7_th_, There may also, in certain situations, be some risk arising from irregularity in the distances at which the same fixed catoptric light can be seen in the different azimuths. This defect, of course, does not exist in the dioptric light. ~Advantages and disadvantages of both systems under certain circumstances.~ There can be little doubt, that the more fully the system of FRESNEL is understood, the more certainly will it be preferred to the catoptric system of illuminating lighthouses, at least in those countries where this important branch of administration is conducted with the care and solicitude which it deserves. It must not, however, be imagined, that there are no circumstances in which the catoptric system is not absolutely preferable to illumination by means of lenses. We have hitherto attended only to horizontal divergence and its effects, and this is unquestionably the more important view; but the consideration of vertical divergence must not be altogether overlooked. Now, while it is obvious that vertical divergence, at least above the horizon, involves a total loss of the light which escapes uselessly upwards into space, it is no less true, that if the sheet of light which reaches the most distant horizon of the lighthouse, however brilliant, were as thin as the absence of all vertical divergence would imply, it would be practically useless; and some measure of dispersion in the arc _below_ the horizon is therefore absolutely indispensable to constitute a really useful light. In the reflector, the greatest vertical divergence below the horizontal plane of the focus is 16° 8′, and that of the lens is about 4° 30′.