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3 the curve of brightness for one component is ABC, and for the other OA'C'; and the curve representing half the combined brightnesses is E'BE.

The maximum brightnesses and the places at which they occur are easily determined with the aid of certain properties of the Bessel's functions.

In considering the relative brightnesses of the different spectra, it is therefore sufficient to attend merely to the principal directions, provided that the whole deviation be not so great that its cosine differs considerably from unity.

Unless the spectrum be of very high order, we have simply Bm : B = {a/(a+d) } 2 (4); so that the brightnesses of all the spectra are the same.

The brightnesses of image points in a median section of the pencil are proportional to the aperture of the lens, supposing that the rays are completely reunited.