252 Prof. Barton and Miss Browning on Coupled 



Thus the inductions are represented by the reciprocals of 

 masses multiplied by the square of gravity. The currents 

 are represented by 



m l l l g6 1 and m 2 l 2 g0 2 (24) 



The electrical and mechanical equations are then shown to 

 be identical in form. Thus the model is indeed an exact 

 analogue in certain very important senses. But when re- 

 flecting on the striking properties of this model, it seems 

 difficult to avoid wishing that the inductions were repre- 

 sented throughout by masses simply and the currents by the 

 speeds of those masses. Possibly, however, the designer of 

 a model in every way analogous to the electrical case would 

 have solved by his design the enigma of Nature's electro- 

 magnetic mechanism which has hitherto eluded all scrutiny. 

 But perhaps, since no known model seems able to claim 

 full perfection, there may yet be room tor one or two more 

 analogies which are confessedly imperfect. 



IV. Theory of Double-Cord Pendulums. 



Description. — We now deal with one of the two very 

 simple devices used by the present writers to imitate in their 

 vibrations the phenomena of coupled electric circuits. No 

 claim for exactness of analogy is made for these. They are 

 remarkable only for their simplicity, facility of adjustment 

 to various desired couplings, and their power of producing 

 simultaneous traces revealing the relative frequencies, ampli- 

 tudes, and phases of the coupled vibrations executed. They 

 accordingly give vivid illustrations of these mechanical 

 phenomena, and these are in broad outline closely akin to 

 those of the electric circuits. 



What may be termed the double-cord pendulum is shown 

 in elevation in figs. 1 and 2, the bobs, board, and traces being 

 shown in perspective in fig. 4 of Plate IV. 



In the normal use of the pendulums the oscillations occur 

 only in the plane of fig. 2. In this figure is shown a stiff 

 connector CC of fibre-tube which forces the bridles ACA, 

 A'C'A' to swing together. Each bob consists of a heavy 

 metal ring holding a glass funnel for sand to give the 

 vibration trace on a moving board below. The length of 

 each pendulum may be adjusted by a sliding tightener 

 (T, T'), and the bridles may be set to any desired droop by 

 adjustments at their ends A or A'. 



Equations of Motion and Coupling. — Reckoning from C 

 the droop of the bridle, let I be the length of the simple 



