254- Mr. Tredgold on a neiv Theory of the Resistance 



the friction of water were made by CoLBeaufoy *, from whence 

 it appears that the friction of water is very nearly as the square 

 of the velocity ; and about -0032 pounds for one foot of surface 

 moving at the rate of one foot per second. It is somewhat 

 greater than this in slow motions ; most likely from the effect 

 of cohesion being sensible in small velocities. The experiments 

 made by the Society for the Improvement of Naval Archi- 

 tecture do not appear to be so nearly in the ratio of the square 

 of the velocity, but at the velocity of four nautical miles per 

 hour the resistance is exactly -0032 pounds (see Dr. Young's 

 Nat. Phil. ii. p. 229). The head of water equivalent to this 



resistance is ~?- = 0-0000512 =/ 



20. If the resistance from the friction of the fluid itself be 

 neglected, the general equation for water will be 



c 2sin3a + sin * c 0-0000512 pi ) TT 



*\ 12*76 + s— * = H >* 



or, — ~g (2 sin 3 a + sin* c + 0*0066 J&XmlJL 



When sin a = sin c = sin 90°, the resistance from friction 



v I 

 is to the resistance from pressure as 3 : 0-0066 - — . 



21. The value of the coefficient A, for water is of very little 

 use, neither are there good experiments for determining it ; in 

 the resistance of air, however, it becomes of importance. The 

 equation for air, when the length of the body may be neg- 

 lected, is 



;l( sin 3 a + sin* c + M±UL) | H. 



And if n be the resistance of the body compared with a 

 plane of equal section when the friction is neglected, the re- 

 sistance of the plane being unity, the best experiments give 

 4>gfA = 0-000000332 n. The results of experiments, how- 

 ever, differ considerably ; and it is difficult to fix on a datum 

 which it never was their object to determine. 



22. Comparison with Experiments. — The experiments of 

 Bossut f were made with a parallelepiped four feet in length, 

 two feet in breadth, and two feet draught of water. It was 

 first tried alone, and afterwards with wedge-shaped prows of 

 different degrees of acuteness (see fig.2.); the time of describing 

 ninety-six feet was observed, when the velocity had become 

 uniform, except in the experiments with the most acute angles 



* Dr. Thomson's Annals of Philosophy, vol. vi. p. 281, 1815. 

 f Traite J? Hydrodynamique, torn. ii. p. 394 -411. 



in 



