580 Prof. F. D. Murnaghan on the Deflexion of a 



creating in each a motion which is made up of three super- 

 posed S.R.M/s of different periods. Thus, in accordance 

 with the general principle, there are as many normal modes 

 of vibration as there are degrees of freedom in the system. 

 Photographic reproductions of the vibrations of the three 

 pendulums under different conditions are given in PL XII, 

 figs. 1-10. These curves show clearly that there are more 

 than two simple harmonic vibrations in each. 



With a modified form of apparatus, experiments are being 

 carried on to illustrate the theory of combinational tones and 

 their objective existence,, showing thereby that when two 

 simple harmonic forces of small but finite amplitude and of 

 frequencies Ni and N 2 are imposed on a vibrating system, 

 there are generated in the system simple harmonic vibrations 

 of frequencies 2N X , 2N 2 , Ni + N 2 , and Ni — N 2 besides 

 Ni and N 2 , the results of which will be published in a 

 separate paper. 



Department ,of Physics, 

 Maharajah's College, 



Vizianagaram City India. 



LXVIII. The Deflexion of a Ray of Light in the Solar 

 Gravitational Field. By Francis D. Murnaghan, M.A., 

 Ph.D., Assoc. Prof, of Applied Math., Johns Hopkins 

 University *. 



PROBABLY the most important experimental test o£ 

 the General Relativity Theory is that dealing with 

 the deflexion of a light-ray in its passage near the Sun. 

 It is essential, therefore, that the mathematical discussion 

 of the amount of deflexion to be expected should be clear, 

 and should avoid all unnecessary assumptions. The treat- 

 ment given in Eddington's classical and excellent Report f 

 does not seem to meet these requirements, since it is 

 somewhat indirect and appeals to theorems of optics which 

 are proven in the text-books for Euclidean space alone ; 

 whilst it is the essence of. the Relativity Theory that the 

 space surrounding the sun is non-Euclidean. It is hoped 

 that the following treatment will appeal to the reader as at 

 once direct and not unnecessarily difficult. 



* Conmiunieated by the Author. 



f The Physical Society of London. ' Report on the Relativity 

 Theory of Gravitation/ 2nd ed. (1920). 



