612 Prof. Barton and Miss Browning: on 



r> 



vibrations. The periods of these vibrations were expected 

 to be the same for each pendulum. The phases and ampli- 

 tudes might, however, differ for each pendulum, thus giving 

 very different resultant vibrations. 



The results obtained with the first form of apparatus were 

 even more complicated than was expected from three super- 

 posed vibrations, and on reflection this was seen to be due to 

 the special arrangement in use. So it is proposed in this 

 paper to describe this apparatus and give the figures 

 obtained without dealing with its mechanical theory. 



Results obtained with a modified apparatus will be dealt 

 with later. 



II. Theory of Three Mutually-interacting 

 Electric Circuits. 



The electric circuits are supposed to have self and mutual 

 inductances, and capacities with resistances negligible. 



Let L : , L 2 . L 3 be the self-inductances of the separate 

 circuits, S 1? S 2 , S 3 their capacities, and M,, M 2 , M 3 the 

 mutual inductances between the second and third, the third 

 and first, and the first and second circuits respectively. Then 

 the simultaneous equations of motion may be written as 

 follows: — 



L w + £= M ^ +M <8' • • • 9) 



L <l + |= Mi £ +M <& • • • (2) 

 L ^ + t M ^ +u ^ ■ ■ • <»> 



where «r, y, and z are the charges on the respective condensers. 

 The three couplings are given by 



M a 2 "1 



coupling y to z, a." = j , , 



M 2 2 

 „ *to.r, /3 2 =t- W > 



M B 2 



(±) 



a? to?/, 7- = 

 Suppose as solution that 



z — Op*'. 



