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M E C H A N I C S.

tiop.al to the Intensity of the Cause, and the Time ofits Continuance: Thus, for Example, the Effect ofGravity on Bodies left to themselves causes them todescend ; their Descent therefore will be proportionateto the Power of Gravity upon them, and thereforegreater in those which fall freely, than in others whichdescend on Inclined Planes in a given Time, wherePart of the Force of Gravity is destroyed by the Re-action of the Plane. But since the Action of Gravityis not instantaneous, but continual, therefore its Effect,j. e. the Descent of the Body, will be greater in Pro-portion to the Time of its continuing to act on the.Body, separately consider’d from its intrinsic Force.But this Force is as the Velocity produced by it in agiven Time; also the Time is as the Velocity, whenthe Force is given ; therefore the Effect, viz. the De-scent of the Body, is as the Square of the Velocity.

15. Or in Symbols thus ; let E — the Effect pro-duced by any Power — P, acting in any Space of Time— T, upon any Body — Q__, moving with any De-gree of Velocity V. Then it is plain, E will be asQ_=: Mass of Matter in the Body, when P, T, andV, are given ; also the Effect E will be as the Intensityof the Power P, when T, Q_, and V are given ; again,when P, Q_, T, are given, E must be as V ; and lastly,we stiall have E as T, when P, Q_, V, are given.Therefore when neither of these are given E : Q_X P XV X T; and in cafe of any different Effect, let

qXpXvXt.

16. Then supposing the Bodies equal, viz. q,we have E:<::PVT : p v t. Thus the fame or twoequal Bodies, descending on two Planes unequally in-clined, will descend thro’ Spaces, which will be as thedifferent Powers of Gravity P and p, as the differentVelocities V and v in any Point of Time, and as thedifferent Times T and t of their Descent, conjointly.

1 j. If not only the Bodies i^and q, but also thePowers P and^> which actuate them, be supposed equal,or P —p\ then E : e : T V : tv. Thus in equal Bo-dies falling freely by Gravity, the Effect, or the Spacewhich they describe, will be as the Time T and t ofthe Falls, the Velocities V and v at any Point of Time

R 3