[ 375 3 
*-— ) and will exprefs the effedt on 
eta, ' * 
the whole 
plane CC BB, equal tt d, the produdt of the 
weight 7r by the length d of the lever on which it 
adts in oppofing the motion of the wheel. 
§ III. If the wheel be plunged as deep as its axle, 
that is, f — o, the equation is changed into this 
»|3 a. ctf 2 
“ U :W — -VZ +• 
4 
~ d7r, where it appears 
1°. That the quantities d, tt, v and js remaining the 
fame, we have (3 inverfely proportional to the fquare 
of a, whence it follows, that if the length (2 is to 
be diminished without altering the effedt of the float- 
board, the height a muft be encreafed proportionally 
to the fquare root of jG ; for example, if (2 is to be 
made four times lefs, it will be fufficient to double 
the height u. 2° That likewife the velocity of the 
float-board remaining the fame, the weight tt will 
be in the compound ratio of the length ( 3 , and of 
the fquare of the height uot. 3 0 Without meddling 
with the dimenlions of the float-board, the more 
the quantity 2; is increafed, the more muff the weight 
7T be diminished. If z be made = 0, we have 
TT— •£— ±vv, and ifs — v we have 77-= vv. 
that is fix times greater than in the fil'd cafe ; which 
is very conformable to the nature of things, for 
when the wheel is-in motion, the Stream then not 
adting upon it but with the excefs of its velocity 
above that of the wheel, it follows, that the greater 
fuch velocity is, the more will the effedt of the dream 
be diminished. 
