Mr Watts’ Observations on the Resistance (^Fluids. 321 
beyond controversy ; and since the process of investigation is 
allowed to be legitimate, we may employ it as a means for dis- 
covering the imperfections of the theory ; for, instead of assign- 
ing the motions by means of the supposed forces and the known 
mechanism, we may, conversely, determine the forces by means 
of this mechanism and the observed motions. 
It appears, both from theory and experiment, that the im- 
pulses and resistances are very nearly in the proportion of the 
surfaces which bodies present to the direct action of fluids. In 
fact, the Chevalier Boiida has found, that, with the same velocity, 
the resistances increase somewhat more rapidly than the sur- 
faces ; and he has remarked, that the deviation from the theory 
increases with the surface. This is a most interesting circum- 
stance, particularly with regard to the extensive surfaces of the 
sails and hulls of ships ; and when taken in connection with the 
eflective oblique impulse, which in acute angles is found to be 
much greater than in the ratio of the square of the sines of the 
angles of incidence, it will be found that it has the “ chief in- 
fluence on all the particular modifications of the resistance of 
fluids.” And as it is on these two circumstances that the whole 
theory' of the construction and working of vessels, and the action 
of water on our most important machines, depend, they certain- 
ly merit the most particular and attentive consideration of our 
naval constructors and civil engineers. 
Having thus completed the investigation of this interesting 
problem, I shall now proceed to answer some objections that 
have been urged against it by the writer of the article Resist- 
ance” of Fluids alluded to above. 
1. The writer begins with stating, that there is nothing in 
experimental philosophy more certain, than that the resistances 
are very nearly in the duplicate ratio of the velocities, and that 
he cannot conceive by what experiments the ingenious author 
(d’Ulloa) has supported the conclusion which is contained in 
the equation (2). The answer to this objection has already 
been anticipated, as it has been proved, that if we assume 
^h — this supposition will give, R = x ; and the 
VOL. IV. NO. 8. APRIL 1821. 
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