If an observer be 100 feet above the water, and the sea have waves as high on the average as 10 feet from trough to crest, or 5 feet above the normal surface of the sea, a line drawn from the observer, tangent to any wave, will strike the normal surface of the sea at a distance beyond the wave, depending on the distance of the wave from the observer. If the wave be 6000 yards distant, the line will strike the normal surface of the sea 300 yards beyond the wave. Inasmuch as waves 10 feet high are about 80 yards apart, this line will meet some part of the slope of another wave before it meets the normal surface of the sea. If that wave is 80 yards beyond the first wave, the line will strike it 1/3 feet lower than its point of tangency with the first wave; that is, 3 2/3 feet above the normal surface of the sea.
Therefore, the line of sight from an observer 100 feet high, which just passes above a lo-foot wave, say 6000 yards away, can never meet the normal surface of the sea, or the water-line of a ship, unless it be directed along the trough, or nearly so, of a very regular swell.
By "water-line" is meant, of course, the line of flotation of a ship in still water. This is her line of contact with the surface of the globe, and is the line called "water-line of the target" in spotting diagrams.
On the ocean, it can rarely be seen. To a distant observer, every ship seems to lie in a basin, of which numberless waves form the sides, and shut out all view of the "water-line."
Sometimes, the rolling or pitching of a ship raises part of the boot-topping so high that it can be seen above the intervening waves. But the very fact that any part of it can thus be seen, is proof that that part does not then form part of the "water-line."