172 On the Measure of 
to have been led into the error pointed out by 
Mr. Atwood, which I have quoted at page 128. 
But if the weights were attached to, instead 
of being suspended from the ends of the 
beams, the case would then be one of pure 
rotatory motion; and would have been in- 
cluded in the 56th prop. of Emerson’s. Princi- 
ples of Mechanics, where it is demonstrated, 
that unequal quantities of motion are produced 
by equal forces in equal times, and where 
the individual forces are made out to be as 
the revolving masses into the squares of their 
velocities. If he had applied the same prin- 
ciples to the solution of the problem quoted 
above from his Treatise on Fluxions, he 
would, no ‘doubt, have brought out the true, 
instead of an erroneous result. 
In his 56th prop. the forces are understood, 
in the usual way, to be modified by the proper- 
ties of the lever, and then their relations to 
each other, and to the squares of the velocities 
generated, are made out. But it is the pres- 
sure only that is modified according to its 
distance from the centre of motion. The 
product of the pressure into the space through 
which it acts, remains the same, whether it be 
taken at the point where the force acts on the 
Jever, or where the lever acts on the body 
which is moved. ‘The force of a body in. 
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