34

Hydraulics.

I shall only observe farther in regardto spouting Water, that the Jet will gofarther through the bare Hole in the Ves-sel

Triangle ACK is similar to the Triangle ACBjtherefore also AC:CK::AB:BC. Consequently,AB : BC :: B C : B K ; therefore AB X BK = BC*.

And so B C = \/ ABXBK =v/ABX \Z1Tk'.

4. Now because the Space the Fluid describes ac-cording to the Horizon, and the Line B C, are bothproportional to the same Thing, (/'. e. to \/ A B X\/ B K) therefore they must also be proportional to eachother; and so the horizontal Distance of any Jet, as B,will be in Proportion to the Line B C ; and the Jetfrom D will be proportional to the Line D F, and soon.

5. If now D be taken into the Centre of the CircleA F K, the Velocity at D would (as being uniform)carry it through twice the Space AD = zDF = D Pin the horizontal Direction or Line D P, as is evidentiromAnnot. XXVI. 7. Because the Particles of a Fluidobserve the same Laws of Motion with larger Bodies.Consequently, though the Fluid goes not in the Direc-tion or Line D P, it will go to the same Distance fromthe Perpendicular D K on the Horizon ; because D K— AD, or the perpendicular Spaces, and consequentlythe Times of the Fall, are equal. Whence, becausethe horizontal Distaftces described by Jets from D andB are as D F and B C, and the horizontal Distance ofthe Jet from D is, a D F = D P = K M, therefore thehorizontal Distance of the Jet from B will be equal to2BC=KN.

6. From what has been hitherto said, ’tis easy toobserve that the Motion of a spouting Fluid is every waysimilar to that of a projected Solid. The Path of the Fluidis a Parabola, because it is impelled by two Forces, onehorizontal, the other of Gravity in the Perpendicular,in the. fame Manner as was Ihewn of the projected So-lid. The Impetus of the Jet B, D, H, E, is theHeight of the Reservoir AB, AD, AH, AE, thegreatest horizontal Random K M is that from the Jet

D, directed