VOL. LXXXVI.] PHILOSOPHICAL TRANSACTIO>fS. 097 



These difficulties will appear still greater, if it be considered that the causes 

 which influence the motion of ships at sea are not separate and independent, but 

 operate on each other, as well as immediately on the motion of the vessel: thus, 

 if the position of the centre of gravity be altered by moving the ballast or lading 

 nearer to the head or stern, this alteration will have the effect of changing the 

 section of the water^ and the form of the immersed part of the vessel ; on which 

 account, the resistance opposed by the water to the ship's motion must neces- 

 sarily be changed; the centre of gravity of the part immersed will also be dif- 

 ferently situated, which must combine with the alteration of the centre of gra- 

 vity of the vessel, and the section of the water, to increase or diminish the sta- 

 bility of the ship; and it must be added, that the inclination of the masts and 

 sails to the horizon, and the direction in which the wind impinges on them, will 

 suffer alteration from the same cause. 



Though theory alone may not be adequate to the solution of these difficulties, 

 yet, when combined with experiments and observations, it may be probably em- 

 ployed with great advantage in these researches. If the proportions and dimen- 

 sions adopted in the construction of individual vessels be obtained by exact geo- 



of the Society for the Improvement of Naval Architecture, and published by their order. I have 

 examined these experiments with a good deal of attention, particularly those which were made on 

 oblong beams or parallelopipeds, denoted in the accoiuit of the experiments by the letters a, b, &c.; 

 and find, that though the surfaces of the moving body were planed very smooth, the res'stance of 

 friction was equal to a weight of no less than QO lb., on a surface of ?38 square feet, when tlie body 

 moved with a velocity of 8 feet in a second. It appears also, by methods of calculation, founded on 

 Sir Isaac Newton's rule for drawing a parabolic line through any number of given points situate in the 

 same plane, and applied to the above-named experiments, that the resistance of friction varies in no 

 power of the velocity expressible by less than 3 dimensions of it, that is, if z is put to denote the 

 resistance of friction, and v to denote the velocity, the resistance requires an equation of the form 

 z = av + bv- + cii* ; in which a, b, and c, are invariable quantities: the force also of pressure on 

 the posterior surface is expressed by an equation equally complex : to these difficulties another is to be 

 added, which is, that tlie resistance varies with the depth of the moving body, as appears by tlie ex- 

 periments referred to. On these considerations it seems manifest, that investigations on the subject 

 of naval architecture, founded on the theory of motion, which takes into account the resistances of 

 the water, considering the velocity to be such as ships usually sail with, must involve algebraic ex- 

 pressions so complicated, as to make it very difficult, perhaps impossible, to infer any useful practical 

 conclusions from this mode of considering the subject. Euler and Bouguer, the principal authors 

 who have attempted to apply the theoiy of resistances to naval architecture, suppose the resistance to 

 be in a duplicate ratio of the velocities ; a law evidently different from that according to which vessels 

 at sea are opposed by the medium in which they move : and one of these most eminent authors, 

 (Euler) doubts whether this theo:y is not too imperfect to be relied on, when it is applied to ascertain 

 tlie motion of ships at sea. Notwithstanding the impediments which arise from the complicated laws 

 of resistance and friction, the general principles investigated in the works of these authors are no 

 doubt capable of being applied to the solution of many difficulties which occur in considering the 

 subject of naval architecture, due allowance being made for those irregular forces which cannot be 

 included in the theoretic solutions — Orig. 



VOL. XVII. 4 U 



