ISO 



NATURE 



\yune 12, 1879 



largely in excess of the truth. A most important practi- 

 cal circumstance is left entirely out of account in the equa- 

 tion, viz., the fact that the oscillations are performed in a 

 resisting medium. The laws of resistance to rolling are not 

 sufficiently well understood to enable their modifying effect 

 to be introduced into a general equation, and a direct and 

 theoretical solution of the question thus attempted. Mr. 

 Froude has shown, however, how in the case of any in- 

 dividual ship an approximate solution may be obtained 

 with certainty by help of data derived from a single ex- 

 periment with the ship herself, or even with a carefully 

 made model of her, tried in still water. He has also 

 pointed out that if a well-selected series of such experi- 

 ments were tried for ships of different forms, and the 

 results tabulated, the series of corresponding solutions 

 would enable him to determine, as if a priori, what 

 modifications the results of his equation would require 

 for any ship whatever. 



The resistance which a ship experiences in oscillating 

 through a given angle among waves is practically the 

 same as it would be if she were performing an oscillation 

 of the same range in still water. If she is set rolling in 

 still water the resistance will rapidly bring her to rest 

 when the force which caused her to roll ceases to act. 

 In the same way, when rolling among waves, the same 

 resistance will reduce the angles of oscillation. It is this 

 circumstance which prevents dangerous angles being 

 reached in the critical case of synchronism, and which, 

 at all times, fixes the limiting position to which a ship 

 will roll. The action of the waves in increasing the 

 angle of roll is I alanced ty the opposing tendency of 

 resistance to reduce it. The aggregate resistance of a 

 ship to rolling is made up of three parts : (i) That due to 

 the friction of the fluid in moving over the skin of the ship ; 

 (2) the direct resistance of the keel and fine parts at the 

 ends to being pushed through the water at right angles, 

 or nearly so, to their planes ; and (3) what Mr. Froude 

 calls the " wave making function," or the element of 

 resistance caused by the successive displacements of 

 fluid in rolling which affect the surface as waves, and 

 travel away from the ship, thus abstracting from her the 

 energy they embody. 



The aggregate resistance to rolling being of such a 

 character, and containing elements which vary in 

 different ways with the rate of motion of the surface of a 

 ship's bottom, its exact computation in a particular case 

 would be very difficult. Mr. Fronde has, however, done 

 much towards enabling a sufficiently close approximation 

 to be arrived at by direct calculation. For practical pur- 

 poses, however, Mr. Froude' s original suggestion of deter- 

 mining the amount of resistance by still water experiments 

 is employed. A ship is set rolling in still water, and upon 

 reaching an angle of sufficient magnitude, she is allowed 

 to come to rest under the action of resistance only. The 

 rate of extinction of her range of oscillation is continuously 

 noted and registered in the form of a curve. It will be 

 obvious that the difference in amplitude of two successive 

 swings measures the aggregate effect of the resistances 

 operating upon the ship, and that by means of a complete 

 curve of extinction a measure of the resistance opposed 

 by her to rolling among waves may be obtained. 



This is, necessarily, but a general description of Mr. 

 Froude' s theory, and does not include many details and 

 some collateral matter which are of importance in making 

 it quite complete ; but it will serve to give an indication of 

 its broad features. 



Mr. Froude' s theory has met with general acceptance 

 as being a sufficiently close approximation to a correct 

 expression of the laws of motion of a floating body among 

 waves. Some of the departures from absolute accuracy 

 contained in the assumptions necessary to the formation 

 of the theory, such as that wave-water is continually 

 changing its form, and a ship being a rigid body, cannot 

 therefore, strictly speaking, be said to accept the dynami- 

 cal conditions of the displaced fluid as it accepts the 



statical conditions of its still-water displacement ; and the 

 objection that a sub-surface of equal pressure does not 

 correctly represent the effective wave surface have been 

 criticised ; but the criticisms have only shown that the 

 errors thus involved are very small in amount and have 

 no appreciable effect upon the general results of the 

 theory. Mr. Froude has always insisted himself upon the 

 existence of imperfections in his theory, but he has con- 

 stantly been at work upon their removal, and upon the 

 determination of the tangible amount of error they intro- 

 duce into the ultimate result. 



Mr. Froude's work was undertaken at first with a 

 practical object, on account of Mr. Brunei's requirements, 

 and it has already accomplished great practical results. 

 It has led to the conclusion that ships of long periods are 

 least likely to meet with waves which will cause them to 

 roll heavily, and that the rolling of a ship can be greatly 

 reduced by means of deep-bilge keels. These ideas have 

 been extensively acted upon in H.M. Service. Our heavy 

 armour-clads and other ships of war have been designed 

 in accordance with this theory, so as to have great steadi- 

 ness at sea, and in 'many special cases their properties 

 have been determined by Mr. Froude beforehand, so 

 that instead of working in the dark the Admiralty have 

 known what behaviour to expect from a ship after she is 

 built. The effect of bilge-keels in extinguishing rolling 

 was clearly shown by Mr. Froude in 1871, with a model 

 of the Dniastatioii. Without bilge-keels the model per- 

 formed 31^ complete oscillations before coming to rest in 

 still water, after being inclined to an angle of 8^°, but 

 with a bilge-keel equivalent to 36 inches in depth on the 

 full scale of the ship, she came to rest in eight oscillations, 

 and with a bilge keel double this depth she came to rest 

 in four oscillations. The same model when tried among 

 waves which capsized her when no bilge keels were fitted 

 only rolled to an angle of 13^° with 3 feet bilge keels, and 

 to 5° with 6 feet bilge keels. These experiments showed 

 conclusively the effect of bilge keels in limiting the range 

 of oscillation among waves. 



The importance of bilge keels was further tested by 

 comparative trials conducted by Mr. Froude off Plymouth 

 in 1872 between H.M. ships Greyhound and Perseus — 

 both of the same class — the former having bilge keels and 

 the latter being without them. Mr. Froude also conducted 

 an elaborate series of experiments on board the Devasta- 

 tion 2X sea in 1873 and 1875, and, by means of a most 

 ingenious machine of his own construction, obtained con- 

 tinuous automatic records of her behaviour. These 

 records showed (i) the relative inclination of the ship and 

 the effective wave slope at any instant ; (2) the inclination 

 of the ship to the vertical at any instant ; and (3) the 

 period of oscillation of the ship at any time, that is, the 

 number of seconds occupied in completing the roll from 

 port to starboard, and vice versd. From the diagrams 

 upon which (i) and (2) are traced in the form of curves 

 ^Ir. Froude deduced, as a differential result, the period 

 and angle of slope of the effective wave surface at any 

 instant, thus determining it with a much greater degree of 

 exactness than that with which the form of a surface wave 

 could be ascertained. 



Mr. P'roude was constantly checking and correcting his 

 theoretical results by the aid of experiment, and though 

 he had succeeded in fully establishing the true theory of 

 the roUing of ships among waves, he did not rest satisfied 

 with his success, but had recently made arrangements at 

 his experimenting tank at Torquay for proceeding with 

 further important lines of investigation by means of 

 observations upon the behaviour of models in waves 

 mechanically generated. 



We have only dealt with Mr. Froude's labours in con- 

 nection with the question of the rolling of ships in this 

 number, and must reserre a description of his investiga- 

 tions into the laws of resistance and propulsion, which 

 are at least of equal importance, for another occasion. 

 (7"(3 be continued.) 



