12C) 
of floating Bodies, and the Stability of Ships. 
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 po- 
sition of the centre of gravity is 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 ne- 
cessarily be changed ; the centre of gravity of the part im- 
mersed will also be differently situated, which must combine 
mensions thereof, that is, if % is put to denote the resistance of friction, and v to denote 
the velocity, the resistance requires an equation of the form z — au - J- bu z -f cu 3 ; 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: |o these difficulties another is to be 
added, which is, that the resistance varies with the depth of the moving body, as appears 
by the experiments referred to. On these considerations it seems manifest, that investiga- 
tions oh 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 expressions 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 at- 
tempted to apply the theory of resistances to naval architecture, suppose the resistance 
to be in a duplicate ratio of the velocities ; a law evidently different from that accord- 
ing to which vessels at sea are opposed by the medium in which they move : and one 
of these most eminent authors,* doubts whether this theory is not too imperfect to be 
relied on, when it is applied to ascertain the 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. 
* Euler. Theorie complelte de la Construction des Vaisseaux, English edition, 
P-93>94- 
MDCCXCVI. S 
