284 Resistance of Liquids to Solid Bodies moving in them. 
_ The results of these experiments exhibit a resistance at all angles, 
greater than the squares of the sines, and also greater than the sines 
for angles between 0 degrees and fifty degrees, but less than the sines, 
between fifty and one hundred and eighty degrees. The brief ac- 
count we have of these experiments appears to be defective, in not 
stating the absolute velocities of the solid; and the method is also 
objectionable, because with the lesser angles of the prow, a solid of 
much greater surface and volume was used than with the greater an- 
gles, without making any allowance for these items; so that between 
the angles of 180° and 12°, the surface in contact with the water, 
(exclusive of the stern,) was increased from 85 to 335.73 square feet, 
and the volume of the water displaced was increased from 100 to 
337.8 cubic feet. If these circumstances are of no consequence, 
then a very large vessel ought to be as easily moved as a very small 
one. 
We want a set of experiments made with solids, all having the 
same volume or displacement, but having bows and sterns of various 
forms, to ascertain what form of bow will displace, and also what 
form of stern will replace, the given volume of water with the 
least motive force. 
To displace the water, and also to replace it with the least dis- 
turbance, is the desideratum. Some attention has been given to the 
displacement, but very little to the replacement; hence the water 
lines of boats and vessels, contiguous to the stern and stern-post, are 
generally concave, which is highly detrimental to fast sailing ; be- 
cause the concavity next to the stern requires a convexity (before 
we arrive at the section of greatest breadth,) of much shorter radius 
than would be required if the water line presented a convexity from 
the stern to the midship section ; and these two curves in contrary 
directions virtually double the inertia of the water—the concavity 
throws it off at right angles to the vessel, and it then has to assume 
a new direction, and pass round a curve of shorter radius to approach 
the stern. ‘The concavity of the stern retards the replacement, by 
causing the water to pass along a curve instead of a straight line, 
which is evidently the shortest ; and because the water will not even 
pass along a straight line, in a direction from the broad part of the 
vessel to the stern post, when the velocity is considerable, but leaves 
a hiatus or cavity near the stern post, and deprives the vessel of the 
benefit of the reaction of the water there—a certain convexity in all 
the water lines near the stern, would therefore improve the sailing- 
