354 NEWTON S PBINCIPIA. 



and fluid must therefore be constant, or, at least, vary 

 slowly. 



If the fluid also be not boundless, but contained within 

 rigid or flexible surfaces, as the body moves on, these may 

 have some effect in disturbing the steadiness of the mo 

 tion. 



The fluid has been supposed incompressible. In apply 

 ing the law to the case of a compressible fluid, we are 

 omitting all consideration of the condensation in front 

 and rarefaction of the fluid behind the body, and also 

 of the vis viva lost by the waves that would be propa 

 gated in all directions round the body. These cannot be 

 said to be unimportant. 



And even if the fluid be incompressible, yet if the 

 body be floating on its surface, the theory takes no ac 

 count of the heaping up of the fluid in front of the 

 vessel, nor the partial lowering behind, nor the consequent 

 waves propagated in all directions round the vessel. 



Having viewed the various considerations which have 

 led to the ordinary law that Resistance varies as the square 

 of velocity, it remains to compare this law with the re 

 sults of experiment. This is the Lydian touchstone by 

 which the true gold of any theory is discovered. To 

 consider in detail all these would be at once uninteresting 

 and unprofitable. We shall proceed to sum up the 

 various results arrived at, and arrange them under the 

 heads of the theory. We shall only mention a few cases* 

 to show the application of the rules. 



1. The resistance is only found to vary as the square of 

 the velocity when the body is wholly immersed, the depth of 

 the fluid not inconsiderable^ and the velocity neither very 

 small nor very large. 



Coulomb found that for very small velocities the resist 

 ance varied as the velocity ; the part depending on the 

 square being inconsiderable. 



* For some of these references we are indebted to the excellent article 

 on Besistances by Sir D. Brewster, in the Encyc. Brit. 



