NEWTON S PRINCIPIA. 355 



The experiments ordered to be undertaken by the 

 French Academy, in the last century, with velocities not 

 greater than 2 miles per hour (7 6 feet per second) showed 

 that the resistance to floating bodies varied as the square 

 of the velocity. 



Hutton found that for low velocities in air the resist 

 ance varied as the square ; but as the velocity increased 

 to several hundred feet per second, the resistance varied 

 as a power of the velocity greater than 2-^. But as 

 the velocity still further increased, the error of the ordi 

 nary law, though -always very great, became slightly less. 



Beaufoy. If the velocity exceed two miles per hour, 

 or 6*2 feet per second, the power of the velocity is greater 

 than 2 ; but this power decreases, and is less than 2, if 

 the velocity be greater than eight miles per hour. 



Speaking of this law of resistance, Robins says &quot; This 

 rule, though pretty near the truth when the velocities are 

 confined within certain limits, is excessively erroneous 

 when applied to military projectiles, where such resist 

 ances often occur as could scarcely be effected on the com 

 monly received principles, even by a treble augmentation 

 of its density.&quot; The actual resistances were found to 

 exceed prodigiously those calculated by the theory, when 

 the velocity exceeded 1200 feet a second, which is the 

 velocity with which air rushes into a vacuum. 



Scott Russell found that in ships, as the velocity in 

 creased, the resistance increased in a much higher ratio 

 than the square of the velocity, and reached a maximum, 

 after which it actually decreased as the velocity increased. 



Beaufoy found that bodies are more resisted just under 

 the surface than at the depth of six feet. 



Borda found a similar result. 



2. The resistance to a plane does not vary as the surface, 

 but increases in a quicker ratio. 



Borda found that when the surfaces were as 9, 16, 36, 

 81 inches, the resistances were as 9, 17-535, 42-750, 

 104-737. 



Nevertheless, the results of many experiments show that 



A A 2 



