17S 
MOVING FORCE. 
Cases of diffi- 
eolty in tlic 
iloct vines of 
inovinst force 
AUhough t hese cases comprehend much of what relates, in 
this question, to rotatory motion, the three follow ing cases apply 
more particularly to that branch of the subject. 
In rotatory motion it is universally admitted, that four times 
the force is necessary to generate the same angular velocity, or 
twice the absolute velocity, in the same body placed at twice the 
distance from the centre of motion ; and it is but reasonable to 
enquirewhy v.'c must have one measure for rotatory, and another 
for rectilinear force ? That inconsistency, (stated incase 3d) is 
overlooked in the usual demonstrations respecting rotatory 
motion ; it is, nevertheless one of considerable importance, 
and it requires explanation. I have alretidy endeavoured to 
show (p. 139) that the explauation which refers us to the pro- 
perties of the lever is by n > means sufficient- If, however, 
the product of tlie mass into the square of its velocity be taken 
as the proper measure of the force of a body in motion, the 
explanation is obvious. 
The case of the balance beams (case 4th) has been adduced 
by many authors in proof of the moving forces being as the 
masses multiplied into their velocities. There is no doubt, that 
after they have been put in motion, the weights will balance 
each other the same as when they were at rest j but the ques- 
tion is, whether or not the motion of n can be generated by 
a moving force no greater than that which generates the motion 
0'' m ? If these two quantities of motion can be generated 
by equal forces, the same forces should generate equal quantities 
of motion in 0 andp ; but equal pressures applied to A and C 
will not produce, in equal times, equal quantities of motion in 
the respective weights. Mr. Emerson, by neglecting this cir- 
cumstance, appears 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 included in the 5C)th prop, of 
Emerson’s Principles of mechanics, where it is demonstmted, 
that unequal quantities of motion are produced by equal forces 
in 
1 
5. 
I ■ 
t' 
