OF A BALL BY A JET OF WATER. 283 



of P ; secondly,, it will assist in supporting the ball ; and, 

 thirdly, since it opposes the rotation, it will balance the 

 tangential force E,, caused^by the friction at p \ and, pro- 

 vided it have the proper magnitude, together with the 

 forces P, R, and W, it is all that is requisite to explain 

 the equilibrium. 



It remains to explain the fact, that the ball will fall 

 back again into the jet after it has been driven out of it. 

 This may be done ; for the force P which forces the ball 

 out, ceases as soon as contact ceases ; but not so with Q, 

 which drives the ball back again towards the jet ; for there 

 will still be some water to be thrown off, so that perhaps 

 for half a revolution Q: will continue undiminished, and so 

 bring the ball back again into the jet. 



Position of Equilibrium. 



With respect to the position of the ball when in equi- 

 librium, nothing very definite can be established, as there 

 are no known laws of adhesion ; but it may be shown by 

 general reasoning, that there are limits between which 

 the point jo must be, so that there may be equilibrium. 



Let the point /? be at a fixed height, and let P equal the 

 full force of the jet at this height when acting on the 

 bottom of the ball or on a perpendicular plane. Then, if a 

 be the angle which the normal at p makes with the vertical, 



P=P'cosa, 



and the horizontal component 



F . P' 



V sm a = 



therefore 



sina =— 2 sm a cos a = — sm 2a; 



2 2 



P' 



P sina = — and is a maximum when a =45°, 



and 



Psina = o when a = o or a = 9o''; 



