252 
DR. J. H. POTN-TING A?[D MR. P. L. GRAY IR" SEARCH OF A 
Value of K. —When there are only natural vibrations 
any complete swing _ ^.j, 
next complete swing 
The value of this ratio was usually near 1‘4. The mean of a number of deter¬ 
minations taken at various times was 1‘3953. Putting 
g 3 o- 2 K _ 1.3953^ 
we get 
K - 0-011033. 
Value of n. —Substituting for k in the value of T in (3) we get 
and 
ir = 0-0027359, 
n = 0-052306. 
Value of e .—The forced period 27r/yi was always 115 secs., whence 
and 
tan e = , = 2-420, 
01- — 
e = 67° 33', 
sin e = 0 - 9242 . 
From equation (1) it wnll be seen that the steady deflection due to F is — while 
from (2) the amplitude of the forced oscillations is ^ ^ or • 
pK pK n- 
Usiug the values found for iik and e we have 
iir sin e 
pic 
— 4-196, 
or the forced oscillations give a cumulative efiect, about four times the steady 
deflection clue to the couple at its maximum value. 
Value of Moment of Inertia, I.—This was found by vibrating the cage hung by 
a short cjuartz fibre, (1) when empty, (2) when containing the sphere, the times of 
vibration being respectively 8-38 secs, and 11-22 secs. The sphere w-eighs 1-004 grams, 
and its radius is 0-45 centim., so that its moment of inertia I M?-" = -08132. 
From this, and the times of vibration, we get 
I = 0-1821. 
Value of F.—The vibrations were observed in scale divisions, each 0-05 centim., 
the distance between mirror and scale beino; 358 centims. If N is the number of 
O 
scale divisions in the amplitude of vibration, i,e., in half the range, we have from (2) 
