﻿194 Dr. J. H. Vincent and Mr. C. W. Jude 



on 



is made of tinned sheet iron. The bases of the struts are 

 soldered together and joined to the centre of the table by a 

 large needle dli. This needle passes through holes at the 

 ends of the wooden rods w 2 and w 3 which proceed from the 

 tops of pendulums D and C respectively, and it also passes 

 through holes in the bases of their tin struts f 2 and f s . 

 Excessive vertical play of these rods and struts on the needle 

 is prevented by the use of glass beads gr, which also serve to 

 diminish friction. 



If the pendulums at the ends of one of the sides of the 

 square ABCD be clamped the others will draw an ordinary 

 harmonogram or Lissajous' curve. In fig. 1 let x be the 

 displacement towards A of the tracing-point from its position 

 of rest, and y that towards B ; the curves drawn by the 

 instrument will approximate to those having equations 

 derived from 



x = a cos \_pt -r a] + c cos \rt + 7] > ,^ 



y = 6cos \_qt + P]+dcos [st + S] i 



by eliminating t. So that this apparatus is capable of 

 drawing a class of curves bearing a relation to Lissajous' 

 figures similar to that which epicyclics bear to circles. 



Initial Amplitude and Phase. 



A very important part of the apparatus is an iron bar of 

 square section which is fixed vertically under the middle of 

 the slate table with its flat surfaces at right angles to the 

 diagonals of the square. Any pendulum can be held at rest 

 with its bob displaced outwards (negatively) by means of a 

 light wooden rod, provided with a screw which rests on the 

 edge of a flat surface of the central iron bar. By altering 

 the length of this rod by means of the screw, the amplitude 

 can be accurately adjusted. A pendulum thus poised can be 

 released at the instant when either of the pendulums adjacent 

 to it has accomplished any desired part of its initial half- 

 swing, by the impact of the end of a rod of adjustable length 

 carried permanently by the releasing pendulum. This re- 

 leasing rod can be either a plain straight rod for knocking- 

 off the propping bar, or one provided with a cross piece at 

 the end to pull off this amplitude-bar. 



When it is desired to release two or more of the pendulums 

 simultaneously, electromagnets are employed. By these 

 and similar means the initial amplitudes and relative phases 



