ON THE FRICTION AND 



the very first mathematicians, The fault has been non artificis 

 sed artis. 



[Vince. Phil. Trans. 1795. 



SECTION III. 



On the Friction and Velocity of Currents* 



THE effects of friction is particularly exemplified by the motions 

 of rivers, in which almost the whole force of gravity is employed in 

 overcoming it. When the inclinations and dimensions of a river 

 continue uniform, the velocity is also every where equal ; for other, 

 wise the depth would become unequal : here, therefore, the force 

 of gravitation must be an exact counterpoise to the resistance which 

 is to be overcome, in order that the water may flow with its actual 

 velocity 3 this velocity having been originally derived from the effect 

 of a greater inclination near the origin of the river. When the 

 river is thus proceeding, with an equable motion, it is said to be in 

 train ; and it is obvious that no increase of ils length will produce 

 any alteration in its velocity. There is, therefore, a very material 

 difference between the course of a river, and the descent of a body, 

 with an accelerated motion, along an inclined surface. For when a 

 solid body is placed on an inclined plane, the force of friction is 

 either great enough to overpower its relative weight, and to retain 

 it at rest, or else the friction is constantly less than the gravitation, 

 and the motion is always accelerated. But the resistance to the 

 motions of fluids arises principally from different causes ; not from 

 the tenacity of the fluids, which, where it exists, is a force nearly 

 uniform, like that of friction, but principally from the irregular mo- 

 tions and mutual collisions of their particles; and in this case, ac- 

 cording to the laws of mechanics, it must vary nearly in proportion 

 to the square of the velocity. For when a body is moving in a line 

 of a certain curvature, the centrifugal force is always as the square 

 of the velocity -, and the particles of water in contact with the sides 

 and bottom of a river or pipe, must be deflected, in consequence of 

 the minute irregularities of the surfaces on which they slide, into 

 nearly the same curvilinear paths, whatever their velocity may be, so 

 that the resistance, which is in great measure occasioned by this 

 centrifugal force, must aho vary as the square of the velocity. 

 Thus also the curvature assumed by the outline of a stream of \va. 



