70S 
MECHANIC S. 
fiiould be equal to the depth of the floatboards. He ob- 
ferves alfo, that a brealt-vvheel (hould be ufed when the fall 
of water is above four feet in height, and. below ten. The 
following are the dimenlionsof an excellent breaft water¬ 
wheel, differing very little from that which is reprefented 
in the figure. The water, however, inltead of falling 
through the height C n, which is 16 inches, is delivered 
on the floatboard op, through an adjutage fix inches and 
a half high. The height n D is four feet two inches ; and 
therefore the whole height C D mult be five feet and a half. 
The radius of the wheel AB is fix feet and a half, the 
breadth of each floatboard fix inches and a half, and their 
depth 28 inches. The point P of the wheel moves with 
the velocity of 7*588 feet in a fecond. The quantity of 
water difcharged in a fecond is 3*266 cubic feet, and the 
force of impulfion upon the floatboards 356 poundsavoir- 
dupois. On fome occasions, buckets have been ufed in 
hreaft-wheels inltead of floatboards ; but this is evidently 
a difadvantage, as the height through which the waterafts 
is diminifhed by the number of inches through which the 
water mult fall in order to acquire the velocity of the wheel, 
and alfo by the verfed fine of the arc above the lowelt point 
of the wheel which may be confidered as not loaded with 
water. 
3. An underjhot-w'aed is a wheel with a number of float- 
boards difpofed on its circumference, which receive the 
impulfe of the water conveyed to the lower point of the 
wheel by an inclined canal. It is reprefented at fig. 99. 
where W W is the water-wheel, and ABDFHKMV 
the canal or mill-courfe, which conveys the water to K, 
where it ftrikes the plane floatboards n 0, See. and makes 
the wheel revolve about its axis. 
In order to conltruft the mill-courfe to the greateft ad¬ 
vantage, we mult give but a very fmall declivity to the 
canal which conducts the water from the ri'ver. It will 
be fufficient to make AB Hope about one inch in 200 
yards, making the declivity, however, about half an inch 
for the firlt 48 yards, in order that the water may have 
fufficient velocity to prevent it from falling back into the 
river. The inclination of the fall, reprefented by the 
angle GCR, (hould be 25 0 50', or CR the radius, (hould 
be to G R the tangent, of this angle, as too to 28, or as 
25 to 12; and, fince the furface of the wafer Sb is bent 
from ab into ac before it is precipitated down the fall, 
it will be neceflary to incurvate the upper part BCD of 
the courfe into B D, that the water at the bottom may 
jnove parallel to the water at the furface of the flream. 
For this purpofe take the points B, D, about twelve inches 
diifant from C, and raife the perpendiculars BE, DE. 
The point of ihterfeftion E will be the centre from which 
the arc BD is to be deferibed; the radius being about 
io*i inches. Now, in order that the w*ater may aft more 
advantageoufly upon the floatboards of the wheel W W, 
it mull affume a horizontal direftion, with the fame velo¬ 
city which it would have acquired when it came to the 
point G. But, if the water were allowed to fall from C 
to G, it would dafh upon the horizontal part HG, and 
thus lofe a great part of its velocity. It will be neceflary, 
therefore, to make it move along FH, an arc of a circle 
to which D F and K H are tangents in the points F and H. 
For this purpofe make G F and G H each equal to three 
feet; and raife the perpendiculars H I, F I, which will in- 
terfeft one another in the point I, dillant about four feet 
nine inches from the points F and H, and the centre of 
the arch FH will be determined. The distance HK, 
through which the water runs before it acts upon the 
wheel, (hould not be lefs than two or three feet, in order 
that the different filaments of the fluid may have attained 
a horizontal direftion. If H K were too large, the ltreatn 
would fuffer a diminution ot velocity by its friction on 
the bottom of the courfe. That no water may efcape be¬ 
tween the bottom of the courfe KH and the extremities 
of the floatboards, ICL (hould be about three inches, and 
the extremity 0 of the floatboard no ought to reach below 
the line HO, fufficient room being left between 0 and 
M for the play of the wheel; or KLM may be formed 
into the arc of a circle KM concentric with the wheel. 
The line L M V, which has been called the courfe of impul- 
fion, (hould be prolonged fo as to fupport the water as 
long as it can aft upon the floatboards, and (hould be 
about nine inches dillant from O P, a horizontal line 
pafling through O the lowed point of the fall; for, if O L 
were much lefs than nine inches, the water, having fpent 
the greateif part of its force in impelling the floatboard, 
would accumulate below the wheel, and retard its motion. 
For the fame reafon, another courfe, which has been called 
the courfe of difeharge, fhould be connefted with L M V by 
the curve V N to preferve the remaining velocity of the 
water, which would otherwife be difcharged by fallinp- 
perpendicularly from V to N. The courfe of difeharge, 
• which is reprefented by the lineVZ, (loping from The 
point O, (hould be about 16 yards long, having an inch 
of declivity for every two yards. The canal which re- 
condufts the water from the courfe of difeharge to the 
river (hould (lope about four inches in the firft 200 yards, 
three inches in the fecond 200 yards, decreafing gradually 
till it terminates in the river. But, if the river to which 
the water is conveyed (hould, when (welled by the rains, 
force the water back upon the wheel, the canal mull have 
a greater declivity to prevent this from taking place. 
Hence it is evident that very accurate levelling is requi- 
fite to the proper formation of the mill-courfe. 
As it is of great importance that none of the water 
(hould efcape either below the floatboards, or at their 
fides, without contributing to turn the wheel, the courfe 
of impulfion KV (hould be wider than the courfe at K, 
as reprefented at flg. 100. where CD, the courfe of impul- 
fiqn, correfponds with LV in fig. 99. AB correfponds 
with HK, and B C with K L. The breadth of the float- 
boards therefore (hould be wider than mn, and their ex¬ 
tremities (hould reach a little below B, like no in fig. 99. 
When thefe precautions are properly taken, no water can 
efcape without exerting its force upon the floatboards. 
It has been difputed among phiiofophers, whether the 
wheel (hould be furniflied with a fmall or a great number 
of floatboards. M. Pitot lias (liown, that, when the float- 
boards have different degrees of obliquity, the force of 
impulfion upon the different furfaces will be reciprocally 
as their breadths: thus, in fig. 101. the force of impul- 
fion upon he will be to the force upon D O, as D O to 
he. Hence he concludes, that the dittance between the 
floatboards (hould be equal to one-half of the immerfed 
arch ; or that, when one floatboard is at the bottom of the 
wheel, and perpendicular to the current, as D E, the pre¬ 
ceding floatboard B C (hould be juft leaving the dream, 
and the fucceeding one FG juff immerging into it. For, 
when the three floatboards, FG,DE,BC, have the fame 
pofition as in the figure, the whole force of the current 
NM will aft upon DE when it is in the mod advan¬ 
tageous pofition for receiving it; whereas, if another float- 
board de were inferted between F G and DE, the part ig 
would cover DO, and, by thus fubftituting an oblique 
for a perpendicular furface, the effeft would be dimi- 
niftied in the proportion of DO to ig. Hence it is evi¬ 
dent that, upon this principle, the depth of the floatboard 
DE (hould be always equal to the verfed fine of the 
arc EG. 
Notvvithftanding the plaufibility of this reafoning, it 
will not be difficult to (how that it is deltitute of foun¬ 
dation. It is evident from the figure, that, when one cf 
the floatboards D E is perpendicular to the dream, it re¬ 
ceives the whole impulfe of the water in the molt advan¬ 
tageous manner; but, when it arrives at the pofition de, 
and the fucceeding one F G at the pofition fg, fo that 
the angle e A g may be bifefted by the perpendicular A E, 
the fituation of thefe floatboards w ill be the molt diiad- 
vantageous, for a great part of the water will efcape be¬ 
tween the extremities g and e of the floatboards w ithout 
Itriking them, and the part ig of the floatboard, which is 
really impelled, is lels than DE, and oblique to the cur¬ 
rent. 
