STABILITY^ PROPULSION, AND SEA-GOING QUALITIES OF SHIPS. 13 



expended in overcoming back pressure and friction in the engine varies 

 directly as the speed — 



H.P. =DJV (-1552 + -0040840 V"), 



the constants being obtained empiricallj-. 



Most modern formula) for resistance take account of the form of the vessel, 

 in such a manner as to require the use of the drawings of the exterior sur- 

 face of the ship. The Swede, Chapman, in his well-known treatise on ship- 

 building, assumes that the surface of the vessel may be divided into small 

 portions, the resistance of each of which will be proportional to the projection 

 of its area, to the sine squared of the inclination, and to the square of the 

 velocitj^ ; with a certain small correction on account of the currents which 

 are set up bj' the ship's own motion, and which modify the pressures. But 

 he himself saw reason from subsequent experiments to doubt whether the 

 law of the sine squared, or even that of the velocity squared, was applicable 

 to the forms which he used. 



Euler* and most of the older writers use the sine squared of the incli- 

 nation as the factor representing the effect of obliquity ; and this theory has 

 been revived by Mr. Hawksley in a discussion at the Institution of Civil En- 

 gineers, reported in their ' Proceedings ' for 1856, vol. xvi. p. 356. But we 

 think that there is now ample experimental ground for believing that, whether 

 or not this law be true with respect to an infinitesimal portion of a plane re- 

 ceiving the impact of a thin jet of water, it is not true either of plane sur- 

 faces of considerable extent, or, as a differential formula, of curved surfaces. 

 It evidently fails to take account of the effect of the stream which is set up along 

 the surface in deflecting the impact of water on the part of the surface further 

 back from the entrance. The assumption that this has no effect is not one 

 which can be admitted without proof ; and the experimental evidence tends 

 the other way. Chapman's later experiments, the experiments of the French 

 Academy, and those of Col. Beaufoyf are all against the hypothesis of the 

 sine squared of the inclination. The supposition that the sine squared of the 

 inclination represents the effect of the obliquity of the afterbody is still 

 more open to doubt than when it is applied to the forebody. 



As a contribution to the history of the subject, the following translation 

 from a tract of M. Dupuy de Lome will be interesting : — 



" Romme, in his Memoir for the Academy of Sciences, in 1784, while 

 giving an account of the experiments made by him at Rochefort on models 

 of ships, one of which represented a 74, and, again, in his work on the ' Art 

 de la Marine,' had very succinctly laid down that this resistance was inde- 

 pendent of form. ' Provided,' he went on to say, ' the water-lines have a 

 regular, fair curvature, as is the case in modern vessels, the greater or less 

 fullness of the bow or stern neither increases nor diminishes the resistance 

 of the water to their progress.' 



" In direct contradiction to this too summary rule, which has long ob- 

 structed the progress of naval architecture, my experience leads to five prin- 

 ciples, which I state as follows : — 



" 1°. Among vessels of similar geometrical form, of different size, but all 

 having their immersed surface exceedingly smooth, and driven at the same 



* See his 'Scientia Navalis' (St. Petersburgli, 17 19), vol. i. p. 213. See also D'Alem- 

 bert, ' Traite de I'Equilibre et du Mouvement des Fluides,' ed. of 1770, p. 226. 



t See Chapman (by Inman), p. 257 ; Bossut, ' Hydrodynamique,' vol. ii. p. 396 ; Beau- 

 foy, p. Ixxxvii. See also Ssott Eussell's ' Naval Architecture,' p. 168 ; or Proceedings of 

 Civil Engineers, vol. xxiii. p. 346, as to the French experiments. 



