Nov. 1 8, 1886] 



NA TURE 



61 



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 ob- 

 struction in passing through another equal length of air, and so 

 forth. Thus, if this fraction is called a, and / is the intensity at 

 any point of a beam of parallel rays, such as a beam of sunlight 

 reflected froai 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 la", and at a distance of d miles to la''. 

 But divergent light, such as is even the most condensed beam 

 from a lighthouse, diminishes also as the square of the distance. 

 Thus, if Z is a lighthouse light whose intensity at one mile 



is La, its intensity at any number of miles, d, is La'' x —..and 



when the combined eflfect of haze and distance is such that its 

 intensity is only equal to that of \ 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 lo8-jet gas-burner, showing as a 

 fixed light of about 14,000 candles, was lost at a distance of lO'g 

 miles, the same light shown in biform would be lost at 1 1 "8 miles, 

 while the corresponding triform and quadriform lights would be 

 lost at I2'5 and I2'8 miles respectively. In a rather thicker 

 haze, in which a single 108-jet gas-burner, showing as a revolv- 

 ing light of 60,000 candles, \\as visible up to 10 miles, but no 

 further, the extreme range of the biform would be 1073 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. 



Light shewn Range in Nautical Miles 



Single loS-jet, M. I. lens ... 2 ... i ... o'5 



Biform ,, ,, ... 211 ... i'05 ... 052 



Triform ,, ,, ... 217 ... ro8 ... 054 



Quadriform ,, ,, ... 2'22 ... 11 ... o"55 



The above results represent the maximum range of the direct 

 beam through uniform haze of lights of the same kind but varying 

 in power. But in certain cases the increase of range gained by 

 increasing the power of the light may be either Ie<s or greater 

 than it is in the foregoing case. 



In the first place, the light which has suffered obstruction is 

 diverted from its direct course but is not lost ; and a portion of 

 this light may reach the eye from a direction slightly different 

 from that of the source of light, producing the impression of a 

 halo or burr. Prof. Stokes, Pres.R.S., who has kindly given 

 me much help in considering this subject, concludes that, 

 especially in a fog in which the particles of water are not very 

 minute, the burr might be .seen at a substantially greater distance 

 than that at which the direct light could be seen. "The 

 intensity of this diffused light will not decrease in geometric 

 progression a^ the distance from the source increases, but rather 

 will tend ultimately to decrease inversely as the square of the 

 distance ; but being so widely spread, there will be danger of its 

 being unperceived unless it be flashy." In this case the more 

 powerful lights would retain in fog more nearly the advantage 

 which they possess in clear weather, in which a fourfold light 

 has double the range of a single light. But since the eye can 

 distinguish between the point of light which is seen by the direct 

 rays and the blurred nimbus, whose properties Prof. Stokes has 

 investigated, the question whether the range of powerful lights is 

 materially increased by the diverted and re-diverted light which 

 surrounds the principal beam could be solved by an appeal to 

 experience. 



In answer to my inquiry whether it often happens that in 

 approaching a lighthouse on a hazy night that which is first seen 

 is an indistinct brightness or halo, not the light itself, and 

 whether this effect is seen at considerable distances or only at 

 short distances, and in what kind of fog, the Deputy Master of 

 the Trinity House tells me that it happens, occasionally, at short 

 ranges, in thick fog or mist, when nothing of the light is seen 

 beyond i or 2 miles. " In clearer weather {i.e., slight haze) this 

 peculiarity is not observable at any range ; it is the direct beam 

 from the lantern (of course lessened and indistinct by reason of 

 the density of the atmosphere) which then comes to the eye of 

 the observer when approaching from seaward." I think, there- 

 fore, it may be concluded that at short distances powerful lights 

 may occasionally have an advantage over feebler lights greater 

 than is indicated by M. A Hard's formula, in consequence 



of the scattered light being less diminished by fog than the 

 direct light. 



There are tvvo other cases in which the formula is not im- 

 mediately applicable ; the second exception being, if the haze is 

 not uniform. This case may be illustrated by taking an extreme 

 example. Suppose that the amount of fog extending 5 miles from 

 a lighthouse were just sufficient to extinguish a light of 6o,o03 

 candles, and that beyond this distance the air were perfectly 

 clear, a light of four times the initial power would have at the 

 margin of the fog four times the minimum visible brightness, and 

 would only disappear altogether at a distance of 10 miles. But, 

 on the other hand, if the fog were thicker further to seaward, 

 the larger light would have scarcely any advantage over the 

 smaller light. 



Thirdly, if the lights compared differ in quality, of which the 

 visible sign is colour, as well as in power. In this case the 

 particles of water of which haze at sea consists (differing from 

 the coloured particles of a London fog) are only likely to exercise 

 a selective action on lights of different refrangibilities when the 

 particles are so small as to be comparable with a wave of light. 

 In a thick mist, in which the particles of water have often a 

 visible magnitude, this effect is probably absent. Clouds are of 

 this character, and sunlight is not reddened by passing through 

 them. But the red colour of the sun when near the horizon, and 

 the assimilation in colour of the electric light to gas-light when 

 seen from a distance through slight atmospheric haze, shows that 

 such haze does interfere with the more refrangible blue rays, to a 

 greater extent than it does with the yellow, orange, and red rays. 

 It is therefore certain that the electric light, which contains a 

 relatively large proportion of the more refrangible rays, suffers a 

 greater loss than the light from gas or oil flames in certain states 

 of the atmosphere. The larger particles of mist or rain probably 

 obstruct light of all sorts in the same degree. If we suppose 

 that the effect of haze is to cut off all the blue and violet rays, 

 the loss to the flame lights would not exceed i or 2 per cent., 

 while that of the electric light, which is perhaps rather bluer 

 than sunlight, may amount to 20 per cent. But this loss, though 

 considerable, would not materially affect the range of the electric 

 light in hazy weather.^ 



It has been claimed as an advantage of nTOltiform lights, 

 comp.ared with the electric arc behind a small lens, that the 

 larger surface of illuminated lens is more favourable to visibility 

 in hazy weather ; and the late Sir W. Siemens gave some 

 countenance to this view. Speaking in the discussion of Sir 

 James Douglass's paper " On the electric light applied to light- 

 house illumination," 1879, he said: — " He had held that, in 

 order to get more penetrating power, not intensity alone, but 

 intensity with quantity as represented by large surface, would be 

 required." M. Allard in his "Note," pp. 10 and II, makes 

 some interesting observations on this subject, but deals rather 

 with visibility at great distances in clear weather than with 

 visibility through haze. I do not know on what grounds, either 

 of theory or observation, the opinion formed by Sir W. Siemens 

 is based. Desiring further information on this and some other 

 points, I have consulted Lord Rayleigh, Sec. R. S., who with 

 Prof. Stokes joined me ia a visit to the South Foreland lights a 

 year ago. I may quote his opinion : — " With the same total 

 brightness of source, and angle of divergence, it can make no 

 difference at a distance (at which the apparent magnitude of the 

 lens is inappreciable), whether the lens be large or small. At 

 smaller distances the advantage might be with the smaller 

 lens. So far as I see, the only advantage that the large 

 lens could ever have would be more room for a bulky 

 light, which, with a small lens, might give too great a 

 divergence." 



While referring to the assistance I have received from Prof. 

 Stokes and Lord Rayleigh, to whom I desire to accord my 

 thanks, I should mention that I have received from both the 

 same emphatic suggestion, that further trial should be made 

 of sudden flashes in fog. Lord Rayleigh writes: "I should 

 like to see proper experiments tried on sudden and periodic 

 flashes, such as might be produced by gunpowder, the periodicity 

 serving for identification and the intermittence being necessary to 



* Since this report was written, a paper has been communicated to the 

 Royai Society by Captain Abney. R.E., F.R.S. ,and Major-General Festing, 

 R.E., F-R.S., giving the result of measurements of the illuminating power 

 of different parts of the spectrum of the electric arc. According to these 

 measurements, the illuminating power of that part of the light from the 

 electric arc which lies beyond the line " E" in the spectrum, including the 

 greater part of the green rays as well as the blue and violet rays, is rather 

 less than one-sixth of the total illuminating power. 



