413 
Lil. 
ON THE MOTION OF A PENDULUM SUSPENDED FROM 
TWO POINTS. 
BY NATHANIEL BOWDITCH, a. a. s. 
Fi fe 4 of the American Philosophical Society at Philadelphia, and of the 
Connecticut Academy of Arts and Sciences. 
— + 
i THE remarkable variety of motions in a pendulum suspend- 
ed from two points, in the curious experiment in Professor Dean’s 
paper on the apparent motion of the earth, as viewed from the moon, 
induced me to examine the theory of such motions, and I have found 
the fluents of the fundamental equations, where the arcs of oscillation 
are small, which is the case usually considered in simple pendulums. 
Some of the most important results of this calculation are contained 
in the following articles. 
2. Let A, B, (Pl. III. Fig. 1.) be the points of suspension of the 
ee which the. ball D is a ac beth by the sea line £0: 
in G, each rotet tone Galen ba Oe off Be iiligde te 
dinates, we shall call GD the axis of z; GB that of x ; and GH, per- 
pendicular to the plane of the figure, the axis of y. If the pendulum be 
supposed to vibrate in the plane of xz, the point D of the body will 
describe an arch of a circle EDF, whose centre is C, and radius CD; 
and if this arch be made to revolve about the axis AB (or chord EF) 
it will generate’a curve superficies which will be the locus of that point 
of the pendulous body in all its successive revolutions. It must how- 
ever be observed, that the arcs of vibration must never be so great as” 
to bring the pendulum in the direction of the line AC or BC, which 
would reduce the double, to a single, point of suspension. , 
3. In calculating the motion of the pendulum, we shall neglect 
the resistance of the ings and shall consider the whole pendulum as a 
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