THE LAW OF RESISTANCE. 73 



It is always found that the commotion produced in the fluid is much greater 

 at velocities less than the wave, than at velocities which are greater than it. 

 The stem of the vessel, in the latter case, enters water which is perfectly smooth 

 and undisturbed, because no wave has previously passed forward before the ves- 

 sel to produce any anterior derangement ; the water which is pushed aside by 

 the bow of the vessel, forms a lateral accumulation proportioned to the increase 

 of volume arising from the sudden entrance of the solid ; and when the vessel 

 has passed forward, the subsequent collapse of the lateral ridge restores the equi- 

 librium. The disturbance of an anterior wave is thus rendered impossible, and 

 the cause of the destructive stern surge is removed ; for the displaced water re- 

 mains to fill up that vacuity into which a stern surge would otherwise have been 

 driven. 



It is evident, therefore, that the nature of the motions communicated to a 

 fluid at velocities greater than the velocity of the wave, are radically different in 

 their nature from those of the less velocities. Lateral currents, breaking surges, 

 can no longer exist. The fluid is simply divided by the entrance of the vessel, 

 stands aside until it has passed, and gently subsides to the original level when 

 the separating body has passed away. 



The practical applications of these facts and phenomena are of great value in 

 the navigation of canals and shallow rivers. (See Sec. VIII and IX.) 



Tables of resistance at various velocities are given from seventeen different 

 forms of the immersed portion of the floating body, at velocities from 3 to 15 miles 

 an hour, in Parts II. and III. 



Section VII. — On a General Expression of the Law of Resistance of a given Solid 



in a given Limited Fluid. 



If the immersion of a floating body were like that of a sohd wholly immersed 

 in the fluid, a constant quantity, and if the surface of the fluid remained horizon- 

 tal and plane, and if the particles of the fluid remained at rest untU immediately 

 acted on by the solid, and were the motion given by the solid to the displaced 

 fluid horizontal without vertical excursions, then the usual simple expression, 



R = — . msp .... (1.) 



would represent the resistance R, being the weight of a column of fluid having 

 the height due to the velocity v, g being the measure of gravity, s the anterior 

 transverse section of the immersed part of the solid when at rest, m being a con- 



VOL. XIV. PART I. K 



