Dynamical Illustrations of Certain Optical Phenomena. 227 



the other end of K by a few inches of bellows, which allows 

 for the focussing adjustment. 



The spectrometer, mounted in the manner here described, 

 has now been in use for more than a year, and has been 

 thoroughly tested. It has been found most convenient both 

 for making eyepiece observations and for taking photographs; 

 it has also been found completely light-tight. In proof of 

 this last statement, we may mention that we have exposed 

 rapid photographic plates in the camera of the instrument for 

 upwards of six hours on bright sun-lit days, during the course 

 of an investigation we have been, and are at present, making, 

 in conjunction with Professor Hartley, F.R.S.,upon the ultra- 

 violet spark spectra of the elements, and have experienced no 

 difficulty whatever from " fogging." 



XVIII. On Dynamical Illustrations of Certain Optical Pheno- 

 mena. By Professor J. D. Everett, F.R.S.* 



Contents. 

 § 1. Introductory. 

 § 2. Chain of vibrating particles. 

 § 3. Simple travelling undulation. 

 § 4. Geometrical theorem. 



§ o. One particle of chain constrained to given motion. 

 § 6. Constraining force and its work. 

 § 7. Stokes' application to fluorescence. 

 § 8. Stationary vibration of chain. 

 § 9. Mutually influencing pendulums. 

 § 10. Double pendulum. 

 § 11. Case of small lower particle. 

 § 12. Applications by Kelvin and Rayleigh. 

 § 13. Case of lengths nearly equal. 

 § 14. Sellmeier on fluorescence. 



§ 1. TN studying the attempts which have been made to 

 A illustrate certain optical phenomena by analogies 

 drawn from chains of particles and from mutually influencing 

 pendulums, I have been impressed with the difficulty of 

 obtaining accurate information respecting the dynamical 

 results in question, and the proofs on which they rest. I 

 have taken some pains to find brief and simple methods of 

 establishing the most important properties, and have here 

 arranged both proofs and results in a form convenient for 

 reference. 



In discussing the chuin of particles, I have not had recourse 

 to theorems in the Calculus of Finite Differences, but have 

 imitated the methods employed in Lord Kelvin's Baltimore 



* Communicated by the Physical Society : read Mar. 11, 1898. 



