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LIII. The Duplex Harmonograph, By J. H. Vincent, 

 M.A., D.Sc, A.B.C.S., and 0. W. Jude, B.Sc; L.C.C. 

 Paddington Technical Institute*. 



[Plate Till.] 



Contents, 

 Introduction. 



construction of the apparatus. 

 Initial Amplitude and Phase. 

 Friction. 

 Description of the Duplex Harmoxog-rams. 



Unequal Frequencies in Simple Patios; Friction Small. 

 Index of diagrams 1-18. 

 Frequencies as 2, 3, 4, o. 

 Frequencies as 1, 2, 3, 4. 



Initial displacements all negative. 

 Various initial conditions. 

 Epicyclics, &c. 



Index of diagrams 19-35. 

 Friction small. 



Frequencies in simple ratio. 

 Frequencies slightly different. 

 Frequencies in simple ratio but unequally damped. 

 Three frequencies ; two opposite pendulums beating. 

 Index of din grains 36-46. 

 The other frequency their mean. 

 The other frequency half their mean. 

 The other frequency twice their mean. 

 Four frequencies ; pairs of opposite pendulums beating. 



Index of diagrams 47-54. 

 «. Mean frequencies and differences of frequencies of opposite 



pendulums as two to one. 

 /3. Mean frequencies equal and differences as in a. 

 y. Mean frequencies as two to one and differences equal. 



INTRODUCTION. 



fJpHE pendulum harmonograph has been developed in 

 _L various ways since its first introduction. By using a 

 vertically vibrating stereoscopic camera to photograph the 

 horizontal movement of the tracing point, pictures which, 

 when combined, show harmonic motion in three dimensions 

 have been obtained. The well-known twin-elliptic pendulum 

 in the forms given to it by Goold and Benhamf draws the 

 resultant of four simple harmonic motions with the con- 

 dition that they consist of two pairs of nearly equal frequency. 



* Communicated by the Authors. 



t "Harmonic Vibrations."' by Goold, Benham, Kerr, and Wilberforce. 

 Xewton and Co., London, n. d. 



