MOVING FORCE. 
in equal times, and where the individual forces are made out to Ca=cs of ditE- 
be as the revolving masses into the s(juares of their velocities. joctrilies'tV 
Jf he had applied the same principles to the solution of the moving force, 
problem quoted above from his treatise on fluxions, he would, 
no doubt, have brouglu 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 properties of the lever, and then their 
relations to eacli other, and to the squares of the velocities 
generated, me made out. Rut it is the pressure 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 lever, or where the lever acts on the body 
which is moved. The force of a body ’in motion cannot be 
! considered greater or less, according to the manner in which 
it has been produced, and when we see a body in motion, if its 
I mass and velocity be given, we never ask by what kind of lever 
it has been produced in order that we may judge of its force. 
The case of a balance beam was noticed by Sir I>aac New- 
ton, near the end of his scholium to the laws of motion j but 
it is not clear that he considered that case in the same light in 
which it has since been taken by De.saguliers and other authors, 
to prove that the moving forces of the weights are not as the 
squares of their velocities. It may, I apprehend, with greater 
rconsistenry, be inferred, that he noticed that case, merely to 
• show, that the pressures of the weights balance each other 
when they are in motion the same as when they are at rest. It 
will be seen, when we come to examine the I4th case, that Sir 
Isaac Newton did not consider quantities of motion to be in 
all cases in the ratio of the forces by which they are produced. 
The 5th case belon.;s to that class of the efllx’ts of force, 
■which are considered by Mr. Atwood to be disproportionate 
'to the forces by which they are produced, which ever way tliey 
rmay be estimated, whether by the mass into its velocity, or by 
iihemass into the square of its velocity. However strange 
1. his opinion may appear, it is perfectly correct as far as it is 
O 2 applied 
