10

NfiW EXPERIMENTS

TRACT 34

been changed for others that are stronger, and which weigh10 lb more than the old ones did. This additional 10 lbof iron must be added to the weight of the pendulum; andnew theorems must be made out, for-determining the change

the lower side of the axis to within 24 inches of the top ofthe block ; consequently its length was 51 "4 inches, and its

the middle of the axis of vibration. . This number 26'6

for the place of the new centre of gravity, where the valueof b is 10 ; which theorem gives

g = 77-3 - 0-76 = 76-54 for the centre of gravity.

And the same values off and b, substituted in the theorem

N = 40'2 + *07 = 40‘27 for the number of oscillations.Hence then, in this new state of the pendulum, the valueofg-is 76'54, and the value of n 40-27, corresponding tothe value 670 of p, or weight of the pendulum. That is,

are the new radical corresponding values of p, g, n. And

theorems to be used now and hereafter for the values of gand n. And where the distance of the centre of oscillation,answering to the number 40-47, is 86.

in the centre of gravity, and the number of vibrations perminute. Now this rod, of uniform thickness, reached from

middle point, or centre of gravity, was at 26-6 inches below

then will be the value of i in the theorem g = 77*3 -{-

i - 77-3

x — / ro ^

660 + r’

P

670

e

76-54

40-27

n

these values, being substituted in the two general theorems,namely,

G = S + j^ b b, and

bin(inn — 140850 )

281700 pg + 6i(inn + 140850) 5they become

or n = 40-27 — ' "" bi nearly. Which are the

1 — 76-54

76-54 +

670 + 5

40-27 bi(i- 86 )8820313 + bi(i + 86 )

40-27

217047