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



table moved* by the pendulums C and D. The upper end of 

 this needle passes through a hole in a strut of thin metal 



(not shown in the figures) rising from the lower of the two 

 rods Ac and Be. The rods from C and D are jointed at the 



* Curves of the character dealt with in this paper could be drawn on 

 a fixed table by the employment of other linkages, or by utilizing the 

 vibrations of coupled systems. For example, let the pendulums situated 

 at opposite corners of the square be similar in all respects, and let each 

 pair be suitably coupled by light springs. The pen is at the junction of 

 two light rods pivoted at the tops of two adjacent pendulums, its 

 position of rest being at the centre of the square. The motion of any 

 pendulum is the sum of two simple harmonic motions whose frequencies 

 depend upon the free frequency of the pendulum and the strength of tho 

 coupling. The motion of the pen will therefore be the resultant of two 

 motions each approximately parallel to a diagonal of the square, each of 

 these motions being made up of the two simple harmonic motions proper 

 to the coupled system, to one pendulum of which the pen is attached. 

 If p' 2 and p 2 be the accelerations per unit displacement along the /r-dia- 

 gonal, due to gravity and relative displacement respectively, while 



