of a rigid body : 37 
: Hence 6 = tan a/p. 
When z/p is small, we have 
| yee 
Pury eee 
If w/p is less than 1/20, it will generally be sufficient to put 
0=a/p. 
When a/p is greater than 1/20 it will be best to calculate 
the value of tan 0 and from this to find @ in degrees. Bottomley’s 
tables may then be used to find the value of @ in radians. 
On dividing each value of @ by the corresponding value of m, 
the result will be very nearly constant, thus showing that the 
angle is proportional to the couple. The mean value of @/m is then 
found and is used in the calculation of w from the formula 
LG GDh) 
EO @lm 
Using this value of w and the value of K already found from the 
dimensions of the inertia bar, the time of vibration of the bar is 
calculated by the formula 
be 
' 
. 
| 5. Practical example. The observations may be entered as 
in the following record of an experiment by G. F. C. Searle, Oct. 
1906. 
| 
, Load | Reading. iP ‘anna 6 6 | 1000 0/m | 
| gm. cm. em. degrees radians radians/gm. 
: 0) 15:00 0) 0) 0) 0) 0 
10 14:43 0:57 0:0142 a 00142 | 1:420 
20 13°87 1:13 0:0282 * 00282 | 1410 
30 13°29 eg 0:0426 * 00426 | 1-420 
40 12°71 2-29 0:0571 * 00571 | 1°428 
50 12°12 2°88 0:0718 4° 6 0°0716 1-432 
60 11°55 3°45 0-0860 4° 55’ 0:0858 1430 | 
70 10°95 4:05 0:1010 5° 46’ 0:1007 1-439 | 
80 10°38 4-62 01152 | 6 34 071146 1-432 
90 9°81 519 0:1294 7° 22! 071286 1429 | 
100 9°20 5°80 071446 8° 14’ 0°1437 1-437 | 
: * @ put equal to tan @ here. 
Mass of inertia bar = /= 826 gm. 
Length of inertia bar=22=37'88 cm. 
