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Let this point of contact be at I, then making KC, QC, DC proportionals, draw DI parallel to CM; also join CI. I say that CI will be the required refraction of the ray RC. This will be manifest if, in considering CO, which is perpendicular to the ray RC, as a portion of the wave of light, we can demonstrate that the continuation of its piece C will be found in the crystal at I, when O has arrived at K.

"Well, four days went by, and then in the Morning Post of February 7th the second advertisement appeared: "Rlxt. ex. sroehnel. 28. Zcokk. zbpl. qc. Ptfrd. Avnsp. Hvfbl. Ucaqkoggwx. "The code was the same as the first, and I deciphered it quite easily. Here it is," and he read from a bit of paper he held in his hand: "Date is February 28. Shall stay at Mount Royal Hotel, Bedlington. Dusky Fowl."

About the centre C, which I suppose to be in the intersection of AH and FE, let there be imagined a hemi-spheroid QGqgM, such as the light would form in spreading in the crystal, and let its section by the plane AEHF form the Ellipse QGqg, the major diameter of which Qq, which is in the line AH, will necessarily be one of the major diameters of the spheroid; because the axis of the spheroid being in the plane through FEB, to which QC is perpendicular, it follows that QC is also perpendicular to the axis of the spheroid, and consequently QCq one of its major diameters.