﻿498 Dr. J. H. Vincent and Mr. C. W. Jude on 



of the pendulums are unchanged. A, B, and C are sup- 

 ported in their negative positions by props adjusted to 

 give equal initial amplitudes. D is released from a cor- 

 responding position and is provided with a wooden arm to 

 remove the amplitude-rod supporting C when D is passing- 

 through its position of rest ; C in like manner releases B, 

 which in turn liberates A. Thus the rods of all the pen- 

 dulums except A carry releasing rods attached to them, 

 which involves the re-adjustment of the periods. If we 

 measure time from the instant when the pendulum A is 

 released, the equations to the trace are 



x — a cos [pt + tt] 4- a cos [3p(t + ir/Gp + 7r/4^) + it] , 



y — a cos [2p (t + tt/4/)) + tt] + a cos [4/> (t + irjSp + ir/6p + ir/lp) + tt] ,, 



the record enduring in this case from t = to t=27r/p. 



By employing a small wooden triangle pivoted near one 

 corner to change the direction of motion due to the impact 

 of a releasing rod through 90° (after the manner of a bell- 

 crank lever) it was arranged in fig. 18 that D should at the 

 middle of its swing release the opposite pendulum B. The 

 pendulum B in its mid-swing releases A and C simultaneously. 

 If we count time from this instant the equations to the trace 

 become 



x = a cos [pt -h tt] + a cos \Zpi + tt] , 



y = acos [2p(£ + w/4p)+7r] +acos [4p(£ + 7r/4/? + ir/8p) +ir]. 



The time occupied in the trace is, as in the preceding- 

 picture, Zirjp. 



Epicyclics, &c. 



If two adjacent pendulums having the same frequency 

 and amplitude form one pair, while the other pair are also 

 equal to each other in these respects, we can draw epicyclics 

 bv releasing one pendulum of each pair a quarter of its 

 period later than the other. 



Friction Small. 



Fioures 19 to 30 include examples of well-known epicyclics. 

 To draw these figures, A was tuned in unison with B, and 

 C with D. All four pendulums were initially supported 

 with their bobs in the outward position. If B liberates A 

 a quarter of a period after its own release, the pen is given 

 a uniform clockwise circular motion. If D similarly releases 

 C the table describes circles in the same sense. The motion 



