In the first days of August, two startling announcements reached us from the United States. They were as follows:

(1.) "The commander of the Cunarder Umbria reports that at 3 o'clock on July 27, about 1,500 miles from Sandy Hook, the vessel was struck by a tidal wave 50 ft. high, which swept the decks, carried away a portion of the bridge and the forward hatch, and flooded the cabins and steerage."

(2.) "The captain of the Wilson line steamer Martello reports that at half-past 8 on the evening of July 25, when in lat. 49° 3' N., long. 31° W., an enormous wave struck the vessel, completely submerging the decks."

In view of these reports, and inasmuch as questions were asked on the subject in Parliament, though it is quite possible that, as regards the "tidal" character of the waves, there may be something of newspaper gobemoucherie in the announcements, we offer a few remarks on waves in general, which may be useful to some of our readers.

Tidal phenomena present themselves under two aspects: as alternate elevations and depressions of the sea and as recurrent inflows and outflows of streams. Careful writers, however, use the word tide in strict reference to the changes of elevation in the water, while they distinguish the recurrent streams as tidal currents. Hence, also, rise and fall appertain to the tide, while flood and ebb refer to the tidal current.

The cause of the tides is the combined action of the sun and moon. The relative effects of these two bodies on the oceanic waters are directly as their mass and inversely as the square of their distance; but the moon, though small in comparison with the sun, is so much nearer to the earth that she exerts the greater influence in the production of the great tide wave. Thus the mean force of the moon, as compared with that of the sun, is as 2¼ to 1.

The attractive force of the moon is most strongly felt by those parts of the ocean over which she is vertical, and they are, consequently, drawn toward her. In the same manner, the influence of the luminary being less powerfully exerted on the waters furthest from her than on the earth itself, they must remain behind. By these means, at the two opposite sides of the earth, in the direction of the straight line between the centers of the earth and moon, the waters are simultaneously raised above their mean level; and the moon, in her progressive westerly motion, as she comes to each meridian in succession, causes two uprisings of the water - two high tides - the one when she passes the meridian above, the other when she crosses it below; and this is done, not by drawing after her the water first raised, but by raising continually that under her at the time; this is the tide wave. In a similar manner (from causes already referred to) the sun produces two tides of much smaller dimensions, and the joint effect of the action of the two luminaries is this, that instead of four separate tides resulting from their separate influence, the sun merely alters the form of the wave raised by the moon; or, in other words, the greater of the two waves (which is due to the moon) is modified in its height by the smaller (sun's) wave. When the summit of the two happens to coincide, the summit of the combined wave will be at the highest. When the hollow of the smaller wave coincides with the summit of the larger, the summit of the combined wave will be at the lowest.

It is necessary to have a clear and distinct conception of the difference between the motion of a wave and that of a current. In the current there is a transfer of water; in the wave the transfer is no more than would be brought about by a particle of water impinging on another where that particle has a motion perpendicular to the surface, and a rising and falling results. The onward movement of the wave itself is always perceptible enough. That the water is not moving with the same velocity is also evident from watching the progress of any light body floating on its surface. This fact may be practically illustrated in the case of a ship at sea, sailing before the wind in the same direction as the waves are moving. When the crest of a wave is near the stern, drop a piece of wood on it. Almost instantly the wave will be seen shooting ahead of the vessel, while the wood is scarcely removed from the position where it fell on the water. The wave has moved onward, preserving its identity as a wave, the water of which it is formed being constantly changed; and thus the motion of the wave is one thing, that of the water in which the waves are formed is quite another thing.

Again, waves are formed by a force acting horizontally; but in the case of the tide wave, that force acts uniformly from the surface to the lowest depths of the ocean, and the breadth of the wave is that curved surface which, commencing at low water, passes over the summit of the tide down to the next low water - this is a wave of the first order. In waves of the second order, the force raising them acts only on the surface, and there the effect is greatest (as in the wind waves) - where one assists in giving to the water oscillating motion which maintains the next, and gradually puts the whole surface in commotion; but at a short distance down that effect entirely disappears.

If the earth presented a uniform globe, with a belt of sea of great and uniform depth encircling it round the equator, the tide wave would be perfectly regular and uniform. Its velocity, where the water was deep and free to follow the two luminaries, would be 1,000 miles an hour, and the height of tide inconsiderable. But even the Atlantic is not broad enough for the formation of a powerful tide wave. The continents, the variation in the direction of the coast line, the different depths of the ocean, the narrowness of channels, all interfere to modify it. At first it is affected with only a slight current motion toward the west - a motion which only acquires strength when the wave is heaped up, as it were, by obstacles to its progress, as happens to it over the shallow parts of the sea, on the coasts, in gulfs, and in the mouths of rivers. Thus the first wave advancing meets in its course with resistance on the two sides of a narrow channel, it is forced to rise by the pressure of the following waves, whose motion is not at all retarded, or certainly less so than that of the first wave.