[ 5 * 3 
Demonstration, 
i. While the Spring is bending thro’ the Space 
C B, let the Space, thro’ which it is at any time 
bent, be called x, t the Time of bending it thro’ 
the Space x, and u the Velocity of the Body at the 
End of the TimeTj and let CL~L> CB — l. 
Then, if p be the Force, with which the Spring, 
when bent thro’ the Space x, refills the Motion of 
the Body ; by Dr. Hook’s Principle, L : x : : *P : p 
P X 
r- 
And fince, in the Cafe of Forces thataft uniformly, 
the Quantities of Motion generated are proportional 
to the generating Forces, and the Times jointly, if 
M v be the nafeent Quantity of Motion taken from 
the Body by the Refinance in the nafeent Time 
t , MV: — M u : : MT : : or, — * — 
VP XT 
Mir' 
Alfo, fince, in the fame Cafe of Forces acting 
uniformly, rhe Spaces are proportional to the Velo- 
cities, and the Times jointly, * : 2 a : : v r : VT, 
„ • _ TVx 
or r r: 
2 a v 
r V P X TVx 
Therefore, — u — ^775- x-7^7-, or, 2 w u — — 
and thc Fluents tllc ^ e Two Quantities 
are u* and But the former of thefe was 
when x, and confequently, the latter was no* 
G 2 thing 5 
