[ 374 ] 
wheel at the point B, fuch that it fliall run through 
z, feet in a fecond ; n pounds the weight of a cubic 
foot of water ; and I will fuppofe the impulfe of the 
ffream on a plane perpendicular to it is (as Dr. Da- 
niel Bernoulli has hated in his Hydrodynamica ) equal 
to the weight of a prifm of water, whofe bafe is 
the plane, and its altitude the generating height of 
the velocity with which the plane is impelled. This 
being fuppofed ; let AP— x, P/>, its differential, 
■=dx, which will give the velocity of the float-board 
at the point/*— -z, and the relative velocity of the 
ffream with which the plane is impelled at the fame 
point — v — - z whofe generating height is — — . 
feet, whence we have the weight of the parallelo- 
piped of that height, and of the bafe PP pp equal 
to - (— v-z) z pounds, which weight multiplied by 
the length A P (x) of the lever which tends to turn 
the plane, will give — - z / for the total effedt 
of the flream on the little rcdtangle PP />/*, whofe 
integral is (vvxdx — — — ^ xxdx x % dx) 
n_& ( 
60 \ 
60 
/ 
V'UXX 
2 .x* .x 
- vz — y-' zz ~ 
•i vvff-^-vz. 
) (p utt ' n g A C —f for the iliftance be- 
tween the axle and the furface of the water when 
the floats board has only its part CB plunged in 
the water) which (putting x = a) will become 
- ( ^nv---oz-\-^zz.a»—ivvfJ + - — 
» 
z 
