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the proper magnitude, together with the forces P, It and W, 
it is all that is requisite to explain the equilibrium. 
Position of Equilibrium. 
With regard to the position of the ball when in equili- 
brium I cannot establish anything definite, as there are 
no known laws of adhesion, but I can show by general 
reasoning that there are limits between which the point in 
which the ball is struck must lie, so that there may be 
equilibrium. 
Let the point p 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 
p/ p/ 
Psina — — 2sina COSa = ^ sin2a ; 
2 2 * 
therefore 
and 
Psina = - and is a maximum when a — 45° 
2 
Psina = 0 when a - 0 or a - 90° 
So that the tendency of the jet to force the ball to one side 
P' 
increases from nothing to as p moves from the bottom to 
a point at which the normal makes an angle of 45° with the 
vertical and then decreases to nothing as p moves to the 
middle of the ball. 
The force Q may be fairly assumed to increase as the 
speed of rotation increases, and this will be as the point of 
contact moves from the bottom to the middle of the ball. 
In the same way the force F, which will necessarily increase 
as Q increases, will increase as p moves from the bottom to 
the middle of the ball, and its horizontal component will 
follow nearly the same law as that of P. 
Considering then the horizontal forces only, there must be 
some position for p in which the horizontal component of 
