of a parabola about its parameter _x b_; F is the focus of the generating parabola; and _l_ _l_ are small pillars, which connect the two reflecting plates, and give strength to the apparatus. [46] Fanal, from φανεν, a lantern. [Illustration: Fig. 45.] ~Fanal à double effet.~ M. BORDIER MARCET has also prepared an ingenious modification of the paraboloïdal mirror, which he has described under the name of _fanal à double effet_; and the object of which is to obtain a convenient degree of divergence from parabolic mirrors, by the use of two flames and two reflecting surfaces, each of which is acted upon by its own flame, and also by that of the other. This modification consists in the union of two portions of hollow paraboloïdal mirrors, generated by the revolution of two parabolas about a common horizontal axis, and illuminated by two lamps placed in the focus of each. The first surface is generated by the revolution on its axis of a segment of a paraboloid intercepted between the parameter and some double ordinate greater than it, and may, from its form, be called the ribbon-shaped mirror. The second surface is that of a parabolic conoid, which is cut off by a vertical plane passing through a double ordinate, which is equal to the parameter of the parabolic ribbon, which is placed in front of it. The elements of the curve which forms the conoïdal mirror, must be so chosen as to have its focus at a convenient distance in _front_ of that of the ribbon-shaped mirror, so as to admit of placing the two lamps separate from each other, as well as to produce the necessary degree of divergence, which is to be obtained by the action of these mirrors respectively on the flame placed in the focus of the other. These two mirrors are joined together in the line of the parametric section of the ribbon, which coincides with the lips of the conoid at some double ordinate _behind_ its parameter. Each mirror produces, by means of the lamp placed in its focus, an approach to parallelism of the reflected rays, which M. BORDIER MARCET has not inaptly termed the _principal effect_; whilst the action of each surface on the lamp which is placed in the focus of the other, causes what the inventor calls the _secondary_ or _lateral effect_. Their secondary action may be described thus: The lamp, which is in the focus of the ribbon, is much nearer the vertex of the conoid than its own focus; so that its rays making, with normals to the surface of the conoid, angles greater than those which are formed by the rays proceeding from its focus, are of necessity reflected in lines diverging from the axis of the mirror. Those, on the contrary, which proceed from the focus of the conoid, meet the ribbon-shaped surface, so as to make angles with its normals more acute than those which the rays from its own focus could do, and which are, therefore, reflected in lines converging to the axis of the mirror. Those reflected rays must therefore cut the axis, and diverge