20

MECHANICS.

[Chap. 1.

be lost by friction, &c.) which we must suppose taketheir direction at an angle of 45 degrees; because a bodyprojected at an angle of 45 degrees, will describethe greatest possible horizontal range. It is known also,that a body falling 4 feet, and reflected with its acquiredvelocity 16,2 feet, at 45 degrees, will reach 16 feet ho-rizontal range, or 4 times the distance of the fall.Therefore, by this rule, \ of 10 feet, equal to 2,5 feet,is the fall that will produce the velocity necessa-ry to this effect, viz. velocity 12,64 feet per second,about I of the striking velocity.

This side force cannot be applied to produce any far-ther forward force, after it has struck the first obstacle,because its action and reaction then balance each other:which I demonstrated by fig. 27.

Let A be an obstacle, against which the column ofwater G A, of quantity 16 with velocity per second 16,strikes; as it strikes A, suppose it to change its direction,at right angles with £ velocity and to strike B B, thento change again and strike forward against C C, and back-wards against D D; then again in the side directionE E; and .again in the forward and backward direc-tions, all of which forces counteract, and balance, eachother.

Therefore, if we suppose the obstacle A to be thefloat of an undershot water wheel, the water can be ofno farther service in propelling it, after tbe first im-pulse, but rather a disadvantage; because the elasticityof the float will cause it to rebound in a certain degree,and, instead of keeping fully up with the float it struck,to react back against the next float. It will be better,therefore, to let it escape freely as soon as it has fullymade the stroke; not sooner, however, as it will re-quire a certain space to act in, which will be in directproportion to the distance between the floats.

From these considerations, we may conclude, that thegreatest effect to be obtained from striking fluids, willnot amount to more than half the power which gives themmotion, and much less, if they be not applied to tbe bestadvantage: and also, that the effect produced by thecollision of non-elastic bodies, will be in proportion totheir non-elasticity.