When Newton's rings are formed between two glasses of the same kind, the central spot in the reflected rings is observed to be perfectly black. This result is completely at variance with the theory of emissions, according to which the central spot ought to be half as bright as the brightest part of the bright rings, supposing the incident light homogeneous. On the theory of undulations, the intensity of the light reflected at the middle point depends entirely on the proportions in which light is reflected and refracted at the two surfaces of the plate of air, or other interposed medium, whatever it may be. The perfect blackness of the central spot was first explained by Poisson, in the case of a perpendicular incidence, who shewed that when the infinite series of reflections and refractions is taken into account, the expression for the intensity at the centre vanishes, the formula for the intensity of light reflected at a perpendicular incidence first given by Dr Young being assumed. Fresnel extended this conclusion to all incidences by means of a law discovered experimentally by M. Arago, that light is reflected in the same proportions at the first and second surfaces of a transparent plate I have thought of a very simple mode of obtaining M. Arago's law from theory, and at the same time establishing theoretically the loss of half an undulation in internal, or else in external reflection.