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Foucault, who employed a scale of equal bright and dark alternate parts; it was found to be proportional to the aperture and independent of the focal length.

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The distance f i, which the actual focal length must exceed, is given by d (f1 2 R2) x; so that f1 = 2 R2/X (1) Thus, if X = p j, R= i ?, we find f1= 800 inches.

They are placed at a distance apart less than the focal length of a, so that the wires of the micrometer, which must be distinctly seen, are beyond b.

Throughout the operation of increasing the focal length, the resolving power of the instrument, which depends only upon the aperture, remains unchanged; and we thus arrive at the rather startling conclusion that a telescope of any degree of resolving power might be constructed without an object-glass, if only there were no limit to the admissible focal length.

If we suppose the diameter of the lens to be given (2R), and its focal length f gradually to increase, the original differences of phase at the image of an infinitely distant luminous point diminish without limit.