Moving Force. 147 
and if we have adopted a proper measure 
in estimating the effect, we shall have 
— It is obvious that this equation will 
constantly be found by Mr. Smeaton’s method, 
and we must therefore conclude that he has 
adopted the proper measure of the force. 
But Mr. Smeaton’s reasoning is farther ob- 
jected to as follows: “ His second general 
maxim is, that the expence of water being the 
same, the effect will be nearly as the height of 
the effective head, or (as it is expressed in - 
maxim third) as the square of the velocity of 
the water. This conclusion seems, at first 
sight, quite in favour of the theory of mechani- 
cal force, as laid down by our author, and the 
other supporters of the vis viva; and yet we 
shall presently find, that it 1s perfectly con- 
formable to the other theory, ‘and to those 
reasonings of Desaguliers and Maclaurin, 
which Mr. Smeaton has censured, as leading 
to conclusions altogether wide of the truth.” 
«“ Let c be the velocity of the stream, v that 
of the wheel, A the area of the part of the 
float-board immersed in the water, g the velo- 
city which a heavy body acquires in one 
second when falling freely. Then c—v will 
be the relative velocity of the stream and the 
wheel,or the velocity withwhich the water strikes 
the wheel; andif we take /, a fourth proportional 
T2 
