yet not very numerous; but the Admiralty instructions provide for such observations to be made when favourable opportunities present themselves, and it is therefore probable that this branch of the subject of the behaviour of ships at sea may before long receive considerable extensions.

Fluid resistance is known to play an important part, as already stated, in limiting the range of pitching oscillations; but the naval architect has not the same control over this feature as he possesses in connection with rolling motions. It would be difficult to fit any appendages equivalent to bilge-keels in order to increase the resistance to longitudinal oscillations; and the under-water forms of ships are settled mainly with reference to their efficient propulsion, the effects of form on pitching usually occupying a subordinate place. Attempts have been made, however, to improve the forms of the bows of the ships in order to lessen pitching; and very diverse opinions have been expressed as to the best form that can be adopted. Many persons are in favour of V-shaped or "flaring cross-sections; the out-of-water parts having a large volume as compared with the immersed part lying beneath them. Others, including Mr. Reed (late Chief Constructor of the Navy), have strongly objected to flaring bows, and have introduced U-shaped cross-sections, with the view of reducing pitching, as well as of reducing the excess of weight over buoyancy at the bow.* Mr. Reed sums up his reasons for prefering the U form to the V form of cross-section as follows:-"First, it increases the buoyancy "towards the bow, and even in still water reduces the ten"dency of the heavy bow to break itself off or to bend the ship longitudinally; and, secondly, the bluff vertical sections

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encounter greater upward resistance than the V-shaped "sections when the ship tends to plunge down through the "water, and receive a greater lifting effect when the sea tends

*See further on the last-named subject the remarks in Chapter VIII. page 261.

"to rise up under the ship." The adoption of pronounced U-shaped sections for the bow has not become general, nor does it appear likely to do so, other considerations leading most naval architects to prefer finer under-water forms; but the use of flaring sections above water is now less common than it was formerly, and naval architects agree that they are undesirable except in special cases, as, for example, where room is required at the bow to work a chase gun on the upper deck.

Pitching oscillations are likely to be more sustained, even if they are not made more extensive, when heavy weightssuch as guns or cargo-are carried far forward or aft. This is a matter of common experience, as well as a condition which theory would predict. Carrying heavy weights near the bow and stern instead of nearer amidships adds to the moment of inertia of the ship; this increase leads to a somewhat longer period of oscillation for pitching, but the change is scarcely such as might be expected to exercise a notable influence on the behaviour of most ships, seeing that the periods of the waves which would produce considerable pitching are likely to be large as compared even with the altered period for pitching. On the other hand, the increased moment of inertia, while it opposes greater resistance to motion being impressed on the ship, when once that motion has been set up acts against the fluid resistance, and tends to maintain the motion. A similar condition has already been discussed for the rolling motion of ships, so that nothing more need be added.

Vessels of low freeboard are subjected to deck resistance when pitching among waves; and the Devastation furnishes an excellent example of this action. When on trial off the Irish coast, and steaming head to sea at moderate speeds,

* Naval Science, No. 12, page 55. The reader may also consult on this subject a paper, by Dr. Woolley, "On the Bows of the Helicon and

Salamis," in vol. vii. of the Transactions of the Institution of Naval Architects.

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waves broke over the fore part of the deck, as it was anticipated they would do under these circumstances, the fittings on this deck having been designed to exclude from the interior water lodging upon it. An eye-witness, describing her motion, says:" It invariably happened that the seas broke upon her during the upward journey of the bow; and there is no " doubt that to this fact her moderate pitching was mainly due, as the weight of water on the forecastle deck, during the "short period it remained there, acted as a retarding force, preventing the bow from lifting as high as it otherwise "would, and this, of course, limited the succeeding pitch, and "so on." In American monitors, with their exceptionally small freeboard, this kind of action would be even more effective, were it not for the fact, that their natural periods for pitching oscillations are probably so small as to make them capable of accompanying very closely the motions of such waves as would produce considerable pitching in the monitors. Under-water projections, like the spur-bows of ironclad rams, may also produce some limitation of pitching and 'scending by creating additional resistance; and are said to have actually done so in reports on French ships. But these are cases of comparatively unfrequent occurrence, and are interesting chiefly as instances of the effect of fluid resistance in limiting the pitching motions of ships which immerse or emerge their decks. In ordinary ships the decks are much higher, and the longitudinal oscillations rarely acquire such a magnitude as to immerse the decks considerably.

*

Finally, on this part of the subject, it may be well to

Mr. Fox (assistant secretary of the United States navy), reporting on the behaviour of the Miantonomoh, head to sea in a heavy Atlantic storm, said, "She takes "over about 4 feet of solid water, "which is broken up as it sweeps "along the deck, and after reaching "the turret is too much spent to

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prevent firing the guns directly "ahead." This confirms the opinion that these vessels move so quickly as to very nearly accompany the wave slope; their actual arcs of oscillation in pitching being considerable, and accurate practice with the guns in the line of keel being impossible.

remark that the actual period observed for pitching motions is not to be taken as equal to the natural period. In the case of rolling, a similar distinction of periods has been explained, and what was there said applies here also. In all probability, the result of more extended observations will show that the periods of the waves which are capable of producing considerable pitching motions practically determine the observed periods of pitching, the natural period being mastered by the wave period just as it is in the case of " permanent " rolling discussed in the earlier part of this chapter.

CHAPTER VII.

METHODS OF OBSERVING THE ROLLING AND PITCHING MOTIONS OF SHIPS.

ENOUGH has been said in previous pages to show how variable, and how liable to mislead an observer, are the conditions surrounding the behaviour of a ship at sea. The ship, herself in motion, is surrounded by water also in motion; and it is extremely difficult, by means of unaided personal observation, to determine even so apparently simple a matter as the position of the true vertical at any instant. To estimate correctly the angles through which a ship may be rolling or pitching, it is therefore necessary to bring apparatus of some kind into action; and in the use of such apparatus there are many sources of possible error which must be prevented from coming into operation. Upon the correctness of these observations we are greatly dependent, since deductions from theory are thus checked, and the extent to which they can be made a safe guide for the naval architect in designing new ships is ascertained. Numerous examples illustrating the substantial agreement of observation with the chief deductions from theory have been given in the previous chapter; but up to the present time the comparison has been mainly of a qualitative character, and before more exact results are obtained, it will be necessary to have compiled and collated much more exact and extensive records than are at present accessible.

The chief problem to be solved is this. What are the conditions of wave motion that will produce the maximum