MILL. 
pntation of the power to produce such an 
effect, allowing the head of water to be 
105.8 inches, gave 264.7 pounds of water 
descending in one minute through the space 
of fifteen inches : therefore 264.7, multipied 
by 15, was equal to 3,970. But as that 
power is found equal to raising no more than 
9.375 pounds to tte height of 135 inches, it 
was manifest that a major part of the power 
was lost; for the multiplication of these 
two sums amounted to no more than 1,266 ; 
of course the friction was equal to |ths of 
the power. 
Mr. Smeaton considers the above to be 
the maximum single eflFect of water upon 
an undershot wheel, where the fall is fifteen 
inches. The remainder of power, it is 
plain, must be equal to that of the velocity 
of the wheel itself, multiplied into the weight 
of the water, which in this case brings the 
tnie proportion between the power and the 
effect to be as 3,849 to 1,266 ; or as 11 to 4. 
Where a wheel revolved 86 times in a 
minute, the velocity of the water must have 
been equal to 86 circumferences of the wheel ; 
which, according to tlie dimensions of the 
apparatus used by Mr. Smeaton, was as 86 
to 30, or as 20 to 7. The greatest load 
with which the wheel would move was 9 lb. 
6oz . ; by 12 lb. it was entirely stopt. From 
this we are to conclude, as Mr. Smeaton 
did, that the impulse of the water is more 
than double what our theory states it to be. 
This he accounts for by the wheel being 
placed in a narrow slit ; so that the water 
could not escape but by passing with the 
wheel’s motion; thus giving a multiplied 
force. Further, it is to be remarked, that 
when a float-board comes in contact with 
the water, it receives a certain check,which 
causes the back, or upper part of the float- 
board to become loaded with a kind of 
wane, which accumulates in consequence of 
the momentary impediment, and conse- 
quently adds to the impetus. This added 
force must ever be in proportion to tlie 
depth to which the float-board sinks into 
the stream ; not exceeding its whole depth 
beyond the rim, or body, of the wheel to 
which it is attached. 
The following conclusions result from the 
velocities of wheels, as acted upon by dif- 
ferent heights of water. 1 . The head, or 
altitude, being the same, the effect will be 
proportioned to the quantity of water ex- 
pended; or in other words according to the 
weight and velocity of tlie impinging fluid. 
2. The expence or quantity of water being 
the same, the effect will be nearly in pro- 
portion to the height of the head. 3. The 
quantity of water expended being the same, 
the effect is nearly as the square of the velo- 
city. 4. The aperture whence, the fluid 
issues being the same, the effect will be 
nearly as the cube of the velocity. Hence, 
if water passes out of an aperture in tlie 
same section, but with different velocities, 
the expence will be proportioned to the 
velocity ; therefore, if the expence be not 
proportioned to the velocity, the section of 
the water cannot be the same. 6. The vir- 
tual head, or that from which we calculate 
the power, bears no proportion to the head- 
water ; but when the aperture is larger, or 
the velocity of the water less, they approach 
nearer to a coincidence: consequently in 
the large openings of mills and sluices, 
where great quantities of water are dis- 
charged from moderate areas, the head of 
water, and the virtual head (determined 
from the velocity) will nearly agree, as ex- 
perience proves. 6. The most general pro- 
portion between the power and the effect 
is as 10 to 3 ; the extremes are 10 to 3, 2, 
down to 10, 2.8. 7. The proportion of 
velocity between the water and the wheel 
is usually as 5 to 2. 8. Although we have 
no certain maximum of the power of a 
wheel ; that is, what it will carry, and no 
more ; we may generally consider tlie limits 
to be, that wheels which work freely with 
15, will stop when 20 are opposed to their 
motion : consequently when 3 is the effect, 
4 will stop the work. But in general we 
find it extremely difficult to ascertain this 
point; though in works that are perfectly 
well executed, and where the powers, with 
the resistances, are judiciously computed, 
the quantity of the latter necessary to pro- 
duce equilibrium, which here amounts to 
cessation, will be found to correspond with 
that scale. 
Speaking of float-boards, it may be pro- 
per to state, tliat they should be rather nu- 
merous than few. Mr. Smeaton found, tliat 
in undershot mills, when he reduced the num- 
ber of floats from tw'enty-four to twelve, the 
effect was reduced one-half, because tjie wa- 
ter escaped between the floats without touch- 
ing them; but when he added a circular 
sweep of such length, that before one float - 
board quitted it another had entered it, he 
found the former effect nearly restored. 
This mode more particularly applies to 
breast-wheels, or such as receive the water 
immediately below the level of the axis. 
In such the circular trough is indispensable ; 
because the water would not communicate 
