suspended from two points. 433 
described must be identically the same, in both cases, but they will be 
« 
described in a contrary direction. 
9. When <= 8, or 8r=r' the equation (H) becomes = = cosine 
c. cosine (3A. ? —sinec.sine (3A. =) whence we easily deduce 
cas 
> =(4. 3-5 - =>) cosine c + (l—4. —— A wf Bl » sine ¢, of the 
sixth order, except sine c=o, when it becomes of the third order. 
In the case of c=o, the curve described will be as in Fig. 14. The 
body being let fall from rest from the point K, will vibrate backwards 
and forwards in the curve KaGdA, which is easily traced by putting 
x=b. cosine 3a't, y=0' . cosine at. 
When c=90°, the curve described will be as in Fig. 15, EaSeWd 
N/E, where x=—4. sine 3a't, y=b' . cosine a't. 
20. When —=4, and c=o, we shall have 2=6.cosine 4a’t,y=0' . co- 
sine at. The body being then let fall from K (PI. Ill. Fig. 16) will 
vibrate backwards and forwards in the curve KaScD. When ea: ! 
x=—b. sine 4a't, y=6'. cosine a’ and the body will hen escribi ee, 
curve Eabed WefghE, Fig. 17. 
By taking ¢ of different values, in this and in the last srt: _ 
should find as great a variety of curves asin § 17: and, if instead of 
taking = 8 or 4, we had taken s =3+— or S=4t+ —,m being a 
large number, we should find that all the varieties of curves thus 83 
. covered would be described by a pendulum adjusted to erat ue 
of eS : - ah 
“, P e* rae 
Sitnilar results would be cindy ing ena veal: 
er whole number, or equal to any rene tay mbes 
3 My ea if ee eo te & 
735 rh. . . . a _ i =. ne 
aN, 
a 
“ 
te 
# a 
3 # 
