330

NEW EXPERIMENTS

TRACT 34.

■which values, by substitution, give

Q.hrl i 1 ! I| 3 . C 2 S 2 0 2 —C* ,%

+ - T7 _( ^ _ 'T2~ s) -

But is the versed sine or height to the chord c, and

2 o °

t 1 r: 4 A. — = — the snuare of the velocity due to that

height; therefore2 h c 2 2 Ar 2 II

S // O A

120*'*

c + —-neari

4c 2 k A

nearly; or, substituting for A

c

3pZ

n n. r* r4 — ^4

c

So that the chord of the arc which is actually described, isto that which would be described if the air had no resistance,

, • . , , nac r 4 — e+ , . nac i* — (A . ,

as 1 is to 1 + ——. - ; and therefore —— . —-— is the

12pg o 2 12 pg o 2

part of the chord, and consequently of the velocity, lost bymeans of the resistance of the air. And the proportion isthe same for the chords described by the lowest point, orany other point, of the pendulum.

Now, to give an example, in numbers, of this effectof the resistance of the air ; the ordinary mean values of theliteral quantities are as here below :

So that the part of the chord, or velocity, lost by thiscause, namely, the resistance of the air on the back of the

namely,i = TOO

therefore

12 pg = 56000

r 4 = 5220

e'* = 1785

t 4 -£ 4 = 3435

c = If

12 pg o 5

3577

pendulum, is but about the

or about; the ^ part of the