Lastly, I shall notice M. BORDIER MARCET’S _fanal à double face_, which consists of two paraboloïdal mirrors, truncated in the vertical plane of the parameter, and united together back to back, so as to be illuminated by the same lamp placed in their common focus. To save the light which would otherwise escape the catoptric action, he adds a parabolic conoid of greater focal distance, and so placed, that while its focus may coincide with the common focus of the other mirrors, its size may be so restricted, that it shall not interfere with the effect of the truncated mirror opposite which it is placed. The obvious consequence of such an arrangement is, that the rays (see fig. 46) produced from a lamp in the common focus of the three mirrors, will produce in opposite directions a luminous ring from each of the truncated mirrors AC, BC, and A′C′, B′C′, while the central or conoïdal mirror MN will fill the interior of one of those luminous rings with a cone of rays, whose intensity will be in the inverse ratio of MN² to _a_ _b_² (or FM² to F _a_²), which latter surface represents the whole amount of naturally divergent rays, which strike on _a_ _b_, and which are spread over MN. Two sets of reflectors of this form facing in opposite directions (each set arranged in one plane, and fixed on a frame which could be made to revolve round a vertical axis), would thus present their brightest effect after considerable intervals of darkness; but, by arranging them with their axes slightly inclined, they were made to prolong the light periods and curtail the dark ones. M. BORDIER MARCET speaks of this apparatus with all the satisfaction generally felt by inventors; but it is no difficult matter to identify its effect with that of the common paraboloïdal mirrors. It is obvious, that all the rays which fall from a true focal point on the three reflectors AC, BC, A′C′, B′C′, and MN, are merely those which would fall on a single reflector, whose double ordinate and the portion of the abscissa between that ordinate and the focus, are equal to those of the first reflector of the compound system, so that the quantity of light reflected by the three reflectors is neither more nor less than that which would be projected by one. All the difference that can exist is, that in the case of a flame which has a notable size, the surface MN being farther distant than _a_ _b_, would produce less aberration and, consequently, a very slight increase of intensity in the small portion of the reflected beam of parallel rays due to that part of the compound mirror. We cannot, therefore, sensibly err in rejecting any advantage to be derived from this arrangement as insignificant.[47] [47] See Peclet′s Traité de l′Eclairage, p. 302, from which fig. 46 is copied. ~Mr Barlow′s Spherical Mirrors.~