158 Lord Rayleigh on the Maintenance of 



direction is ultimately totally reflected. For example, we may 

 so choose the values of R and S that at the origin of x there 

 is a wave (of given strength) in the positive direction only, 

 and we may imagine that it here passes into a uniform medium, 

 and so is propagated on indefinitely without change. But, 

 in order to maintain this state of things, we have to suppose 

 on the negative side the coexistence of positive and negative 

 waves, which at sufficient distances from the origin are of 

 nearly equal and ever-increasing amplitudes. In order there- 

 fore that a small wave may emerge at x = 0, we have to cause 

 intense waves to be incident upon a face of the medium cor- 

 responding to a large negative x, of which nearly the whole 

 are reflected. 



It is important to observe that the ultimate totality of re- 

 flexion does not require a special adjustment between the 

 frequency of the waves and the linear period of the lamination. 

 The condition that c should be imaginary is merely that © 1 

 should numerically exceed (1 — © ). If A be the wave-length 

 of the vibration corresponding to e ipt and to density p , 



7T 2 T-\ 2 ' ^ 6) 



and thus the limits between real and imaginary values of c 

 are given bv 



£-"*& < 74 > 



If p! exceeds these limits a train of waves is ultimately totally 

 reflected, in spite of the finite difference between -J A, and I*, 



* A detailed experimental examination of various cases in which a 

 laminated structure leads to a powerful but highly selected reflexion 

 would be of value. The most frequent examples are met with in the 

 organic world. It has occurred to me that Becquerel's reproduction of 

 the spectrum in natural colours upon silver plates may perhaps be expli- 

 cable in this manner. The various parts of the film of subchloride of 

 silver with which the metal is coated may be conceived to be subjected, 

 during exposure, to stationary luminous waves of nearly definite wave- 

 length, the effect of which might be to impress upon the substance a 

 periodic structure recurring at intervals equal to half the wave-length of 

 the light; just as a sensitive flame exposed to stationary sonorous waves 

 is influenced at the loops but not at the nodes (Phil. Mag. March 1879, 

 p. 153). In this way the operation of any kind of light would be to pro- 

 duce just such a modification of the film as would cause it to reflect 

 copiously that particular kind of light. I abstain at present from deve- 

 loping this suggestion, in the hope of soon finding an opportunity of 

 making myself experimentally acquainted with the subject. 



