suspended froin two points. 435 
iri:aa:ad 3: 14,4: L nearly, hence r= =, which agrees exactly 
with Professor Dean’s experiment mentioned in the 245th page of the 
volume. 
22, I made a few experiments in order to compare the preceding 
theory with actual observation. ‘The first was similar to Mr, Dean’s 
jast mentioned, corresponding to the case of } 16. ‘Yaking AB (Fig. 
1, Pl. 111) equal to 43 inches, r’=0°65 inches, r=46'5 inches, and at- 
taching to the point D a leaden ball of about half an inch diameter. 
These values give (by § 14) Im=S = 286, hence (by § 15) the cycle 
of the motions would be completed in 286 vibrations of a pendulum 
of the length r. The mean result of three different trials, in which ” 
GK (Fig. 2) was three inches, and the angle SGK successively 22°, 
45°, 67°, made the number of vibrations 282, differing about yh. 
from the theory. The ball being let fall from the point corresponding 
to K, vibrated at first nearly in the diagonal KA, the path then gradu- 
_ ally became elliptical, and at the end of about 70 vibrations, corresponded 
- to the figure SWNE (Pl. IIL. Fig. 3) deseribed according t0 the order 
E (Pl. panes si naif main) opin gue cemche.. Le Tay eae 
ofthese letters; this by degrees became more eccentric, and at the end 
of 140 vibrations the motion was nearly in the diagonal CD (fig. 4); of- 
ter a few more vibrations the curve again became elliptical and gradual. 
ly opened till the 210#h vibration, when. the ellipsis was as in lig. 5, sim- 
ilar to that of Fig. 3, but described in a contrary order ENWS. dn 
about 282 vibrations the pendulum had completed its cycle of motions and 
recommenced the description of the diagonal KA (Fig. 3). These re- | 
sults are nearly conformable to the theory. 
In another experiment made to compare with the theory of 18, : 
AB was made equal to 69 inches, r'=64'4 inches, r=21-9 inches, 4 
* ; . Pepe Se a >." é 
' which correspond to the latter case of that article where jee 
