342 Mr. E. S. Pearson on the Advance of 



shows that the agreement between theory and experiment is 

 satisfactory. 



Figs 9-1 G (PI. X.) are traces obtained for the case 

 p — 1 and 7) = 1*083. The figures show clearly the pheno- 

 menon of beats with a progressive increase in the difference 

 between the frequencies of the component vibrations. 



Figs. 17-24 (PI. X.) are traces obtained for the case 

 ,p = 067 and 77 = 1*4.5. They show well the dependence o£ 

 the traces on the initial condition s, the trace of the bob 

 which was started being in this case almost a simple sine 

 curve throughout, while the other trace is complex. The 

 figures show that the bob which is first started can have a 

 very considerable amplitude of vibration without pro- 

 ducing any great amplitude in the coupled vibration of 

 the other bob. 



V. Summary. 



1. In the present paper, the mathematical theory of a 

 coupled system consisting of a gravity and an elastic pen- 

 dulum is developed for the general case, in which the masses 

 and periods of the two pendulums were both unequal. 



2. The paper is illustrated by 24 photographic repro- 

 ductions of the double traces obtained for the motions of the 

 pendulums under various conditions of starting and coupling. 



3. This mechanical case possesses features analogous to 

 the electrical case of coupled circuits of which both the 

 inductances and periods are unequal and can be used to 

 illustrate the latter. 



Physical Department, 



University College, Nottingham, 



Jane 10th, 1920. 



XXXVIII. Advance of Perihelion of a Planet. 

 To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



N the May number of the 'Philosophical Magazine,' 

 Prof. Anderson, applying the transformation, 



'K^y. « 



