44 REPORT — 1869. 



these propositions true, the ascertained resistance of a model, at given velo- 

 city, would supply a complete scale of resistance for all velocities, both for 

 the model and for any ship similar to the model. 



Since, however, the resistance of a model or ship deviates from the law of 

 the square of the velocity, as under certain cuxumstances it is known to 

 do, in a manner dependent on its actual dimensions, it is obvious that 

 the simple scale of comparison, which seemed prima facie probable, can he no 

 longer accepted, and it has hence been hastily concluded that no assignable 

 scale of comparison can be found instead. 



Now it appears to me to be pretty well established, and it is scarcely 

 questioned, that, for deeply submerged bodies of tolerable size and fair shape, 

 the resistance does foUow the law of the squares with a high degree of 

 approximation. Such deviations from this law as appear in Beaufoy's expe- 

 riments are, I think, explicable by the angularity of the shapes tried and by 

 the mode of trying the experiments, under which the considerable distance 

 between the bodies tried and the conducting float by which they were carried 

 involved some deviation of the body from true axial motion, when the velocity 

 and the consequent resistance became considerable. 



That surface-friction, in particular, follows the law of the squares of the 

 velocity very closely, is well established by the experience of the flow of 

 water through pipes, in reference to which, I may observe, I have myself 

 experimentally verified on a five-mile length of 9 -inch pipe, the law that the 

 deiiveiy is almost exactly as the square root of the steepness of the hydravdic 

 gradient. The experiments were tried with very great variations in the steep- 

 ness*. N'ow Professor Rankine's admirable stream-hue investigations have 

 definitely established the conclusion that for symmetrically shaped bodies of 

 "fair" lines, not excluding by that description certain very blunt-ended 

 ovals, when wholly submerged, the entire resistance depends on the conditions 

 of imperfect fluidity, of which surface-friction is the only one so considerable 

 that we need take account of if we deal with bodies of rational dimen- 

 sions ; and this, as I have pointed out, does follow the law of the squares. 

 I set aside the condition of "viscosity"; for though this defect, even as it 

 exists in water, is certainly sufficient to afl'ect difl'erently the resistances of 

 bodies of different dimensions, this is not sensibly the case unless the bodies 

 are very minute ; and havrag regard to the great vitality of such small sur- 

 face-waves as (say) one foot in length, and to the fact that discharge of water 

 through pipes and orifices exhibits no results indicative of this special action, 

 unless the diameters are very small indeed, it seems extremely improbable 

 that the resistances of bodies five or six feet in length will be afl'ected by it. 

 If, therefore, we were deahng with submerged bodies, we shoidd have no 

 reason to mistrust the primd facie deductions founded on experiments with 

 models. 



"When, however, we deal with a body moving at the sui-face, we at once 

 meet with a vera causa, which alters those simple relations that exist be- 

 tween the resistances of differently dimensioned submerged bodies. This 

 vera causa is the generation of surface-waves, which accompanies the transit 

 of the body along the surface ; and it is, I believe, not merely the only 

 known cause, but a suificient one. 



What absolute conformation and magnitude of waves a given vessel moving 

 with a given velocity may create, and what excess of resistance may thus bo 



* Though I regard these experiments as sufficiently conclusive in reference to the point 

 to which they were directed, I am inclined to think tliat the theory of surface-friction in 

 its application to a ship's resistance requires considerable reyision. 



