ON THE PROPAGATION OF WAVES THROUGH A STRATIFIED MEDIUM, WITH SPECIAL REFERENCE TO THE QUESTION OF REFLECTION.
[Proceedings of the Royal Society, A, Vol. LXXXVI. pp. 207 — 206, 1012.]
THE medium is supposed to be such that its properties are everywhere a function of but one coordinate x, being of one uniform quality whore x m less than a certain value a^, and of another uniform quality (in general, different from the first) where sc exceeds a greater value #m_i; and tho principal problem is the investigation of the reflection which in general ensues when plane waves in the first medium are incident upon tho stratifications. For the present we suppose the quality to bo uniform through strata of finite thickness, the first transition occurring when IG — xl) the second at a?=a;2»and the last at ,«=«m_1.
The expressions for the waves in the various media in order may be taken to be
-ai (*-»>>] -f JB10i[
~a* (x~x^ -f- Jg2^
and so on, the A's and £'a denoting arbitrary constants. The first terms represent the waves travelling in the positive direction, the second those travelling in the negative direction; and our principal aim is the determination of the ratio JBJAi imposed by the conditions of the problem, including the requirement that in the final medium there shall be no negative wave.
As in the simple transition from one uniform medium to another (Theory of Sound, § 270), the symbols c and 6 are common, to all the media, the first depending merely upon the periodicity, while the constancy of the second is required in order that the traces of the various waves on the surfaces off the corona, there are other astronomical problems to which one or other of the methods above described, or a combination of both, might be applied with a prospect of attaining i\ further advance.