be itself worn down and rounded, we have satisfactory proof that the remanié quartz-grain has undergone a second wearing and rounding, and has been remodelled and fashioned anew.

B0

Such evidence of double wearing is not uncommon in the Skerries sands, and we have a good specimen of quartz so encrusted and worn in the pear-shaped grain in photo. No. 2. This grain, which is about inch in greatest diameter, shows a primary rounding, then deposition of quartz at its narrower end, and then a second rounding of the deposited quartz, nearly as complete as the first. If the hypothesis of rounding by waves be inadmissible, we are forced to account for the condition of this grain, either by a double exposure to long-continued æolian action, or to a double exposure to long-continued stream action, or to each of these actions in succession. In either case, between these two exposures to wear, the grain was a component part of a sandstone rock, which sandstone rock was in all probability disintegrated by the tearing action of waves. The point we have to consider is, whether this grain might not have passed through all the changes its condition indicates, without the intervention of either wind-action or stream-action.

So far we have seen that the sand of the Skerries Shoal not only contains many grains greatly rounded, but that some of these grains have been rounded more than once at distant periods of time; a combination of circumstances indicating, according to accepted views, either the action of two geologic Saharas, or two geologic rivers of great extent, or both Sahara and river combined. I shall now endeavour to show that, under conditions now existing, sands may be rounded on the Skerries, and similar shoals, by waves, without the necessary intervention of any other agency whatever.

Near the two extremities of the Great West Bay, at Portland and the Start, we have notable examples of two banks kept in position by tidal currents in the face of heavy waves. Referring to the former headland, the Admiralty Chart states that "from about II to XI. F. and C. there is an outset from the west bay of Portland of nearly nine hours' duration, which closely skirts the rocky shore, and gradually increases in strength as it approaches the Bill. It rushes past the Bill and over Portland Ledge at the rate of six or seven knots at springs. A short distance eastward of the Ledge this outset is met in the latter half of its course at nearly right angles by the stream which sets for 9 hours (viz., from VI.h 20m to III 50m F. and C.) out of the east bay of Portland; the united streams then press on towards the Shambles." Accord

ing to the same document the tidal streams rush to and fro over the Shambles at a rate of from three to four knots at springs. As the Shambles shoal is composed of light broken shells, and reaches within two fathoms of the surface of the water at its highest point, it is clear that it is kept in place by the conflicting tides. It is evident that light shells could not offer any resistance to a strong current. They have actually been observed to be in motion even when there was very little current at the surface, on the occasion of Mr. Deane's descent in December, 1851.*

We have no such interesting particulars in the case of the Start Bay Skerries'; no engineer has taken a stroll on that sandbank. But we have again here the strong conflicting tides, the ebb setting right off shore at the Start, and the flood sweeping up Channel at right angles, or thereabouts, to the course of the ebb. We have also the very fine sand and broken shells collected by Mr. Pannel to prove that here also the action of these tidal currents is to retain in place rather than to dissipate the light material, which to some extent, at any rate, goes to form the bank. I think it is clear that in the Skerries, as in the Shambles, we have an exposed shoal collected together by the tides, and battered by the assaults. of the waves. One point may be noticed in passing, the Skerries is not quite so exposed to westerly seas as the Shambles, though it is attacked by heavier easterly seas than the Shambles ever encounters. We find that in the Shambles wave and tide are balanced at a depth of 13 fathoms; in the Skerries at 1 fathoms. The tidal and undal actions on these shoals are in conflict; the tides would collect a sandbank, the waves, though powerless to disperse it, would level it. The opposing forces seem balanced at the depths indicated. Having shown that the light sand is retained in place on the Skerries bank by tidal action, I will now proceed to indicate the nature of the wave action to which it is necessarily exposed.

It is very difficult for a non-mathematician to arrive at the most elementary facts as to submarine wave action, as the whole subject is locked up in mathematical formulæ inaccessible to the uninitiated. Some text-books of geology go so far as to state the amount of motion existing at the depth of one wave length, an amount equal to only about th of that at the surface, and practically of no account whatever; but the amount of disturbance at different points between this depth and the surface is not to be found, so far as I am aware, in * Discussion on Mr. J. B. Redman's paper on Alluvial Formations," &c., Proc. Inst. C. E., vol. xi.

any geological work. This varying amount of motion may be ignored, but not with impunity.

Finding the lack of this information a bar to any satisfactory progress, I asked Lord Rayleigh, who had often previously come to my assistance, to supply me with the amount of disturbance set up by a wave at a depth of one-eighth of the wave-length, and at every succeeding multiple of oneeighth. This he kindly did in the following concise rule: "For each step downward of (ie. wave-length) divide by 2-2." This rule is as easy to work as it is concise. Let us assume the disturbance at surface to be indicated by a circular oscillation of five feet, then at a depth of one-eighth the wave-length the disturbance is; at a quarter wave-length it is (22)2; at three-eighths wave-length it is

5

5

(2:2); and so on. All we require to know in any case is the height of the wave and the length of the wave, to calculate the decreasing disturbance at any depth below the surface. This formula is of course not absolutely accurate, but it is surprising how nearly it is so. For instance, according to Sir G. B. Airy, the disturbance at one wave-length is 554 of that at the surface. According to Lord Rayleigh's approximate formula, the motion at one wave-length is that at the surface divided by (2.2), or 548, omitting decimals; so that if the motion at the surface be taken as unity, the difference in the two is only as between 5 and 15.

535

1

This formula being calculated for an infinitely deep sea does not give us the actual horizontal disturbance set up by a wave on the bottom, but it supplies us with the needed. information whether any given wave can appreciably affect the bottom at any given depth.

Let us apply this formula to the case of the Skerries and other such shoals, taking the height of wave 4 feet with varying wave-length.

A 72-foot wave, 4 feet high, would set up in deep water a rolling circle of about 2 feet diameter, at 9 feet deep, the minimum depth of the Skerries. A 144-foot wave of the same height would create the same disturbance at 18 feet or three fathoms.

But the Skerries bank, according to the chart, deepens on its highest ridge from 1 fathoms near the Start to 3 fathoms at its north-east end, thus the whole shoal is within the action of a wave 144 feet long and 4 feet high-a very

* Encyclopædia Metropolitana, vol. v. p. 294.