perhaps not to the same extent as in the little float. Actual observation shows this to be true. Captain Mottez, of the French navy, reports that on long waves about 26 feet high the apparent weights at hollow and crest had the ratio of 12 to 8. According to the preceding rules we must then have, Length of waves (by theory)=2πR = 6·28 × 65=408 feet. This, in proportion to the height recorded, is not an unreasonable length; but, unfortunately, Captain Mottez does not appear to have completed the information required, by measuring the actual length of the waves. The important fact he proved, however, is one that theory had predicted, viz. that the heaving motion of the waves may produce a virtual variation in the weight of a ship equivalent to an increase or decrease of one-fourth or one-fifth, when the proportions of the height and length of the waves are those common at sea. Instead of the raft in Fig 62, if the motions of a loaded pole or plank on-end (such as SS) be traced, it will be found that it tends to follow the originally vertical lines, and to roll always toward the crest as they do. Here again the motion partakes of the nature of an oscillation of fixed range performed in half the wave period, the pole being upright at the hollow and crest. A ship differs from both the raft and the pole; for she has both lateral and vertical extension into the subsurfaces of the wave, and cannot be considered to follow either the motion of the surface particles like the raft or of an originally vertical line of particles like the pole. This case will be discussed in the next chapter. As a mathematical theory, that for trochoidal waves is complete and satisfactory, under the conditions upon which it is based; but sea-water is not a perfect fluid such as the theory contemplates; in it there exists a certain amount of viscosity, and the particles must experience resistance in changing their relative positions. There is every reason to believe that the theory closely approximates to the phenomena of deep-sea waves, but it is very desirable that extensive and accurate observations of the dimensions and speeds of actual waves should be made, in order to test the theory, and determine the closeness of its approximation to truth. The recorded observations on waves are not so complete or numerous as to furnish the test required; and by adding to them during their service at sea, naval officers will do much to advance one important branch of the science of naval architecture. The Lords Commissioners of the Admiralty have recently issued orders that careful observations of waves shall be made in her Majesty's ships, simultaneously with the observations of rolling; so that the relations between the state of the sea and the behaviour of the ships may be more readily discovered. In the French navy similar observations have been made, and the published results are very valuable.* Mr. Froude has furnished to the Admiralty a memorandum on the method of determining at sea, by simple observation, the periods and dimensions of waves; and the importance of correctness in making such observations renders it desirable to introduce here a reprint of the official method of observation in the Royal Navy. It should be premised, however, that no test of the theory can be applied by means of observations made in a confused sea; it is when a ship falls in with a series of waves of nearly regular form and period that the See a paper on "The Experimental Study of Waves," by M. Bertin, in the Transactions of the Institution of Naval Architects for 1873; observations become most valuable from a scientific point of view. A regular series is that which is most likely to produce the heaviest rolling in a ship exposed to its action; and for these reasons the greatest attention should be devoted to observations of regular series of waves. It is not, however, desirable that only such observations should be made; for much light might be thrown upon the question of the superposition of series of waves, if the phenomena of a confused sea were carefully noted. Moreover, the actual determination of the dimensions of the solitary waves of exceptional size, as compared with neighbouring waves, of which all sailors speak, would furnish very interesting and much needed information. Supposing a single series of waves to be encountered, the following is a reprint of the most important parts of the METHOD OF OBSERVING THE DIMENSIONS AND PERIODS OF WAVES PROPOSED BY MR. FROUDE AND APPROVED BY THE ADMIRALTY. The method of observation to be adopted on board a ship for the purpose of determining the periods and dimensions of the waves she encounters will naturally be somewhat different accordingly as the ship is (1) stationary, or (2) in motion. If she be stationary, the wave period may be at once determined by a single observer, noting successively the moment at which successive wave crests pass the particular part of the ship on which he stands. In describing the observations by which the length of wave is to be determined, it is convenient to assume first that the ship is "end-on" to the wave crests. If the length of the wave be less than that of the ship, two observers should watch two consecutive wave crests which are rolling past the ship-one, one; the other, the other; and should each simultaneously, on the word being given to them, notice the position on the ship's side occupied by the wave he is watching. The interval between the positions when measured on the ship's deck is simply the wave length. If the length of the wave be greater than the ship's length, the process is less simple. Let a convenient length (the greater the better) be set out along the ship's deck; and at each end of the line, transversely to it, let a pair of battens be erected so as to define, when used as sights, a pair of parallel lines at right angles to the ship's keel, the interval between them being the length measured out on the deck; and let an observer be stationed at each, say No. 1 at the end of the line which the waves first meet, No. 2 at the other. Let observer No. 1 note the instant of time when a wave crest passes the line of sight marked by his pair of battens; and let observer No. 2 note it when the same wave crest passes the line marked by his; and let the observation be repeated for the succeeding wave crest by one or other of the observers. This latter observation at once fixes the period of the wave, as has already been mentioned. If the times noted by observers No. 1 and No. 2 be compared, the difference will give the time occupied by the observed wave crest in passing the interval between the two parallels. The time occupied by the crest in passing this known interval defines the speed of the wave. Thus, the period being known and the speed being known, the length may be immediately deduced, since it is the distance which the wave having that speed will traverse in the period. If the ship, though stationary, be not end-on to the waves, but deviate from that position by a known angle, the values of the speed and length of the wave thus deduced will be alike too great, but they will give the true values when multiplied by the cosine of the deviation. If the ship be not stationary, but moving with a known speed, it is convenient to assume as before that she is end-on to the waves, her motion being also end-on to them, so that she is either running exactly before the sea or is exactly heading it. Under these circumstances the same observations are to be made as already mentioned; but the period, speed, and length, primarily deduced from them require the following corrections: The time which elapses between the transits of two consecutive wave crests past observer No. 1 or No. 2 is greater or less than the true period, because the distance actually travelled by the wave during the time is greater or less than the true wave length by the distance travelled in the meantime by the ship, either from the waves or towards the waves. But as the speed of the ship is known, the true speed of the wave may be at once inferred from its apparent speed as primarily deduced from the observations, by adding to it, or deducting from it, the speed of the ship, according as she is running before the waves or heading them; and by help of this correction the true wave length and true wave period may be readily found. The process of correction may best be expressed algebraically If V be the speed of the ship, in feet per second. L the interval between the parallel lines defined by the battens, in feet. V the speed of the wave, in feet per second. 'L the length of the wave, in feet. P the period of the wave, in seconds. Then, if the time occupied by the wave crest in passing over L be (t) in seconds, it follows that L And if the observed time between the transits of two successive wave crests past observer No. 1 or No. 2 be ('t), it follows that |