GENERAL PHENOMENA. ' 53 



delphia, I am indebted for much valuable information regarding the state of prac- 

 tical navigation in America, of part of which I have availed myself in illustrat- 

 ing the subject. Whatever is still wanting to complete this investigation, I hope, 

 in the course of a few years, if I enjoy life so long, to be able to accomplish; but, 

 in the mean time, one series of the observations has appeai-ed sufficiently entire 

 to be presented by itself, and I have been induced to give them publicity, by the 

 kind recommendation of Professor Whewell, who has taken a generous interest 

 in their progress, by which I have been encom-aged to pursue the investigation 

 through the many annoyances and disappointments and dangers that necessa- 

 rily accompany an undertaking of this nature. 



PART I. 



General Observations on the Phenomena that accompany the Motion of a Floating 

 Body on the surface of a Quiescent Fluid. 



Every instance of the want of perfect agreement between the predictions of 

 theoretical mechanics and the results of practical experience, may be traced al- 

 most invariably to the existence of certain latent conditions that have been omit- 

 ted from the fundamental hypotheses. Discrepancies of this nature ai'e suffi- 

 ciently numerous in the subject of hydrodynamics ; so much so, indeed, that in re- 

 lation to it, the appellations " practical" and " theoretical" are continually ap- 

 pMed as terms of antithesis. The various hypothetical constitutions assumed for 

 fluids by Newton, Bernoulli, Eulee, D'Alembert, and their followers, have en- 

 abled them to obtain one law regarding the resistance of fluids to the motion of 

 solids, which accords very closely with the phenomena of certain solids in certain 

 circumstances and at certain velocities, but that law has not been found ade- 

 quate to the solution of the case of a sohd partly inmiersed, as when a floating 

 body moves along the surface of a quiescent fluid. This law, which connects the 

 resistance of the fluid with the second power of the velocity, is in very close ac- 

 cordance with the motion of bodies that are wholly immersed, and with the mo- 

 tion of floating bodies that have certain velocities and are placed in certain cir- 

 cumstances ; but it has proved widely erroneous in its direct appUcation to the 

 motion of floating bodies in different circumstances and at higher velocities. So 

 far, indeed, does the resistance actually obtained in these cases differ from the 

 theoretical resistance, that examples may be found in every large collection of 

 experiments, and are to be met with in almost every page of those which I have 

 given at the end of this paper, where the resistance, instead of following the law 

 of the squares of the velocities directly, has been found to vary, not only with 

 every different power of the velocities from the first to the fourth power, but also 



