7)U>.1I- OF THE MOTION OF FLUIDS. 179 



the plane. Hence as the division of fluids* may be effected without the 

 application of force, nothing will be altered if we suppose the plane to 

 become rigid and to intercept the communication of the fluid on one side 

 with that on the other. The motion on each side will then be reflected, 

 and the angle of incidence will be equal to the angle of reflection. - 



8. I propose now to adduce an application of the proposition 

 above demonstrated (Art. 3.) respecting the general law of fluid motion, 

 which may serve to shew its utility. Suppose water in a cylindrical 

 vessel (for instance, a glass tumbler,) to be caused to revolve with con- 

 siderable rapidity about the axis of the cylinder. There is no practical 

 difficulty in making the fluid revolve so that every particle shall de- 

 scribe approximately a horizontal circle about the axis. Then, the fluid 

 being left to itself after the disturbance, each particle may be considered 

 to move as it does, by reason of a centripetal force tending to the 

 axis in a horizontal plane. This force must be owing to the action 

 of the cylindrical surface on the fluid particles in contact with it, 

 deflecting them continually from a rectilinear course. If V be the 

 velocity of the particles in contact with the surface, and a the radius 



V- 

 of the cylinder, the force tending to the axis is — , the effect of 



friction being neglected. The deflections which this force is continually 



producing in the directions of radii, are transmitted through the fluid, 



and as they tend to a centre, will vary, according to the proposition 



above proved, inversely as the distance from the centre.f Hence the 



V^ a V^ 



centripetal force at the distance r is — x -, or — . This shews 

 ^ a r r 



that at any distance r the velocity is still V. Experience seems to 



confirm this result. For if light substances be strewed on the surface 



of the water, those nearer the centre always perform their revolutions 



* The introduction of this consideration here is merely reverting to a principle -which 

 Professor Airy (very properly, I think,) has proposed to make the basis of the mathematical 

 treatment of fluids. Without referring to a principle of this nature, I do not see that 

 problems of reflection can be satisfactorily solved. 



+ The total motion is compounded of these deflections and rectilinear motions along 

 tangents to the circles, which by Art. 6. may be considered separately. ''' ' •"'-'■'■ 



