This Memoir is the prosecution of a subject on which the author had previously touched in a paper which is printed in the seventh volume of the Transactions of the Cambridge Philosophical Society. It has for its object the investigation of the quantity of light which is received on a screen of unlimited dimensions, after passing through a certain aperture, or suffering reflexion at two mirrors. The end for which the investigation is undertaken is to ascertain the constant which must be introduced in using Huygens's principle.