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[Nov. 12,
Mr. H. Bateman

The linear magnification in the new system is

Let c be the distance of the second interface from the first; then we associate the length -c with the second interface B, and the formulæ of the transformation become

The last of which may be written


where z and x' are measured, as before, from the first surface. This is exactly the former relation between two corresponding points; consequently the whole course of a ray in one instrument corresponds in the transformation to that of the corresponding ray in the corresponding instrument.[1]

  1. We can verify the equation

    connecting two conjugate points in the second instrument as follows


    since Q" and Q' are conjugate points in the first instrument; hence the relation is satisfied.