imagined.

Two kinds of motion are here obviously active, a motion of translation and a motion of undulation—­the race of the river through its gorge, and the great waves generated by its collision with the obstacles in its way.  In the middle of the stream, the rush and tossing are most violent; at all events, the impetuous force of the individual waves is here most strikingly displayed.  Vast pyramidal heaps leap incessantly from the river, some of them with such energy as to jerk their summits into the air, where they hang suspended as bundles of liquid pearls, which, when shone upon by the sun, are of indescribable beauty.

The first impression, and, indeed, the current explanation of these Rapids is, that the central bed of the river is cumbered with large boulders, and that the jostling, tossing, and wild leaping of the waters there are due to its impact against these obstacles.  A very different explanation occurred to me upon the spot.  Boulders derived from the adjacent cliffs visibly cumber the sides of the river.  Against these the water rises and sinks rhythmically but violently, large waves being thus produced.  On the generation of each wave there is an immediate compounding of the wave-motion with the river-motion.  The ridges, which in still water would proceed in circular curves round the centre of disturbance, cross the river obliquely, and the result is, that at the centre waves commingle