568 Prof. A. L. Narayan on Coupled Vibrations 



of which A consists of a steel rod furnished with a heav}^ bob 

 which can be screwed at different points so as to vary the 

 moment of inertia of the system, and it can turn freely about 

 a horizontal axis by means of a knife-edge which can be fixed 

 at different points — thus varying the point of suspension also. 

 Similarly the pendulum B consists of a steel rod and a heavy 

 bob. and it is suspended from A by means of a highly polished 

 steel knife-edge resting in a V-groove of a small steel bracket 

 which can be screwed at different points along the length of A. 

 Thus the degree of coupling can be varied at will. 



The paper includes twenty photographic traces of the motion 

 of the pendulums under various conditions. The method 

 adopted in this case for photographing the vibrations is 

 wholly different from that adopted by Prof. Barton and 

 Miss Browning and Mr. Jackson in their various experiments 

 on coupled oscillations. Each of the pendulums A and B 

 carries (as can be clearly seen from the second photograph) 

 a small galvanometer mirror of about 1 m. radius, with its 

 plane perpendicular to that of the vibration of the pen- 

 dulum, and the mirror can be turned (by means of a simple 

 mechanism) about a horizontal and a vertical axis, for final 

 adjustment to get the two reflected spots exactly one above 

 the other on the slit of the camera. When the pendulum 

 vibrates, the mirror mounted on it rotates about the axis of 

 rotation of the pendulum. A beam of light proceeding from 

 a pinhole is projected on to the mirror, and the reflected spot 

 moves up and down, when ihe pendulum vibrates ; and the 

 two spots formed by reflexion from the mirrors are made 

 toiall on a narrow vertical slit of a moving plate camera, 

 the plate inside which is moved at a uniform speed by 

 means of a chronograph, as shown in the photograph of the 

 apparatus. Throughout this work Ilford Empress Plates 

 are used and are developed in a normal solution of metol- 

 hydroquinone. 



Theory of the Double Pendulum. Equation of Coupling . 



The annexed figure represents the projection on a vertical 

 plane perpendicular to the axis of rotation. 



Let m x and m 2 be the masses of the two pendulums 

 A and B ; 

 Gc 1 and Gr 2 , their mass centres ; 

 Ox and 2 , their axes of rotation ; 



Kj and K 2 , radii of gyration of (i.) A about and 

 (ii.) of B about G 2 respectively ; 

 and 1 Gr 1 — h l ; 2 G 2 = h 2 ; l 2 = a; 



6 and cp the inclinations of C^Gj and 2 G 2 to the 

 vertical. 



