The following illustration, representing a segment of the profile of a dioptric apparatus, will give the reader a sufficient idea of the manner in which the rays proceeding from the focus of a lamp are refracted on issuing from the lens; it also shows the central disc, and the rings placed above and below it.
When the drum is circular instead of being polygonal, the lenses are cylindrical and not annular; the luminous rays are uniformly distributed in the horizontal plane, and act—in a meridian section—in the same manner as those of the annular lenses.
Yet there is something more than lenses in a dioptric apparatus, for this reason, that the lamp does something more than illuminate the frame. The rays streaming below it vainly poured their light at the foot of the tower, and those which rose above it were diffused in the upper region of the atmosphere, and consequently, for all purposes of marine illumination, would have been useless, had not Fresnel conceived the idea of collecting, concentrating, and despatching them in the same direction as the lenses threw the others. This he effected by means of the cylindrical rings of glass which, above and beneath the lenses, cover over the framework, as it were, or make use of it as a base, in expanding themselves as they approach the centre of the apparatus.
[Illustration: DIAGRAM, ILLUSTRATING THE PROGRESS OF A LUMINOUS RAY IN A CATADIOPTRIC RING.]
The subjoined illustration represents the progress of a luminous ray in one of the rings of glass, technically termed _catadioptric rings_. Issuing from the focus F at the summit of the angle formed by the lines G and I, it is refracted at A in the direction A B, undergoes a complete reflection on the surface M N, takes the direction B C, and finally emerges from the ring in the horizontal line C H.
At this solution of the difficulty Fresnel did not arrive all at once, owing to the absolute want of workmen suitable for carrying out the novel industry which his genius had created. But by degrees these were trained and perfected; and the inventor had, moreover, the good fortune of discovering in an able and ingenious optician, M. Soleil, an efficient assistant in the construction on a large scale of the novel instrument he required. Afterwards the erection of lighthouses becoming an important branch of industry, he completed several edifices, which prospered all the more that strangers immediately gave up any attempt at rivalry, and left to him the work of supplying every maritime nation with lenticular apparatus.