On the occasion above referred to when the ship was hove-to the speed of the waves (determined in unusually favourable con ditions) was about forty-seven miles an hour when the velocity of wind, calculated from the recorded number on Beaufort's scale, was 52 miles an hour. It appears therefore that only a 5 mile-an hour wind was blowing over the wave-crests, just enough to turn a weather-cock or to make leaves rustle. Thus the wind, which had blown all night with great violence in the direction of the heavy swell already running in the Bay, had increased its speed so much that there was no longer any buffeting, wave and wind being an harmonious procession.
Observers are agreed that the waves finally formed in a great storm of long continuance are not so steep as those in a moderate gale. According to mathematical theory, if the speed of the waves be doubled their length is increased four-f old, and so on, the wave-length increasing as the square of the speed. But the height only increases in simple proportion with that velocity, so that the steepness of the final waves would diminish in exact pro portion to the violence of the storm.
In pursuit of the enquiry into the final dimensions of waves produced by wind by the writer, obser vations were made during a voyage from Southampton to Trini dad and back in 1912 upon the period of the waves. The interval of time between the arrival of successive wave-crests at a fixed mark is necessarily the same as the time of subsidence and up heaval of a wave-crest. It was found during the course of the voyage that a single observer could easily determine the period, and hence by calculation the speed, of the waves by timing with a stop-watch the up-and-down oscillation of patches of foam, and that the period of the swell then running could also be deter mined by the same means. Later observations of movement of foam patches with and against wind made at the turn of cur rent on a tidal river proved that the drift of the foam was too slow to invalidate the results. On a subsequent voyage from Trinidad to Southampton, with a fresh breeze most of the way, a cup-and-ball anemometer was mounted on the navigating bridge, and from the reading of the instrument, combined with observa tion of the direction of the wind relative to the course of the ship, the speed of the wind which drove the waves was measured.
The daily record of results showed no definite relation be tween speed of wind and wave, although in the trade-wind belt the weather conditions were steady. Fortunately, however, the direc tion and speed of the ocean swell, the longer undulation produced by former winds or derived from a distance, had also been re corded. The daily observations having been grouped according to the direction of the swell, it was found that when this was the same as the direction of the waves proper, the speed of the waves was nearly as great as that of the wind, which blew across the ridges as a "light air," the force 1 of Beaufort's scale, sufficient to impart a drift to the smoke from a chimney but not strong enough to turn a wind vane. When, however, the swell met the
waves or crossed their direction, the speed of the wave was much less than that of the wind. The height of the waves was also greatly reduced by these conditions, an observation which sug gests that the rapidity with which wind raises waves on lakes and enclosed seas is connected with absence of conflicting swell. The most rapid increase of wave-height, however, occurs on the somewhat rare occasion when a rising wind on the open ocean blows in the same direction as that in which the swell is running and with a speed greater than that of the swell. This was the condition which produced the large and regular waves observed in the Bay of Biscay on Dec. 21, 1911.
In a rising sea the tops of the waves are cut off and blown away in spray during the squalls of a few minutes' duration which punctuate the gale, but when the storm has con tinued for a long time the effect of a squall is to increase the height of the waves, and this action is especially noticeable when the storm is abating. Thus on December 22, 1906 on a voyage from Liverpool to Puerto Colombia, while still in the North Atlan tic, with a heavy sea and a following wind having the force of a moderate gale, the writer judged that a violent squall lasting four minutes increased the height of the waves by about seven feet. As the squall travelled on, the rear of the group of higher waves could be seen travelling ahead, soon to pass out of sight. On the next day, Dec. 23, when the gale had dropped to a strong breeze, a squall of three minutes' duration increased the height of the waves by about six feet, and considerably in creased their crest-length. Two minutes after the passing of the squall the ship was among waves of the average size, but a group of several great ridges could be seen ahead. On the following day, Dec. 24, the wind fell considerably and the waves were much lower. At about 5 P.M. a narrow band of black cloud stretching from the zenith to the horizon on either hand passed over the ship. Its transit, which occupied about five minutes, was attended by only a slight increase of wind but was nevertheless accom panied by a group of at least a dozen large waves among which the ship rolled heavily. Ten minutes after the passing of the cloud the ship was among waves of the same size as before.