128 Mr. Atwood's Propositions determining the Positions 
cularly the laws of the different resistances to the ship's mo- 
tion,* it would be unsafe to rely entirely on deductions a priori 
for explaining this subject. 
* The laws of resistances, opposed to bodies which move in fluids, and varying in a du- 
plicate ratio of the body’s velocities, are demonstrated bySirIsAAcNEWTON,inthe second 
book of the Principia, on conditions restrained to the particular case in which the motion 
of the resisted body is extremely slow, and the fluid perfectly compressed. On these 
conditions, the pressure which resists the motion of the body is exactly balanced by the 
pressure -on the posterior part, and consequently the only force opposed to the body’s 
motion, is the inertia of the fluid, which is displaced while the body moves through it : 
for the resistance of friction depending on the body’s velocity must be, in a physical sense, 
evanescent, when the motion is very slow. Tt is evident, that the theory of resistances 
founded on these principles ought not to be applied to the solution of cases in which the 
velocity is much increased, without great care and circumspection; for by the increase of 
velocity, three different forces begin to have operation, of which the Newtonian theory 
takes no account ; i. e. the pressure on the anterior part of the body, the pressure on 
ihe posterior part, and the resistance of friction. The pressure on the anterior part will 
evidently be a constant or invariable quantity as long as the moving body continues 
at the same depth. The pressure on the posterior part will depend on the velocity of 
the body’s motion, and when that velocity is zr o, the pressure will be precisely equal, 
and contrary to that which acts on the anterior part. Moreover, when the body’s velo- 
city is equal to that with which the fluid rushes into empty space, the pressure on the 
posterior part will be — o, and of consequence all the pressures on the posterior sur- 
face, corresponding to the intermediate velocities, must be found between these limits. 
When the surfaces of the moving body are smooth, it has been supposed that the effects of 
friction are not very considerable. This opinion is however disproved, to the satisfaction 
of any one who consults the account of the very accurate and well devised experiments 
on the motion of bodies through the water, made under the direction of the committee 
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 account of 
the experiments by the letters A, B, See. ; and find, that although the surfaces of the 
moving body were planed very smooth, the resistance of friction was equal to a weight 
©f no less than ninety pounds, on a surface of 258 square feet, when the body moved 
with a velocity of 8 feet in a second. It appears also, by methods of calculation, founded 
on Sir Isa a c 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 three di- 
