Note 1 — IV. THE MICROSCOPE.

Its importance will be realised, however, when it is stated in the words of the late Professor Abbé: "The numerical aperture of a lens determines all its essential qualities; the brightness of the image increases with a given magnification and other things being equal, as the square of the aperture; the resolving and defining powers are directly related to it, the focal depth of differentiation of depths varies inversely as the aperture, and so forth."