

Triple Pendulums with Mutual Interaction. 1 7 



The results confirm the accuracy of the measurements 

 and o£ the theoretical assumptions, since they indicate the 

 correct number o£ electrons in the atoms o£ chlorine and 

 sodium. 



An estimate of the distribution of the electrons around 

 the nuclei o£ these atoms may be obtained by analysis of 

 the results, since the forms o£ the diffraction curves are 

 dependent on the arrangement of the electrons. We hope 

 to publish this analysis shortly. 



Manchester University, 



20th March, '1921. 



II. Triple Pendulums ivith Mutual Interaction and the 

 Analogous Electrical Circuits. — II. By Prof. E. H. 

 Barton, F.R.S., and H. M. Browning, M.Sc, F.Inst. P.* 



[Plate I.J 



Contents. 



Page 



I. Introduction 17 



II. Experimental Arrangements 18 



III. Theory of Triple Pendulums 20 



(a) Pendulum Lengths and Eelations . 20 



(b) Equations of Motion and their Reduction 21 



(c) General Solution 25 



(d) Initial Conditions 28 



IV. Mechanical and Electrical Systems 31 



V. Experimental Results 32 



VI. Summary 34 



I. Introduction. 



THE present paper deals with the theory and confirma- 

 tory experiments carried out with the modified 

 apparatus referred to in the previous paper on this subject f. 

 All three pendulums in use still have bobs of equal masses 

 as before, and their total lengths are still all equal. But a 

 rather simpler system of suspension is here adopted which 

 both facilitates the experiments and simplifies the theory. 

 This mechanical form still secures a degree of generality 

 equivalent to that which could be obtained with three equal 

 electrical circuits in which each pair had a different mutual 

 induction. 



The equations of motion for these pendulums lead to a 

 general solution, showing that each pendulum may execute 



* Communicated by the Authors. 



t See " Triple Pendulums," etc. I., Phil. Mag. Nov. 1920. 



Phil. Mag. S. 6. Vol. 42, No. 217. July 1921. C 



