Mechanics.'

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From these Properties of Bodies descend-ing on Inclined Planes, we deduce the fol-lowing Corollaries, viz. (1.) That theTimes in which a Body descends through

the

presses or acts upon the Plane; but since the Planeequally acts upon the Body in a contrary Direction, thatf orce CE is wholly destroy’d. The Remainder there-fore, EF, is that which carries the Body down thePlane, as acting in a Direction parallel thereto ; andthis is called the relative Gravity.

2. Now because of the similar Triangles CFE,DFG, DBC, we have CF : FE :: DF : FG : : BD : BC •that is, the absolute Gravity CF is to the Res,dual or Re -lative Gravity FE, as the Length of the Plane BD to theHeight thereof BC.

3. Also since the Triangles BDC and BCI are simi-lar (CI being drawn perpendicular to BD) ; and sincethe Spaces described in the same Time in the Perpen-dicular and on the Plane will be as the Powers of Gra-vity, or accelerating Forces in those Directions, that is,as BD to BC, or as BC to BI (for BD : BC : : BC :BI). Therefore BI will be the Distance descended onthe Plane in the same Time as a Body would descendfreely in the Perpendicular from B to C.

4. Since the Motion on the Plane is accelerated, theTime of describing BI will be to the Time of describing

BD, as ^/BL : ctBD : : t : T ; and so P : T 2 : : BI:BD j but, (because BI : BC :: BC : BD) we have BI :

BD : : Bl 2 : BC 2 ; therefore r 2 : T 2 : : ST : BC 2 ; andso t : T ::BI:BC::BC:BD; consequently the 'Timeof describing BI or BC will be to the Time of descendingthrough the Plane BD, as the Height of the Plane BC toits Length BD.

5. Hence the Time (T) of descending thro’ anyother Plane BH of the same Height (Fig. 6.) is to theTime (i) of the Descent thro’ the Perpendicular BC,as BH to BC; that is, T: t: : BH : BC ; but it is alsoT: t :: BD : BC ; therefore ex œquo, \ye have T : T::

BD ;