Resistance, or Resisting Force, denotes in general any power which acts in an opposite direction to another, so as to destroy or diminish its effect. (See Mechanics, Hydrodynamics, and Pneumatics.) Of all the resistances of bodies to each other, there is undoubtedly none of greater importance than the resistance or re-action of fluids. It is here that we must look for a theory of naval architecture; for the impulse of the air, which is our moving power, must be modified so as to produce every motion we want by the form and disposition of our sails; and the resistance of the water, which is the force to be overcome, must also be modified to our purpose, in order that the ship may not drive like a log to leeward, but, on the contrary, may ply to windward; that she may answer her helm briskly, and be easy in all her motions on the surface of the ocean. The impulse of wind and water makes these elements ready and indefatigable servants in a thousand shapes for driving our machines, and we should lose much of their service did we remain ignorant of the laws of their action; they would sometimes become terrible masters if we did not fall upon methods of eluding or softening their attacks. We cannot read the accounts of the naval exertions of Phoenicia, Carthage, and of Rome,—exertions which have hardly been surpassed by anything of modern date,—without believing that the ancients possessed much practical and experimental knowledge of this subject. It was not perhaps possessed by them in a strict and systematic form, as it is now taught by our mathematicians; but the master-builders, in their dockyards, did undoubtedly exercise their genius in marking those circumstances of form and dimension which were, in fact, accompanied with the desirable properties of a ship, and thus frame to themselves maxims of naval architecture in the same manner as we do now. The ancients had not made any great progress in the physico-mathematical sciences, which consist chiefly in the application of analysis to the phenomena of nature; and in this branch, in particular, they could make none, because they had not the means of investigation. A knowledge of the motions and actions of fluids is accessible only to those who are familiarly acquainted with the fluxionary mathematics; and without this key there is no admittance. Even when possessed of this guide, our progress has been very slow, hesitating, and devious; and we have not yet been able to establish any set of doctrines which are susceptible of an easy and confident application to the arts of life. If we have advanced farther than the ancients, it is because we have come after them, and have profited by their labours, and even by their mistakes.

Sir Isaac Newton was the first who attempted to make the motions and actions of fluids the subject of mathematical discussion. He had invented the method of fluxions long before he engaged in his physical researches, and he proceeded in these sua mathesi facem preferente. Yet even with this guide he was often obliged to grope his way, and to try various bye-paths, in the hope of obtaining a legitimate theory. Having exerted all his powers in establishing a theory of the lunar motions, he was obliged to rest contented with an approximation instead of a perfect solution of the problem which ascertains the motions of three bodies mutually acting on each other. This convinced him that it was in vain to expect an accurate investigation of the motions and actions of fluids, where millions of unseen particles combine their influence. He therefore endeavoured to find some particular case of the problem which would admit of an accurate determination, and at the same time furnish circumstances of analogy or resemblance sufficiently numerous for giving the limits of those other cases that did not admit of this accurate investigation. Newton figured to himself a hypothetical collection of matter possessing the characteristic property of fluidity, viz., the quaquaversum propagation of pressure, and the most perfect intermobility of parts, and forming a physical whole or aggregate, whose parts were connected by mechanical forces determined both in degree and in direction, so that the determination of certain important circumstances of the motion of the parts might be rendered susceptible of precise investigation. And he concluded that the laws which he should discover in these motions must have a great analogy with the laws of the motions of real fluids; and from this hypothesis he deduced a series of propositions which form the basis of almost all the theories of the impulse and resistance of fluids which have been offered to the public since his time. It must be acknowledged that the results of this theory agree but ill with experiment, and Retford. that, in the way in which it has been prosecuted by subsequent mathematicians, it proceeds on principles or assumptions which are not only gratuitous, but even false. But with all its imperfections, it still furnishes (as was expected by its illustrious author) many propositions of immense practical use, they being the limits to which the real phenomena of the impulse and resistance of fluids really approximate; so that when the law by which the phenomena deviate from the theory is once determined by a well-chosen series of experiments, this hypothetical theory becomes almost as valuable as a true one. It continues to be the groundwork of all our practical knowledge of the subject.

We know by experience that force must be applied to a body in order that it may move through a fluid, such as air or water; and that a body projected with any velocity is gradually retarded in its motion, and generally brought to rest. Analogy leads us to imagine that there is a force acting in the opposite direction, or opposing the motion, and that this force resides in or is exerted by the fluid; and the phenomena resemble those which accompany the known resistance of active beings, such as animals; therefore we give to this supposed force the metaphorical name of resistance. We also know that a fluid in motion will hurry a solid body along with the stream, and that force is required to maintain it in its place. A similar analogy makes us suppose that the fluid exerts force, in the same manner as when an active being impels the body before him; therefore we call this the Impulsion of a Fluid. And as our knowledge of nature teaches us that the mutual actions of bodies are in every case equal and opposite, and that the observed change of motion is only the indication and measure of the changing force, the forces are the same, whether we call them impulsions or resistances, when the relative motions are the same, and therefore depend entirely on these relative motions. The force, therefore, which is necessary for keeping a body immoveable in a stream of water flowing with a certain velocity, is the same with what is required for moving this body with this velocity through stagnant water. A body in motion appears to be resisted by a stagnant fluid, because it is a law of nature that force must be employed in order to put any body in motion. Now the body cannot move forward without putting the contiguous fluid in motion, and force must be employed for producing this motion. In like manner, a quiescent body is impelled by a stream of fluid, because the motion of the contiguous fluid is diminished by this solid obstacle; the resistance, therefore, or impulse, no way differs from the ordinary communications of motion among solid bodies. Experiments on this subject have been made by Sir Isaac Newton, D. Bernoulli, Du Buat, Sir Charles Knowles, Euler, D'Alembert, S'Gravesende, Coulomb, Hutton, and Vince. A detailed account of the theories of those authors will be found in the article Hydrodynamics, ii., c. 3.