By Lawrence M. Graves

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Keller [40], etc. Whenever possible, the fields constructed by the ray method were compared A GEOMETRICAL THEORY OF DIFFRACTION 51 with asymptotic expansions (for large k) of exact solutions. In all such cases perfect agreement was obtained. In other cases numerical results were compared, and good agreement was obtained for ka >_ 2, where a is a typical length in the problem. All of these results suggest that the ray method does yield the leading terms in the asymptotic expansions of solutions of diffraction problems.

Houston, 1949. 9. B. Friedman, Comm. Pure Appl. Math. vol. 4 (1951) p. 317. 10. I. Imai, Die Beugung electromagnetischer Wellen an einem Kreiszylinder, Zeit. Physik vol. 137 (1954) pp. 31-48. 11. W. Franz, Zeit. Natur. vol. 9a (1954) pp. 705-716. 12. K. Depperman and W. Franz, Theorie der Beugung an der Kugel unter Berucksichtigung der Kriechwelle, Ann. Phys. Ser. 6 vol. 14 (1954) pp. 253-264. 13. F. G. Friedlander, Proc. Cambridge Philos. Soc. vol. 38 (1942) p. 383. 14. E. Gerjuoy, Comm. Pure Appl.

A junction of two or more edges), it produces infinitely many diffracted rays which leave the vertex in all direc- tions (see Fig. 6). Thus at a vertex a single incident ray produces a twoparameter family of diffracted rays. , when it is tangent to the surface), the ray splits in two (see Fig. 7). One part continues, unaffected by the surface, as an ordinary ray. The other part travels along the surface. , a curve which satisfies the differential equations for a ray, when these equations are specialized to a surface.

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