It is well known, that when light is incident on a refracting surface, a portion of it is reflected, whilst both the transmitted and the reflected light undergo polarization. The obvious mode of accounting for this, is to attribute to the particles on whose motion light is supposed to depend, the property of transmitting one class of vibrations more freely than another, limited, however, by the direction and mode of action of the adjacent particles. M. Fresnel, in order to determine the intensity of light reflected and refracted under different circumstances, assumed that the density of the particles of ether is greater in refracting media than in vacuo. By means of this assumption, and other subsidiary ones, he deduced formulæ for the intensity of the reflected and refracted light, by means of which the amount of polarization, as well as the change which the plane of polarization undergoes, can be readily deduced. The obvious interpretation of the formulæ coincided precisely with discoveries which had been long known, and the more difficult deductions from them have been tested by numerous experiments of Sir David Brewster and others. It appears that, although for highly refractive media, they may be only approximations, yet, in most cases, they are so close as to deserve the most careful attention of those who endeavour to establish a correct mechanical theory.