suspended from two points. 423 
described by the pendulum, we shall endeavour to give an idea of it 
for various values of a, a’, by tracing its projection on the plane of ay, 
and for brevity we shall speak of the motion of the body as if it were 
actually made on that plane. Denoting therefore by A> the 
arch, whose cosine is — we shall have from the equations (E) 
att+c=A ~ and at =A 4 » whence, by exterminating t we shall obtain 
the equation of the curve projected on the plane of ay. 
A = =e+ <, A 4 (G) 
and taking the cosine of each side of the equation 
y 
This equation is generally transcendental, but may be easily re- 
duced to an algebraical form when , is a whole number. To il- 
lustrate Pe en OOS) pe: Ree a few 
a . . * al a 
== cosine ¢. cosine (< AZ) —sine e.sine (5 AZ) (H) 
By ee, pe Sosa 
ae OS 0 3 an Geyer a vey am quantity. 
13. When =i, or 7'=o, the points C and G (Fig. 1) coincide, 
and the pendulum is of the common simple form, suspended from the 
point G. In this case, the equation (H) becomes ==cos, ¢. COS. (Az) 
—sine ¢. sine (AS ) , or by reduction 
=< . cosine e—y 1— sine ©. 
When sine c=o, this becomes —= and if b & 0 are both finite the 
b 
equation is that of a right line, Wee to the diagonal. KA, or 
CD. If 4 or é'=0, x or y must be respectively 0, aud we shall obtain 
