Illustrations of Certain Optical Phenomena, 235 



which by (15) reduces to 



*f&+N/(£ 2 -4)} _ k co' 2 - 2fi 



j{h*-4)\k+ >/(F-4)} ~ ^(F-4) J{co*(co*-^)Y 

 When « has its least value 2 v//* this is infinite, as it ought to 

 be, since we have in this case an infinite train of equal oscil- 

 lations. As ft) increases, the value steadily diminishes to the 

 limit unity, showing that the frequency may be so great as 

 practically to confine the energy to the first particle. 



§ 7. This discussion of the simple harmonic vibrations of a 

 chain of particles serves to explain Sir George Stokes's 

 illustration of fluorescence, as quoted in Tait's ' Light,' 

 pp. 161-163. 



When the frequency of the setherial vibrations is below the 

 critical value, any nascent disturbance is carried off to a 

 distance by undulations ; but when it is above the critical 

 value the effects accumulate at the origin of the disturbance. 

 In the latter case, when the applied force ceases to act, the 

 subsequent motion is compounded of free simple harmonic 

 vibrations ; and for none of these does the frequency exceed 

 the critical value. Hence there is a change from higher to 

 lower frequency, and therefore a lessening of refrangibility. 



In support of the view that there is a critical frequency for 

 a fluorescent substance, Sir G. Stokes says : — 



" In dealing with a single fluorescent substance — not a 

 mixture of two or more — I have generally found that the 

 following feature is (very approximately, at any rate) 

 observed : — As we take incident light of increasing re- 

 frangibility, it is at first inactive ; then, on, reaching a 

 certain point P of the spectrum, it begins to produce 

 fluorescence, and the heterogeneous fluorescent light contains 

 refrangibilities not extending beyond P. As we continue to 

 progress in the incident spectrum, the highest refrangibility 

 of the fluorescent light does not follow the- refrangibility of 

 the incident light, but remains about P." 



Professor Preston maintains that there is no difference in 

 kind between fluorescence and the process by which lamp- 

 black transforms luminous into non-luminous radiation. In 

 the application of our analogy to lamp-black the critical 

 frequency will be below the range of visibility. 



§ 8. The fundamental modes of stationary vibration for the 

 chain are most easily deduced from the consideration of two 

 travelling undulations. If the fixed ends coincide with two 

 of the particles, and the intervening length is ma, the equation 

 for a fundamental mode is 



y = 2 A sin 2tt.ivXcos 2?rf/T, 



