of the Motion and Resistance of Fluids. 41 
the whole weight ; and even this might be diminished one 
hundred times more by using friction wheels ; but this is a 
degree of accuracy which, I think, can never be required. We 
might also diminish the friction at the nut, if required, by let- 
ting the axis on those two sides towards which the lines act 
rest between two friction wheels. If the arms should be very 
long, it may be necessary to fix an upright piece upon K, and 
connect the extremity of the sails to the top thereof by a string 
or wire. When this machine is applied to find the resistance of. 
water, the axis m n must be produced up above K, and the 
string applied to that part ; the machine must be immersed 
in a large reservoir of water, leaving the part of the axis to 
which the string is applied above the surface. Before we pro- 
ceed to the application, we must investigate a point called the 
centre of resistance. 
Def If a plane body revolve in a resisting medium about ail 
axis by means of a weight acting therefrom, that point into 
which if the whole plane were collected it would suffer the 
same resistance, I call the centre of resista?ice. 
Let a be the area of the plane, and a the fluxion of the area 
at any variable distance x from the centre of the axis, and d 
the distance of the centre of resistance from that of the axis. 
Now the effect of the resistance of a to oppose the weight is, 
from the property of the lever, as the resistance multiplied 
into its distance from the axis, or as x a ; but the resistance is 
supposed to vary as the square of the velocity (which is 
found by experiment to be true under certain limitations), or 
as the square ( x 2 ) of its distance from the axis ; hence the 
effect of the resistance of a to oppose the weight is as x 3 a ; 
therefore the whole effect is as the fluent of x 3 a. For the 
G 
MDCCXCV. 
