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The Author then proceeds to prove the Truth of 
the common Opinion of the Forces in equal Bodies 
being proportional to their Velocities. This he does 
by Three Mediums, the Firft taken from the Adion 
of a fingle Spring upon the fame Body : The Second 
from fome Experiments of Mr. Mariotte ; the Third 
from the joint Adion of feveral Springs upon Two 
unequal Bodies. 
I. A fingle Spring, fixed to a moveable horizontal 
Table, is made to communicate to the fame Body, 
Degrees of Force unqueftionably equal, while the 
Degrees of Velocity communicated at the fame time 
are alfo undoubtedly equal ; therefore the Forces are 
proportional to the Velocities. 
II. In Mr. Mariotte s Experiments, the Impreflions 
made upon equal Surfaces in the fame Point of Time, 
are found to be in the Duplicate Ratio of the Velo- 
cities but the Maffes or Numbers of impinging Par- 
ticles are in the fimple Ratio of the Velocities; con- 
fequently, the Maffes and Velocities conjundly being 
in the Duplicate Ratio-, i. e . as the Impreflions, muft 
alfo be as the Forces which made them : Which is the 
old Opinion. 
III. A complicated or bent Spring interpofed be- 
tween Two unequal Bodies, ading upon each with 
an equal Preffure, and during an equal Time, muft 
communicate equal moving Forces to each ; but their 
Velocities are by Experiment reciprocally propor- 
tional to their Maffes ; therefore their Maffes, drawn 
into their refpedive Velocities, arc alfo equal, as 
were their moving Forces ; and by confequence their 
moving Forces are as the Maffes and Velocities con- 
jundly : Which is the generally received Opinion. 
In 
