On the subject of the illuminating power of the lenses, it seems enough to say, that the same general principle regulates the estimate as in reflectors. Owing to the square form of the lens, however, there is a greater difficulty in finding a _mean focal distance_ whereby to correct our estimate of the angle subtended by the light, so as to equate the varying distance of the several parts of the surface; but, practically, we shall not greatly err if we consider the _quotient of the surface of the lens divided by the surface of the flame_ as the increased power of illumination by the use of the lens. The illuminating effect of the great lens, as measured at moderate distances, has generally been taken at 3000 Argand flames, the value of the great flame in its focus being about 16, thus giving its increasing power as nearly equal to 180. The more perfect lenses have produced a considerably greater effect. ~Arrangement of the Lenses in a Lighthouse.~ The application of lenses to Lighthouses is so obvious as scarcely to admit of farther explanation than simply to state, that those instruments are arranged round a lamp placed in their centre, and on the level of the focal plane in the manner shewn in Plates XIII. and XIV.,[61] so as to form by their union a right octagonal hollow prism, circulating round the flame which is fixed in the centre, and shewing to a distant observer successive flashes or blazes of light, whenever they cross a line joining his eye and the lamp, in a manner similar to that already noticed in describing the action of the mirrors. The chief difference in the effect consists in the greater intensity and shorter duration of the blaze produced by the lens; which latter quantity is, of course, proportional to the divergence of the resultant beam. Each lens subtends a central horizontal pyramid of light of about 46° of inclination, beyond which limits the lenticular action could not be advantageously pushed, owing to the extreme obliquity of the incidence of light; but FRESNEL at once conceived the idea of pressing into the service of the mariner, by means of two very simple expedients, the light which would otherwise have uselessly escaped above and below the lenses. [61] The Plates shew the nature of the mechanical power which gives movement to the lenses. It consists of a clockwork movement driven by a weight which sets in motion a plate bearing brackets that carry the lenses. All this, however, can be seen from the Plates; and I am unwilling to expend time in a detailed explanation of what is obvious by inspection. ~Pyramidal Lenses and Mirrors.~