14 
PHYSICS: C. BARUS 
Proc. N. a. S. 
center of the mass M from the center of the shot m were obtained by caH- 
pering. 
The moment of inertia of the needle 2/ = 22.0 cm. long between centers 
oim = .6295 g has for its main part 2mP = 152.5. To this is to be added the 
moment of inertia of the stem wire (p = .0044 grams per cm.), 3.9; of the 
oblique wire brace or tie, 1.0; and of the glass filament added for ridgity, 
2.0; making a total of A^= 159.4 = = 152.5(1 + .0452). 
The torsion coefficient of the wire was found from the period Ti of the 
needle vibrating in vacuo, by a stop watch. As T is over 5 minutes, it is 
necessary that the arc of vibration be relatively large ; otherwise the pas- 
sage through equilibrium is too slow. Periods were found as follows: 
ri = 311.5, 310.0, 312.0, 311.5, 311.0, 311.2; Mean ri = 311.2 =^=.28 sec. 
The discrepancies result from the presence of radiation forces. 
The logarithmic decrement, X, obtained from observations of consecutive 
elongations showed = 1.35 in the first and 1.34 in the (better) second series, 
which makes X = .293 nearly. Hence the true period T of the needle is 
7=Ti/Vl+XV47r2= Ti/LOOll. 
The intervals on the stop watch moreover were corrected (on comparison 
with a chronometer) by the factor 1.0055, This with the preceding equa- 
tion gives 
r=ri(1.0012) =312.6 sec. 
2. Equations. — The approximate equation for the gravitation constant 
7, containing all quantities to be measured when the needle of semi-length 
/ is used to find the torsion coefficient of the quartz fibre, is 
(1) y'= {TrmRyLTHMm) Ay 
Ay being the ultimate double amplitude for the scale distance L, when the 
attracting weight M passes from side to side of m. 
Since the stem is also appreciably attracted, a correction must be made 
for it. If t/r is the ratio of torques for stem and mass m separately 
(2) t/T=ipR/lm){yJW+J^-R) 
when p is the mass per cm. of the stem. 
Hence finally the corrected constant is 
(3) y = y'/{l+ t/r). 
For the case of two attracting masses M' and M'\ one at each end of 
the needle and cooperating, we should have 
y = K' Ay' = K" Ay" = {Ay+ Ay')/{1/K'+1/K"); and Ay=A/+Ay', 
whence 
(4) y=&y/{l/K'+l/K") 
K' and K" , the corrected coefficients, are usually not very different in 
value. 
If in equation (1) we replace by 2mP{l-\- s) where 5 = .0453, m vanishes 
from the equation (except in the corrections) which now takes the simpler 
form 
