suspended from two poirits. ) 421 
Hence the vibrations of the pendulum ADB, (Plate Il. Fig. 8) about 
the axis AB would be performed in the same time as those of a sim- 
ple pendulum of the length GD=r++’. : 
10. From the preceding articles it follows, that if at the moment 
the compound pendulum is set in motion, from a point whose ordi- 
nates are e, e’, and velocities v, v’, in the directions of the axes a, 7, as 
mentioned in § 5, two simple pendulums are also projected —One of 
the length 7, suspended from the point. C, and projected in the plane 
za with the velocity v, from a point where a=e: The other of the 
length r+r’, suspended from the point G, and projected. in the plane 
zy with the velocity v', the distances of these simple pendulums from 
the axis of z at any time will be respectively equal to the values of x, y, 
in. the motion of the compound pendulum. For in all these pendulums 
the values of a, y, will be given by the same equations (B), since the 
constant quantities a, b, c, a’, b', c’, will be the same in the compound 
pendulum as in the simple ones.- It being always understood that 
the arcs of vibration are small in SOMpArison: of the lengths of the pen- 
dulums, and the bodies are srr ie not-to interfere with each « 
intheir diferent motions. <2 | 
The same result might also be obtained in the peers manner. 
Suppose the pendulum were projected from the point D (Plate III. 
Fig. 1.) in a direction corresponding to the diagonal GA, (Fig. 2) with 
a force represented by GA, that would make it ascend to the point 
corresponding to A. This force might be decomposed into two, 
GN, GE. . If the first of these only acted on the body it would vi- 
brate in the plane of za about the centre C, (Fig. 1) and if the. last 
only acted, the vibratians would be in the plane zy about the centre 
G, and when these forces are very small, they may be considered as 
acting at the same time independently of each other, as is well known’ 
rg OR! 
702 2s 
