SECTION III., 1882. pees) = Trans. Roy. Soc. CANADA. 
The Motion of a Chain on a Fixed Plane Curve. 
By J. B. CHERRIMAN, M.A. 
(Read May 26, 1882.) 
1. The chain being supposed inextensible, the velocity of each point of it at a given 
instant must be the same, and therefore so also is the acceleration. 
dv +s the acceleration. Let F be the impressed force 
Let v be the velocity at time #; i 
along the tangent on the element mds at this time. 
Then the element is acted on by F m ds, and the tensions — 7, T+ dT, at its ends: 
therefore 
m ds =m Fds— T+ (T+ dT) cos. dip. 
=m Eds + aT. 
Integrating this along the whole length / of the chain, 
dv 
m Cares — mf Fds + faT, 
or, if 5, & are the distances of the ends of the chain measured along the curve from some 
fixed point in it, and P, Q are the tensions at those ends, 
mt À =m I” pas + Q—_P, 
; S1 
from which the motion can be determined. 
Cor. 1. In the above the chain is assumed to be of uniform density. If otherwise, the 
equation of motion would be 

dv Sy 8 
= ds = \Fd DE 
= VA m ds 2s m F' dst Q— P 
1 1 
or 
Mass chain X <= = he mFds + Q — P. 
a 8 
ge 
Cor. 2. If the ends are free, then 

Iv 8 
ET Te 
dt sl 3 
1 
