OF A BALL BY A JET OF WATER. 281 



is easily answered ; for these forces are necessarily in the 

 same plane ; but they do not all pass through the same 

 pointy and, therefore they are not in equilibrium. To 

 balance these forces^ then^ there must be some other force 

 acting on the ball in the same plane with them^ and which 

 does not pass through p, or the centre of the ball. Now, 

 besides the water which leaves the ball at p, there is the 

 water which adheres to the ball until thrown off by centri- 

 fugal force ; and to this we must look for the required 

 force. The effect of a drop adhering to the ball will be 

 very complex, being due to its weight, centrifugal force, 

 and friction. However, if we neglect the weight as being 

 very small, and therefore only able to increase slightly the 

 weight of the ball, and to shift the point at which it acts a 

 little way from the centre, the forces which the drop will 

 produce may be stated accui'ately. For whenever a drop 

 whose weight is w (lbs.) comes on to the ball with a 

 velocity v (feet per second), and leaves with a velocity u, 

 its whole effect, minus that of its weight while it is on the 



ball, is equivalent to a force — (lbs.) acting for one second 



in the direction in which the drop was moving and at the 



xvu 

 point at which it comes on to the ball, and a force — at 



9 

 the point at which it leaves and in a direction opposite to 

 that in which it flies off. The first of these forces will form 

 part of P and R ; and therefore, besides the forces at the 

 point P, the effect of any adhering di'op will be equivalent 

 to a reaction such as would be produced if the force neces- 

 sary to throw the drop from the ball were concentrated at 

 the point at which it leaves. If several drops be leaving 

 the ball at the same time, the several reactions will have a 

 single resultant, which will not pass through p, or the 

 centre, unless they should be distributed equally all round 

 the ball, in which case the reactions would simply produce 



