Faraday report to Trinity House   October 1836

Report of Professor M. Faraday, on experiments relative to the penetrating power of Lights, through such obstructions as Fog, Mist, &c., dated October, 1836.

The consideration of the various proposals for the production or direction of Light, which have already come before me, either directly or indirectly, in consequence of my having the honor of being connected with the Trinity Corporation, has led me to observe, that, in most cases, one great point proposed, is to obtain penetrating power, through the obscurity which always exists in a greater or smaller proportion in the Atmosphere; and which sometimes rises to so high a degree, as to render invisible the brightest and most luminous object, though placed at a very small distance from the eye. It is at such times as these, indeed, that Light-Houses would have one of their greatest uses, if the luminaries in them could be made effectually to pierce the obscurity with their rays; and as new proposals for Lights are brought forward, it is probable, that this object will be the chief one set forth as of easy, or at least possible attainment: as indeed it would be now the most important one to obtain.

These considerations led me to desire the acquirement of some general results or principles, upon which the mind might rest, when called upon to judge of the probable effects of any proposed method of rendering an object visible through a haze; and though aware that the penetrating power of light through obscurity is a subject which can, in a considerable degree, be judged of from scientific considerations and principles alone; yet as the subject of Light-Houses is altogether a practical one, I thought it far more desirable to obtain, if possible, results of a practical nature under the form of experiments, which might supply direct evidence to the observer, than to trust altogether to deductions from acknowledged principles. I was thus led insensibly into very numerous experiments, a few of which, with their evident consequences, I have the honor of submitting in the present report.

My first object was to obtain an obscure, translucent medium, which should perfectly represent the action of a Mist or Cloud on light; which yet might be apportioned in any given measured quantity at pleasure; and could also be rendered constant for an observation, or, upon occasion, for a long series of observations; and, as natural Cloud or Fog, was at once excluded, because of it’s shifting character, both as to place and degree, and the utter ignorance in which an Experimenter would be left as to the State of it’s intermediate parts, I was driven, in the attainment of my object, to artificial means.

I first tried to make an artificial Fog or Smoke, not easily condensible [sic], uniform, and confinable in glass vessels, so as to supply the means of measuring out certain quantities or thicknesses at pleasure. Such a Fog, I produced by chemical means; but it was impossible to render it permanently uniform for a time sufficiently long to allow of accurate arrangements and observations. Still, the results which I did obtain were found to agree well with those to be given in the sequel, which were procured by other means.

White, translucent fluids, were then employed in several preliminary experiments. They gave results agreeing generally with those yet to come; but not being convenient in use, were dismissed for a solid substance, now to be described.

There is a material known to Artists by the name of Tracing Paper. The kind I selected consisted of very thin, fine, uniform paper, which had been oiled and pressed and was so nearly transparent, that when laid on a printed page, it offered scarcely a sensible obstruction to the reading of it, and was so uniform that many sheets might be selected, equal in the degree of translucency in every part, and to each other. The light of a candle, several hundred feet off, was able to pierce through one, two, or even three thicknesses of this Paper.

Assuming that this Paper might in single thicknesses be allowed to represent a certain constant, and standard degree of obscurity, arising from Mist or Cloud, it was evident that great facility as to the measurement of the obscuration, or rather, as to the measurement of the interposed, and obscuring object could be obtained by it’s use; but before arriving at this conclusion it was also evident, that the great difference between an uniform medium like Mist, or Fog, and a mixed medium, consisting of alternate strata of transparent Paper, and clear air, would require to be examined, that it might be ascertained whether such difference had any effect on the results of the contemplated enquiry.

From thirty to fifty Sheets of the paper were therefore procured, and suspended parallel to each other in one row, so that light proceeding from a lamp at one extremity of the row might pass through them all before it came to the eye at the other extremity; and then the sheets were placed in various positions, and the light, which passed through to the eye, observed. Sometimes they were equi-distant from each other throughout; sometimes a parcel were placed together near the light the rest being stationed at intervals; and sometimes, they were brought altogether near the eye, or near the light, or into other positions. In all these cases, they represented, as it were the elements of a cloud or mist, but variously disposed; and the result was, that, though when the variations were very great the quantity of light passing through an equal number of sheets, was not the same, (an effect mainly dependent upon the want of lateral extension of the screens), yet, that when the variations were small, no apparent alteration in the transmitted light occurred. Thus, it made no sensible difference, whether, when the screens were together in one bundle, that bundle was so loose, that the first screen was two or three inches from the last, or whether the screens were so close together, that the distance was less than a quarter of an inch, or as little as possible; equal quantities of light passed through; for equal obscuration of the light by the intervention of the same number of screens was obtained.

These results were sufficient to justify the general conclusion that such paper might be taken as producing the effects of Mist or Cloud; and though in a space filled by Mist, there is great diffusion of the light, so that much passes laterally; and much also of that which comes from the luminary to the eye passes through a circuitous course, and is at last received from a direction which in fact is greatly on one side of the direction of the light, which of course can not be the case to any considerable extent in the photometer; yet, that is a consequence of the extent of misty space through which the ray has to pass, and is compensated for, where, as in the photometer, that space is compressed so that it’s depth is but a very small portion of the lateral extent. It has already been found that slight, or even considerable differences, in the vicinity of the successive layers of paper, intended to be used in the instruments to be constructed, did not interfere, with the general results obtained; and therefore, the addition together of one, two, or three thicknesses of paper, may be assumed as equivalent to the measuring out of one, two, or three degrees of an obscuring agent generally.

Having proceeded thus far, I next endeavoured to construct a photometer with this paper, which should have this advantage above the usual photometers, (at least, as respects one of the great uses of Light-Houses,) that it should give indications depending on the direct observation of the penetrating power of a light through hazy obscurity; and I was the more encouraged to hope for ultimate success, by finding that two continental Philosophers, namely Lampadues¹, and Horner², had proposed photometers upon similar principles, (in Bibliothéque Universelle November 1817 page 162³.).-

The first that I made consisted of a little cylindrical chamber, open at the back and front, into which, discs of the paper already described, could be introduced in any number and the light looked at through them. The discs were made into collections of 2, 3, 5, 10, 20, 30, 40, 50 thicknesses each, and numbered, so that by the varied associations of these and single discs, any required combination could be easily obtained. A single thickness of the paper, i.e., a single disc, I called one degree of obscuration; ten discs 10°; and so on in proportion to the number. All light was prevented from passing by the edges of the discs when in the box, and a tube with a lens of short focus was applied to the observing side of the photometer, so as to bring the surface of the posterior disc into distinct vision, when the eye was applied to the aperture. The whole is about the size of a small opera glass.

The use of this instrument is in it’s nature very simple. A light, as for instance a candle, is placed at a certain distance, and then the eye with the photometer applied to it, directed towards the light. If the light freely pervades the discs of paper already in the chamber, so as to render that nearest the eye very visible, more discs are added, until the number is such as that the eye can barely perceive the last by the light passing through it. To assist this observation, there is a small opaque bar passing over the middle of the discs, and when the eye can but just perceive this dark line upon the feebly illuminated ground, the number of discs in the box, represents the degrees of obscurity requisite to extinguish the light of that candle at that distance.

Then if a lamp be placed at the same distance, and the observation be made in the same way, the number of degrees now necessary to extinguish the light which is passing towards the eye, gives the penetrating power of the lamp: and by comparing these, with those of the former observation, the relative penetrating forces of a lamp and a candle are obtained. Or if the lamp alone be taken, and whilst burning steadily be observed by the photometer at distances, which are as 1: 2: and 3 to each other; then the number of degrees at the three stations, corresponding to the extinction of the rays, will indicate the penetrating powers of three lights, which are to each other, as 9: 4: and 1.

This instrument has the great advantages of simplicity and compactness; but was found very inconvenient as to the arrangement of the requisite number of degrees, in consequence of the necessity of opening the box during the adjustment, for the change, even, of a single degree; and also, because the exposure of the number of discs necessary to make the variations, rendered them liable to accidents; and as the previous experiments seemed to show that, the discs, if near each other, did not require to be in very close contact, I constructed a second photometer, similar to the first in all things, except, that though the tens of degrees were put into the box as before, the units from 1 to 9 were brought between the eye and the light, by means of a slide; and being thus capable of variation, whilst the eye was actually observing the effect produced, an observation was obtained, not only with more readiness, but also more exact in it’s nature.

But as the work proceeded and observations became more refined, new causes of error presented themselves, and new precautions were needed. It hardly requires the remark, that, the eye is so variable in it’s sensibility, as to differ, very much in it’s power of perception at different times; or, that it is so easily affected in this respect, as in a moment to have it’s perception changed. Thus a tint of light, which can be perceived with facility by a person who has been for a short time in an obscure or dark room, or whose eyes have been closed, will be quite invisible to one coming from daylight or a well illuminated place; and the very person to whom a degree of light in the photometer, is, at one moment distinctly visible, will, if he suddenly look at the illuminated objects around him, at the next moment be quite unable to distinguish it. I found these effects rise to such a degree, with an eye which had been rendered sensible by being some time in the dark, that if, whilst the eye was applied to the photometer, the degrees were changed so as to allow more light to pass, the organ was so much affected by the change, that it could not tell when the removed degrees were restored again:- and if it happened that the eye was removed from the photometer, and for a moment directed toward the unshaded light, then on returning to the photometer, the organ did not seem as if it had the same degree of light before it, although nothing there had been changed.

Thus the eye could not be trusted alone as the judge of equal degrees of obscuration at different times, even when the interval of time was very short, and the circumstances were of considerable uniformity; much less could confidence be reposed in it at distant times, and under varying conditions. But, still, considering the object in view as very important, I bent my endeavours, to the procuring of a standard of light, by which the eye might be regulated in it’s judgment, and to which the tint produced by the degrees of obscurity employed might be compared. This gave rise to a third photometer, much more complicated in it’s details though the same in principle as the former.

In this photometer the eye observes two portions of surface at once, placed side by side, and consisting each of the prepared paper already spoken of, illuminated from the opposite side. One of these surfaces is, in fact, the surface of the degrees which measure the penetrating power of the light under investigation; but the degrees themselves are brought into position in a different manner to that before adopted. There are two scales, moving vertically, the one contains successive folds of the translucent paper in the following order, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; and the other, 0, 10, 20, 30, 40, 50; and from the manner in which these are placed and adjusted, any number of the thicknesses of the paper, or degrees, from 1° to 59°, can be brought between the eye and the light with the utmost facility. A tube, blackened inside, is always used to cut off lateral rays of light, and prevent the passage of any but those from the luminary under examination, to the place of observation. The other surface is that appropriated to the production of a constant and standard degree of illumination, very feeble in itself, but being independent of the eye, intended to be used by that organ as a regulator of it’s perception. This surface, as already said, is the posterior surface of a bundle of twenty or thirty thicknesses of the translucent paper. These are placed over an aperture opening into a dark chamber, about four inches in width, at the further end of which is a dark lanthorn, containing a single round-wicked lamp. The lamp and the chamber are of course divided from each other, but there is a slide in the division, having a circular aperture of a given dimension, and when the lamp in the lanthorn is trimmed and placed before this aperture, the light shines through it, and forms an inverted image of the flame on the side of the dark chamber nearest to the eye, which is easily adjustable, so that the translucent paper in the standard aperture can be brought into the middle or any other part of it. The aperture in the slide is 1/40 of an inch in diameter, and the lamp flame is placed about one third of an inch from it; whilst the translucent paper is about four inches from the aperture. It can easily be shewn, therefore, that, though the flame varies in it’s brightness in different parts, yet if a part only the 1/10 of an inch or even much less, in diameter is of uniform brightness, it may be selected and made use of to illuminate the translucent screen, without any reference to the largeness or smallness of the whole flame, or without being interfered with by slight variations in the distance of the flame from the aperture. It was upon the hopes that a lamp of the same kind, constantly trimmed in the same way, and burning steadily in a quiet chamber would always present a portion of flame of this extent, very nearly indeed, of the same intensity, in the same part, that I rested for final success.

After several trials, I adopted the following quantities as those needful to produce the standard illumination. The lamp was the round-wicked one already mentioned; and the brightest part of the smokeless flame towards the top, was selected for the illumination; the light aperture was 1/40th of an inch in diameter; and there were thirty thicknesses of paper in the opening towards the eye. The degree of illumination therefore, perceived by the eye and to be used as a standard, was that produced by the light from a little circle of flame 1/40th of an inch in diameter, at about 4 inches distance, after it had been obscured by the successive action of thirty thicknesses of the paper. This light was very distinct from perfect darkness, but could not be perceived by an eye in broad daylight. At any time when the standard was required to be raised to a higher degree, it could be done by using another slide, with a larger aperture, or introducing fewer folds of paper into the course of the ray.

The first tests of this instrument were of the following kind. Two Lights of very different intensity, (as a large and a small lamp), were placed at unequal distances and moved, until the shadows thrown by an opaque substance on to a fixed screen, were equal: this is known as the usual, and I think the best, method of comparing lights. When the new photometer was put in the place of the screen, one of the lights observed, and the number of degrees required to be introduced into the aperture, to bring the light to the same degree of obscuration as that on the standard side of the instrument, ascertained, it was found that the same number of degrees produced, in the same place, exactly the same obscuration of the other light. In many repetitions of this experiment the same result was obtained; and thus the two modes agreed in indicating equal intensities for equal lights.

On reversing the procedure, i.e., on first adjusting the distance of the lights by the new photometer until of equal penetrating power, and then observing the strength of shadows cast by the lights at the same distance, the results came near to each other, but not always together as before; for when the photometer would shew equal intensities, the shadows would show a difference; but then, on obtaining the distances by shadows the photometer always agreed with them.

The latter effect indicated a want of sensibility in the instrument, or at least an uncertainty in the obscuration, which would interfere with it’s use as an actual measurer of light, a point greatly to be regretted as the photometer appeared capable of carrying it’s own standard of light with it. I was therefore induced to test it very closely and at great length; that I might remove, if possible, this uncertainty. The result of all these trials is, that the instrument will not serve as a delicate and accurate measurer of light; though it can be rendered available in obtaining highly valuable practical general results.

The principal difficulty which stands in the way of the application of the instrument as a measurer, lies in the uncertainty which the eye is in, with regard to the accordance of the degree of light, sent to that organ, by the two surfaces looked at. When the adjustment of the degrees in an experiment, is so nearly complete, that the luminosity of the surface next the eye is very nearly the same with that of the standard light, then, a doubt arises in the mind which is the darker or lighter of the two; and whilst, by moving the scales 2°, or 3°, the light at the measuring aperture can very evidently be increased or diminished, still the eye is often puzzled to tell, which is in accordance with the standard by it’s side. Nay, more than this, if the two illuminations be left the same and the eye be continually applied to the aperture, so as to suffer from no distraction produced by external light, still the mind is so uncertain, that sometimes it will decide that one surface is rather lighter than the other, and the next moment that it is darker.

This effect I have found produced in the minds of others as well as my own. It occurs also in other arrangements where two illuminated surfaces are to be compared, as in Dr. Ritchie’s⁴ photometer⁵, and also in the ordinary mode of measuring lights by their Shadows. As far as my own observation goes, it is less in the latter case than any other; and for that reason, (as well as others), I consider the mode by shadows as the most accurate at present known.-

A second difficulty is a certain degree of variation in the standard light, dependant upon changes in the size and character of the flame, which, if care be not taken, bring different parts of it before the aperture, varying in intensity from each other. But I feel certain that the principle is good, and that a lamp (probably an Argand), might be easily constructed upon trial, which should, by the aid of the aperture, supply a constant standard. This point, I did not pursue, inasmuch as the photometer was thrown out of use, as an accurate measurer, in independant observations, by the inability of the eye to decide upon the agreement or disagreement of the illuminated surfaces.

Whilst speaking of the difficulties of the instrument, I may refer to another which occurred, for the sake of pointing out how I have been in the habit of avoiding a similar one, when using the method of Measurement by shadows. Lights which are of different intensities differ very much in their tint; they then throw differently coloured shadows, and I also found that in my photometer, the difference was preserved through all the papers, giving at last two illuminated surfaces to look at, of different colours. This difference seriously embarrasses the eye, and increases the uncertainty whether the two portions looked at, are of equal luminosity or not; nor is there any means in my photometer of removing it. In the method by shadows, I think I avoid much of the uncertainty, which the difference in colour of the light occasions, by casting the shadows on to a prepared surface: this is not white but consists of a series of colours in horizontal stripes, about an inch and a half long, and half an inch broad, put one above the other, to the amount of seven or eight, upon a black ground: in this way they form an upright column, about four inches in height, and being covered completely by the two shadows, the effect of the lights under observation is observed, not upon white alone, (though that is of course present amongst the colours), but on the coloured surfaces also; and as there are reds, blues, yellows, greens &c. the difference of colour in the light which will exalt the effect on one side with one colour, will exalt it on the other side with another. I have two series of these colours, the one consisting of very pale tints, but little removed from white; the other of more decided colours.

I will allow myself to make one other observation on the circumstances which interfere with the accurate measurement of light, by the methods now practised, and then dismiss the subject. When a light is to be measured by my photometer; or when two lights are to be compared by Ritchie’s photometer, it is necessary that the lights should be entirely freed from the neighbourhood of substances which can reflect or send light towards the instrument; or else, that extreme precautions should be taken to make the circumstances in every case have a proportionate effect, which can hardly ever be accurately done. Thus a wall beyond the light throws light towards the instrument, and by adding it’s effect to the effect of the light to be measured, very often confuses the results. But this effect is of no consequence in the method by shadows; for it is very easy so to arrange that these extra rays shall fall equally on the two shadows, as they are always side by side and under the same circumstances; and though it is best, when measuring two lights in this way to have no other light than that of the luminaries present; still I have found experimentally, that a great flood of extra light does not disturb the equality of the shaded surfaces. I threw the shadows of a small, and of a powerful lamp, on to one of the coloured surfaces before spoken of, adjusting the distances until they were equal, there being no other light in the place; I then gradually raised six gas Argand burner lamps up to their highest brilliancy, letting their light shine full upon the place of the shadows; and though, as this general light became more intense, the shadows became more and more faint, still their equality was preserved throughout the whole of the gradual change. This circumstance gives me great confidence in the mode of measuring lights by shadows, and will induce me on some future occasion to combine with it, a standard light measured out by an aperture in the manner I have already described.

I will now proceed to the general results obtained with regard to penetration of light through a Mist, Fog, Cloud, or other similar obscurity. These results have been procured with lights unassociated with mirrors, lenses &c., for they are of course quite independant of any such association; and when ascertained, are equally true with these compound arrangements, as with a single light. The penetrating power of a beam of light does not at all depend upon it’s originating directly from a naked powerful luminary, or it’s issuing from a reflector or lens, in the focus of which a smaller light is placed; provided that, in both cases, the beam is of equal force; and as beams from naked lights are far more uniform and regular, than those from catoptric or dioptric arrangements, the former were preferred for the experiments.

Six Argand gas burners, were arranged in a line near together, in the Theatre of the Royal Institution, so as to burn with equal flames, and allow of a gradual extinction, one by one, the rest retaining their original brilliancy unchanged. A point equi-distant from them all, twenty-eight feet off was marked, and my photometer placed there so that the light of all the flames fell upon the measuring degrees of the scale, all other light being excluded from the room; and then the number of thicknesses of paper or portions of obscuring agent, which I have elsewhere called degrees, requisite to bring the light from any number of these lamps down to the constant standard, was observed;- the table, below. expresses these results.

These results shew that an extremely rapid extinction of light takes place by accumulations of the obscuring agent, the extinction being in a geometrical ratio for equal increments of the translucent medium. Thus the light of one Argand lamp could pierce through 28° of obscurity but the addition of a second portion of light, equal to the first, was only able to penetrate 3½ degrees more, or but one eighth of that obstruction which the first portion of light had overcome; and even when the light had been increased to six times it’s first quantity, the increase of penetrating power was little more than half as much as that which the single light possessed. Hence is manifest, the extraordinary rapidity with which light is extinguished by small additions to the thickness of a Mist, or Fog; or to the length of the interval through which the ray has to pass: and indeed every one must have noticed in a foggy night, how rapidly a light has disappeared from the eye, as the observer has increased his distance from it.

Another illustration of the rapid extinction of light may be given, in the following series of results, in which the light and the photometer were retained at the constant distance of eighteen feet, ten inches, but the light itself varied so as to give extreme differences in power. A wax-candle flame was able to pierce through the obscurity of 14°. The Trinity standard Argand lamp was able to penetrate 27° or nearly double the former. The Bude Light which gives between two and three times the light of the Argand lamp, could only pierce though 32°; and the light of the French lamp of four concentric wicks, burning extremely well was only able to penetrate 42°, or three times what was done by the flame of the wax candle. Other cases of a similar kind I could quote in abundance, if that were necessary.

I then varied the mode of testing this striking result, respecting the rapid extinction of light by equal increments of obscurity, in the following manner. A light, or lights, were left to burn regularly; the photometer placed at different measured distances, and the number of degrees required for obscuration noticed. As the light would vary inversely as the square of the distance, the quantity at the first surface of the measuring degrees could always be deduced; and as the quantity at the last surface, or that nearest the eye, was always brought as nearly as possible to the same standard, and as the number of intervening degrees of obscurity were known, it was easy to deduce the direct relation between the light and its penetrating power.

The above set of results, illustrates the effect in question; but perhaps the following are more striking. They were obtained with a steady Argand lamp flame, and the obscurity was increased by regular degrees, so as to give the necessary corresponding intensity of light required to penetrate it.

Hence it appears that the light which could penetrate 10° required to be increased more than four and a half fold before it could penetrate 20°: that upon a second addition of obscuring agency to the same amount, the last light had to be again increased nearly four and a half fold so as to raise it to nearly twenty times the first light:- that upon the third increase of obscuring power by the same quantity, the last light had to be increased again in the same ratio. It results also, that the light which could penetrate through 10° of such obscurity, must be increased to four and a half times it’s amount, before it could pierce through 20°:- that that which could pierce through 20° of obscurity, or mist equal to it, must be exalted twenty times before it could penetrate 40°:- and that the light able to send rays though 30° of such obscurity would require to be raised in the enormous proportion of one hundred and forty fold, before it could do the same through twice that obscuring agent. The last case amounts in another form to this; supposing a uniform fog to exist which in each fathom had the degree of obscurity belonging to a single sheet of the paper* I have used in the instrument; and that an Argand lamp light could just penetrate through thirty fathoms of it; upon only increasing the distance to sixty fathoms, the power of a hundred and forty Argand lamps would be required to produce the same effect, in relation to the obscurity alone of the air:- but as the intensity of the light is diminished, as the square of the distance by the circumstance of distance only, this quantity of one hundred and forty would be required to be increased four fold to compensate for that circumstance.

It is not difficult to see the reason of this rapid decrease of light, as it passes through more and more of a fog, or other similar impediment; for suppose a lamp burning steadily, and that sheets of the paper I have described, or any other obscuring agent, are used in equal portions; and let us assume, what is easily attainable by adjustment; that each portion shall extinguish about half the light which falls on it; then one portion will diminish the light of the ray from the lamp to one half; a second portion will bring it down to the half of the half, or one fourth of the original light; a third portion will reduce it to one eighth; a fourth to one sixteenth; a fifth to one thirtysecondth; a sixth to one sixtyfourth; a seventh to 1/128th; and eighth to 1/256th; a ninth to 1/512th; and a tenth to 1/1024th. Or if it were required that the light should in all cases pierce through these different added portions of obscurity, until the last was always illuminated to the same degree at it’s posterior surface, then the source of light would require to be increased as the denominators of the fractions above. I do not mean to assert by the above illustration, that this ratio is exact, or that no circumstance interferes with it’s simplicity; but, that as the obscurity increases in an arithmetical ratio, the light necessary to penetrate it increases in a geometrical ratio, which is nearly as simple as the above:- I will now give one tabular result from amongst those which I have obtained, for the purpose of supplying the actual ratios of extinction observed in experiments, where the single degree of obscurity was one thickness of the translucent paper before described. The first two or three results with small numbers of discs, I know to be inaccurate; for, amongst other difficulties, I could hardly obtain the distances in perfect darkness, which I required; other causes of error also interfered, and as I have before said, the instrument after all, can only give approximations to the true results.

I need hardly refer to the many cases of common occurrence, which illustrate the rapid extinction, occasioned by mist, cloud, fog, or similar obscuring causes, on rays of light. Even in a clear evening, how great a difference is produced on the Sun’s rays at his setting, to that which existed when he was on the Meridian, solely because of an effect of this kind. Again a cloud of very moderate thickness, is able to hide the Sun’s disc from us even at Mid-day, and diffuse his light, so that we know not in what direction he is; and fogs have not unfrequently occurred, which have caused all loss of the Sun’s figure, and of by far the greatest portion of his light, before the rays had passed through thirty yards of them. But suppose the fog, or mist were so thin, that it required a mile of it to produce this effect, (and such mists are not at all uncommon), still it would be impossible to penetrate such a barrier to light effectually, by any artificial arrangement; for if a ball of lime were placed at that distance from the observer, and heated by the oxy-hydrogen flame up to the high temperature which Lieutenant Drummond has applied, in his illuminating apparatus⁶, it would require to be at least 45 feet in diameter, to produce an effect equal to that of the Sun; or if accurately adjusted in the focus of a mirror, would need an arrangement equivalent to such a ball.

It became a question, resolvable by the photometer I have described, whether, a small intense light and a large duller light, possessed the same relation as regarded penetrating power: this I proceeded to examine, as far as I could practically. In the first place, I found that a bright Bude light gave the same general result of rapid extinction by the addition of successive portions of obscuring agency, as the candle, and the Argand lamp had done. Then, by comparing three Argand lamps acting together on the photometer with a Bude lamp, and adjusting the former so that they produced the same effect of penetration at the same distance as the Bude light did; when the distance was changed for any other, greater or less, but alike for both sets of lights, it was found that the degrees which obscured the rays from the one, also exactly obscured the rays from the other.

Thus it appears, that, as to penetrating power, quantity and intensity of light are convertible qualities, and are subject to exactly the same kind of action by fog, Mist, or cloud. And this agrees with the general fact before described, namely, that when two lights of different intensity are made by adjustment of the distances to give equal shadows, they are found to give equal penetrating power in the instrument also. The results, in fact, are necessary consequences of our modes of measuring lights by comparison of their shadows; and so long as that method is resorted to, to give the intensity or illuminating ratio of two lights, their penetrating force will be found to be in proportion. If two luminaries, therefore, are equal in the quantities of light which emanate from them; they will have the same penetrating power, however different they may be in intensity.

As in the common Argand lamp, the French lamp, the Bude lamp and others, one part of the flame is behind another, I made a few experiments with the Bude light, placed edgeways and sideways, to ascertain whether that circumstance caused any sensible difference; but I could not find that it did. For the same penetrating powers were given for it in either position, whilst the distance remained the same.

The conclusion I have arrived at from these experiments is, that it would be vain to expect to obtain a light, which, either by itself or in association with catoptric or dioptric arrangements, should be able to penetrate to any great distance through a mist or fog of considerable thickness. On the other hand, it must not be supposed that I intend to imply, that with regard to a thin haze or veil of vapour, a large and a small light, or a bright and a dull light, are the same. There can of course be no doubt that if two lights are employed being in the proportion of 1:10; that the large or bright light will penetrate a haze which will completely obscure the smaller one. But the fact is, that the superiority of a powerful light over a feeble one, as to the distance to which it can send its rays, being at its maximum in a perfectly clear atmosphere, any introduction of haze into the atmosphere tends to make this superiority less, at the same time that it diminishes the distance to which the rays from either of these lights can penetrate. As the haze increases into a mist or fog, these effects increase with it, until at last the strong light penetrates very little further than the weak one, and neither of them sends it’s rays to any considerable distance.

I shall conclude this report by appending to it some curves roughly drawn, illustrating the ratio of the diminution of light by haze; and the relative distances to which lights of different powers would penetrate such hazy or foggy atmospheres⁷.

(signed) M. Faraday.

Royal Institution | October 1836.

*Note. Unless the ray be a very feeble one, a single thickness of this paper is able on the average to quench about one seventh of the light impinging upon it.