II. V.—Range of Lights in Hazy Weather THE observations on this subject of the Trinity House Com mittee have served to confirm the conclusions announced by M. Allard in his "Mémoire sur l'intensité et la portée des phares,” 1876, and in his more recent “Notes sur quelques objections relatives à l'emploi de la lumière électrique dans les phares.” The Committee find that the gas and oil lights which are equal in clear weather are equal also in fogs; that in rather dense fog the more powerful light had but little advantage over the less powerful, for example, “the triform electric appearing at 1500 feet, while the quadriform gas and triform oil showed up together a little before the observers reached 1400 feet,” and that the electric light, while suffering, according to the photometric results, a somewhat greater loss in hazy weather than the flame lights, is “visible at a greater distance than the highest powers tried in gas or oil.” Using M. Allard's formula, which appears to rest on well-established physical and physiological data, I have calculated the range in fogs of various degrees of thickness of some of the lights exhibited at the South Foreland. The range of a light, or the limit at which it is just lost or just picked up, is that limit at which its intensity is diminished by distance and haze to the minimum intensity perceptible by a good eye, such as the practised eyes of seamen are. M. Allard gives this minimum intensity, on the authority, of “des expériences qui ont été faites sur ce sujet au Champ de Mars,” as that of 1/100 Carcel at a distance of one kilometre on a perfectly clear night. This corresponds to 1 3 candle at a distance of one nautical mile. When the air is not perfectly clear, its degree of transparency may be expressed by stating the fraction of light which escapes obstruction in passing through a certain length. Of this fraction the same fraction escapes obstruction in passing through another equal length of air, and so forth. Thus, if this fraction is called a, and l is the intensity at any point of a beam of parallel rays, such as a beam of sunlight reflected from a plane mirror, after the beam has traversed a mile of hazy air its intensity is diminished to la, at two miles its intensity is diminished to la2, and at a distance of d miles to lad. But divergent light, such as is even the most condensed beam from a lighthouse, diminishes also as the square of the distance. Thus, if L is a lighthouse light whose intensity at one mile is La, its intensity at any number of miles, d, is Lad × I/d2, and when the combined effect of haze and distance is such that its intensity is only equal to that of 1 3 candle at one mile, at that point the light ceases to be visible. Thus it is possible to calculate for any particular degree of haze what will be the range of any given light. To give some examples:—In a moderate uniform haze such that a single 108-jet gas-burner, showing as a fixed light of about 14,000 candles, was lost at a distance of 10.9 miles, the same light shown in biform would be lost at 11.8 miles, while the corresponding triform and quadriform lights would be lost at 12.5 and 12.8 miles respectively. In a rather thicker haze, in which a single 108-jet gas-burner, showing as a revolving light of 60,000 candles, was visible up to 10 miles, but no further, the extreme range of the biform would be 10.73 miles, of the triform 11.16 miles, of the quadriform 11.48 miles. In still thicker haze the increase of range obtained by increasing the power of the lighthouse light becomes not only absolutely but relatively less.