246

Mechanics.

in the Fall. ^\nd because in this Cafe the Velocity isalways proportional to the Time, that is % T : t:: V : v fif we multiply each Ratio by the fame Ratio V : v, theAnalogy will still be the fame, viz. TV : t v :: V 1, : v 1 $whence E : e :: V 1 : v* ; or the Effect of falling Bodiesin describing the Space, will be as the Square of theVelocities.

18. If we suppose the Times given, that is, T — t,then (the rest as before) we have E : e :: V : v ; that is,the Forces or Effects of equal Bodies, falling in equalTimes, are proportional to the simple Velocities.

19. If V — v, or the Velocities given ; then E : e :;T ; t. Thus if two equal Bodies lying on an horizon-tal PJane, receive a Stroke each from Springs of equalForce, then will the Velocities be equal in every Partof the Motion, and the Effects E and e, in this Cafe,being the Spaces described, will be as the Times oftheir Motion.

20. Hence we have seen every possible Cafe whereinthe Forces of Bodies or their Effects can be supposed tovary; and it is plain there is none where the Force isas the Square of the Velocity but where the Time isconcerned; or where some one of the Factors Q_, P,V, T, is proportional to the Velocity; thus in spout-ing Water, because Q_ is always as V, therefore, tho’T be given, E will be as Q_V, or as V 2 ; for P alsoin this Cafe is given, the Power of Gravity whichgives Motion to the Particles of the Fluid being alwaysconstant.

21. Nor have they any Experiment which shews theForce or Effects of Bodies proportional to the Squaresof the Velocities, but where the Time in which theEffect is produced ought to be considered. Thus intheir famous Experiment of Cavities, formed in softClay by falling Bodies, it is true, those Cavities arethe Effect of the falling Bodies, and proportional tothe Squares of the Velocity. But what is this to thePurpose, unless they will fay, those Pits are instanta-neously produced, which I believe none will pretend to

sto?

It is evident, this Cavity must be proportionalso the Quantity of Matter put in Motion in the Clay,

' by