642 
EXPERIMENTS OF MESSRS. FINCHAM AND RAWSON. 
If T= time of oscillation of a simple pendulum, 
2 ^= angle of amplitude of oscillation, 
r= length of pendulum, 
g= 32-19084 feet, 
3-1415927, &c. &c., 
we have 
nn /r{ , /iX^/versflx , /1.3\^ /vers , /1.3.5\^ /vers . A 
T=V^{i + (2) {-T-) + {ja) (— ) +(^) (— ) 
Put R= radius of oscillation of a compound pendulum. 
Then the time of oscillation of the compound pendulum will be the same as in the 
case of the simple pendulum, if we put R instead of r in the above formula. 
r=V7i>+Y (— ;+(w {—) +( 2 X 6 ; c 
We may here observe that 
versin fl\ ® 
• (26.) 
R: 
F + 
' h ’ 
where k— the radius of gyration about the centre of gravity, A= the distance from 
the centre of suspension to the centre of gravity of the model. 
Since 
versin 0 , 1 — cos 9 , 9 
2 2 2’ 
we shall have 
’’= 1+ 5 + sm| + &C.J. . 
If we put 
/(^)=Q) + sin^^+&c.&c. 
equation (4.) will become 
From which equation we obtain 
. / 4 . If— ^9^ y T 
( 27 .) 
(28.) 
(29.) 
If T,, T 2 , T 3 be the time of the first, second and third oscillations during the time that 
6 and s remain constant, we shall have 
ns/ -h ^ ^ 1 +/^9) &c. to n termsj, 
-. s/k'^-\-ki 
Vgs fr 
11 +/(«)} I 
Ti+Ta+Tj&c. to n terms 
1 
(30.) 
* See Poisson’s Traite de Mecanique, p. 348. 
