On Variably Coupled Vibrations. 329 



the perihelion of a planet and the deflexion of a ray of light 

 thus appear, according to this view, as different manifesta- 

 tions of the same effect. 



Solving (I) by successive approximations, we have, 

 neglecting (mu)* 3 



1 /a \ , 2m m 2 , Q . 

 u=j£cos(0 — a)+ -jg — ^ 2 cos J (0-a), 



where R, « are constants. 



Putting n = 0, we obtain for the directions of the 

 asymptotes, to the same degree of approximation, 









Hence the ray is deflected through a total angle 4/h/R which 

 agrees with the usual theory. 



It appears that the deflexion of a ray of light is the same 

 whether we regard r or r x as the actual measured distances, 

 but that the difference is important in the problem of the 

 orbit of a planet. 



XXXVII. Variably Coupled Vibrations : Gravity-Elastic Com- 

 binations. — II. Both Masses and Periods Unequal. By 

 L. C. Jackson, F.P.8.L., University College, Nottingham *. 



[Plate X.J 



I. Introduction. 



IN a previous paper f the author described a model of a 

 coupled system consisting of a gravity pendulum and 

 an elastic pendulum, tbe separate periods and the masses 

 of the two being equal. The present paper deals with the 

 same system for the case in which both the masses and 

 periods of the two pendulums are different. 



The model may thus be considered as analogous to the 

 case of coupled electrical circuits, in which the inductances 

 and periods are both different. The apparatus, though still 

 the same in principle, has been entirely re-made and im- 

 provements effected in certain details, as experience showed 

 them to be desirable. The chief points in which the present 

 apparatus differs from the one previously described, are such 



* Communicated by Prof. E. H. Barton, F.R.S. 

 ■f Phil. Mag. vol. xxxix. p. 294. 

 Phil. Mag. Ser. 6. Vol. 40. No. 237. Sept. 1920. Z 



