]58 DR. J. BOTTOMLEY ON THE CHANGING 



XV. On the Change produced in the Motion of an Oscil- 

 lating Rod by a Heavy Ring surrounding it and attached 

 to it by Elastic Cords. By James Bottomley, B.A., 

 D.Sc, F.C.S. 



Eead October 2nd, 1883. 



At a meeting of the Mathematical Section on January 16th 

 Dr. Joule brought under the notice of the members a 

 method which he had devised for damping the small oscil- 

 lations of a telescope, or any other heavy mass which it is 

 desirable to keep as steady as possible. The arrangement 

 consisted of a heavy ring surrounding the vibrating mass 

 and attached to it by extensible strings. 



Possibly a telescope may not vibrate as a single mass ; 

 for the parts of which it is composed may not be so rigidly 

 connected as to prevent small relative motions. For 

 simplicity I have considered a case where the period and 

 amplitude of the oscillation may be assigned. Suppose 

 we have a heavy rod supported from a fixed beam by two 

 elastic cords of given length, and attached to the rod at 

 points equidistant from the middle. Suppose an impulse 

 to be given to the rod in the plane of the cords; then it 

 will execute harmonic motions. Now suppose a single 

 damper placed at the middle of the rod, how will this 

 affect its motion ? 



Let m denote the mass of the rod, m l mass of the ring, 

 X modulus of elasticity of cords connecting the rod with 

 the ring, X ; modulus of elasticity of cords supporting the 

 rod, D diameter of ring, d diameter of rod. 



