NOTE E. 



On the Resistance of Fluids. 



One of tlie most important but at the same time most difficult practical 

 questions connected with the subject of this book is the determination 

 of the resistance experienced by a solid moving through a fluid, e.g. by 

 a ship moving through the water, or by a projectile through the air. 



The effect of a liquid on the motion of a solid through it has been 

 discussed, on certain assumptions, in Arts. 105 119. It was there 

 found that the whole effect was simply equivalent to an increase in the 

 inertia of the solid. The latter yields more sluggishly to the action of 

 force than it would do if the fluid were removed, whether the tendency 

 of the force be to increase or to diminish the motion which the body 

 already has ; but there is no tendency to a total transfer of energy of 

 motion from the solid to the fluid, or in any other way to reduce the 

 solid to rest. Thus a sphere immersed in a liquid will move under the 

 action of any forces exactly as if its inertia were increased by half that 

 of the fluid displaced, and the fluid then annihilated. For instance, if 

 set in motion and then left to itself, it will describe a straight path with 

 uniform velocity. 



These theoretical conclusions do not at all correspond with what is 

 observed in actual cases. As a matter of fact a body moving through a 

 fluid requires a continual application of force to maintain the motion, 

 and if this be not supplied the body is quickly brought to rest. 



This discrepancy between theory and observation must be due to 

 unreality in one or more of the fundamental assumptions on which the 

 investigations referred to were based. These assumptions are 



A. That the fluid is * perfect, i.e. that there is no tangential action 

 between adjacent portions of fluid, or between the fluid and the solid j 



B. That the motion is continuous, i.e. that the velocities u, v, w 

 are everywhere continuous functions of the co-ordinates ; and 



C. That the fluid is unlimited except by the surface of the solid. 



