328

NEW EXPERIMENTS

TRACT 34.

c = the chord which would be described by it if the air-made no resistance.

Then o: x ::» : — the velocity of the point f of the pen-

dulum ; and 4 h z : -— : : h : —— the height descended by

gravity to generate the velocity —. Now the resistance ofthe air to the line dfe, is nearly equal to the pressure ofa column of air upon it, whose height is the same and

therefore that pressure or weight is where n is the

specific gravity, or weight of one cubic measure of air,

or n = --74b. = --lb. Hence then ■■ ■ .. ■■■ is the pressure on850 08 4 ho* 1

D E e d, and na \J~ the motive force on the same d e, or the

fluxion of the force on the block of the pendulum ; and the

correct fluent gives nay r4 ~~ f4 p I for the force of the air on

the whole pendulum, supposing that on the stem a C to be

nothing, as it is nearly, both on account of its narrowness,

and the diminution of the momentum of the particles by

their nearness to the axis. Put now a = the compound

coefficient nay so shall aw* denote the motive force

16 h 0* 7

of the air on the back of the pendulum.

But the motion of the pendulum is also obstructed by itsown weight, as well as by the resistance of the air; andthat weight acts as if it w r ere all concentred in the centre ofgravity, whose distance below the axis is g; therefore pgis its momentum in its natural or vertical direction, andpg s its momentum perpendicular to the motion of the pen-dulum, where s is the sine of the angle which it makesat any time with the vertical position, to the radius 1.Hence pgs + a» s is the momentum of both the resistancestogether, namely that of the pressure of the air, and of theweight of the pendulum. Consequently ^ + k " *= s + — v zis the real retarding force to the motion of the pendulum,at the centre of oscillation ; which force call f.

Now if z denote the arc described by the centre of oscil-lation, when its velocity is v, or ^ the arc whose sine is s;we shall have