STABILITY^ PROPULSION^ AND SEA-GOING QUALITIES OF SHIPS. 37 



appears, howeTcr, that the periodic time of the free oscillations has an im- 

 portant influence on the extent of the forced oscillations, especially in roll- 

 ing, the most unfavourable proportions for the periodic time of free rolling 

 to that of passive rolling being those which lie near equality, and between 

 equality and y' 2 : 1 ; for the equality of these periods tends to produce an 

 excess of rolling to which it would be difficult to fix a limit, and the ratio 

 of V2 : 1, and those near it, make the shij) roll against the waves, thus 

 throwing her into positions in which there is a risk of the wave-crests 

 breaking into her. 



A period of free rolling much less than that of passive rolling gives great 

 stiffiiess, and makes the ship accompany the motions of the effective wave- 

 surface. A period of free roUing exceeding s/ 2 times that of passive rolling 

 is favourable to steadiness, provided that this lengthened period be produced 

 by the inertia of the ship, and not by insufficient statical stability. 



The action of the water on a deep keel, on a sharp floor, or on fine ends 

 below water tends to moderate the extent of rolling produced by coinci- 

 dence, whether exact or approximate, of the periods of tree and passive roll- 

 ing ; but at the same time it lessens the effect of a long period of free roUing 

 in producing the same result. 



A deep draught of water is favourable, on the whole, to steadiness, but not 

 to stifliiess. 



Should the centre of gravity rise and fall relatively to the water in roUing, 

 and the periodic time of the dipping motion so generated happen to be either 

 exactly or nearly one half of that of the passive rolling, the result will be 

 uneasy motion. 



The steady pressure of the wind on the sails promotes steadiness, at a 

 certain angle of heel depending on the moment of that pressure; the sudden 

 gusts of the wind produce lurching. 



As to intchinci, scending, and yawing, it is chiefly important that, for the 

 Bake of dryness and safety, those oscillations should be performed in a lively 

 manner among waves ; and that object is best promoted by keeping the 

 longitudinal radius of gyration short, as compared with the length of the 

 ship — that is, by taking care not to place heavy weights in her ends. 



The true principles of a ship's rolhng among waves and their leading 

 consequences were first set forth by Mr. Proude, in a series of papers in the 

 ' Transactions of the Institution of Naval Architects,' in 1861, 1862, and 

 1 863. Mr. Froude appears to have been the first to state the proposition 

 that the tendency of the ship to roU among waves is primarily due to her 

 tendency to keep upright to the effective wave-surface, and that the force 

 which induces this tendency is very approximately the same as her stiff- 

 ness or resistance to heeling in still water. The disposition of a ship' to 

 follow the average motion of the portion of the wave which she displaces is, 

 however, controlled (as has been pointed out by Mr. Crosslaud) by the 

 circumstances that the wave-water is continually undergoing a deformation 

 of which the ship's huU is not susceptible. Mr. Froude has also shown * 

 that if two plates be hinged together, so that, when in still water, they 

 would float at an inclination of 45° to the vertical, and if the hinge be pa- 

 rallel to the wave-crest, the effect of the wave-motion is simply to open or 

 close the angle between them, and not to alter (sensibly) the horizontal and 

 vertical lines which bisect the angle externally and internally. 



As there is nothing to show that the rigidity of the angle between the 



* See Trans. I. N. A. vol. vi. for 1865, p. 181. 



