LAMP

LAMP, p. 67. of this volume) will be expressed by the fraction $\backslash frac\{1\}\{100^2\}\; =\; \backslash frac\{1\}\{10000\}$; and the relative intensity of any other light which is compared with it, may be found by the following proportion: Calling this light B, putting $y\; =$ its intensity at its source, and $n\; =$ its distance from the field of the photometer, expressed in

English inches, as it is $\backslash frac\{y\}\{n^2\}\; =\; \backslash frac\{x\}\{m^2\}$, as was shown in the article LAMP referred to; or, instead of $\backslash frac\{x\}\{m^2\}$, writing its value $=\; \backslash frac\{1\}\{10000\}$, it will be $\backslash frac\{y\}\{n^2\}\; =\; \backslash frac\{1\}\{10000\}$; and consequently $y$ is to 1 as $n^2$ is to 10000; or the intensity of the light B at its source, is to the intensity of the standard light A at its source, as the square of the distance of the light B from the middle of the field of the instrument, expressed in inches, is to 10000; and hence it is

Or, if the light of the sun, or that of the moon, be compared with the light of a given lamp or candle C, the result of such comparison may best be expressed in words, by saying, that the light of the celestial luminary in question, at the surface of the earth, or, which is the same thing, at the field of the photometer, is equal to the light of the given lamp or candle, at the distance found by the experiment; or, putting $a\; =$ the intensity of the light of this lamp C at its source, and $p\; =$ its distance, in inches, from the field, when the shadows corresponding to this light, and that corresponding to the celestial luminary in question, are found to be of equal densities, and putting $z\; =$ the intensity of the rays of the luminary at the surface of the earth, the result of the experiment may be expressed thus, $z\; =\; \backslash frac\{a\}\{p^2\}$;

or the real value of $a$ being determined by a particular experiment, made expressly for that purpose with the standard lamp, that value may be written instead of it. When the standard-lamp itself is made use of, instead of the lamp C, then the value of A will be 1.

The Count's first attempts with his photometer were to determine how far it might be possible to ascertain, by

by direct experiments, the certainty of the assumed law of the diminution of the intensity of the light emitted by luminous bodies; namely, that the intensity of the light is everywhere as the squares of the distances from the luminous body inversely. As it is obvious that this law can hold good only when the light is propagated through perfectly transparent spaces, so that its intensity is weakened merely by the divergency of its rays, he instituted a set of experiments to ascertain the transparency of the air and other mediums.

With this view, two equal wax candles, well trimmed, and which were found, by a previous experiment, to burn with exactly the same degree of brightness, were placed together, on one side, before the photometer, and their united light was counterbalanced by the light of an Argand's lamp, well trimmed, and burning very equally, placed on the other side over against them. The lamp was placed at the distance of 100 inches from the field of the photometer, and it was found that the two burning candles (which were placed as near together as possible, without their flames affecting each other by the currents of air they produced) were just able to counterbalance the light of the lamp at the field of the photometer, when they were placed at the distance of 60.8 inches from that field. One of the candles being now taken away and extinguished, the other was brought nearer to the field of the instrument, till its light was found to be just able, singly, to counterbalance the light of the lamp; and thus was found to happen when it had arrived at the distance of 43.4 inches. In this experiment, as the candles burnt with equal brightness, it is evident that the intensities of their united and single lights were as 2 to 1, and in that proportion ought, according to the assumed theory, the squares of the distances, 60.8 and 43.4, to be; and, in fact, $60.8^2\; =\; 3696.64$ is to $43.4^2\; =\; 1883.56$ as 2 is to 1 very nearly.

Again, in another experiment, the distances were,
With two candles = 54 inches. Square = 2916
With one candle = 38.6 . . . = 1489.96

Upon another trial,

With two candles = 54.6 inches. Square = 2981.16
With one candle = 39.7 . . . = 1576.09

And, in the fourth experiment,

With two candles = 58.4 inches. Square = 3410.56
With one candle = 42.2 . . . = 1780.84

And, taking the mean of the results of these four experiments,

which again are very nearly as 2 to 1.

With regard to these experiments, it may be observed, that were the resistance of the air to light, or the diminution of the light from the imperfect transparency of air, sensible within the limits of the inconsiderable distances at which the candles were placed from the photometer, in that case the distance of the

two equal lights united ought to be, to the distance of one of them single, in a ratio less than that of the square root of 2 to the square root of 1. For if the intensity of a light emitted by a luminous body, in a space void of all resistance, be diminished in the proportion of the squares of the distances, it must of necessity be diminished in a still higher ratio when the light passes thro' a resisting medium, or one which is not perfectly transparent; and from the difference of those ratios, namely, that of the squares of the distances, and that other higher ratio found by the experiment, the resistance of the medium might be ascertained. This he took much pains to do with respect to air, but did not succeed; the transparency of air being so great, that the diminution which light suffers in passing through a few inches, or even through several feet of it, is not sensible.

Having found, upon repeated trials, that the light of a lamp, properly trimmed, is incomparably more equal than that of a candle, whose wick, continually growing longer, renders its light extremely fluctuating, he substituted lamps to candles in these experiments, and made such other variations in the manner of conducting them as he thought bid fair to lead to a discovery of the resistance of the air to light, were it possible to render that resistance sensible within the confined limits of his machinery. But the results of them, so far from affording means for ascertaining the resistance of the air to light, do not even indicate any resistance at all; on the contrary, it might almost be inferred, from some of them, that the intensity of the light emitted by a luminous body in air is diminished in a ratio less than that of the squares of the distances; but as such a conclusion would involve an evident absurdity, namely, that light moving in air, its absolute quantity, instead of being diminished, actually goes on to increase, that conclusion can by no means be admitted.

Why not? Theories must give place to facts; and if this fact can be fairly ascertained, instead of rejecting the conclusion, we ought certainly to rectify our notions of light, the nature of which we believe no man fully comprehends. Who can take it upon him to say, that the substance of light is not latent in the atmosphere, as heat or caloric is now acknowledged to be latent, and that the agency of the former is not called forth by the passage of a ray through a portion of air, as the agency of the latter is known to be excited by the combination of oxygen with any combustible substance? See CHEMISTRY, n° 293, Suppl.

The ingenious author's experiments all conspired to shew that the resistance of the air to light is too inconsiderable to be perceptible, and that the assumed law of the diminution of the intensity of light may be depended upon with safety. He admits, however, that means may be found for rendering the air's resistance to light apparent; and he seems to have thought of the very means which occurred for this purpose to M. de Saufure.

That eminent philosopher, wishing to ascertain the transparency of the atmosphere, by measuring the distances at which determined objects cease to be visible, perceived at once that his end would be attained, if he should find objects of which the disappearance might be accurately determined. Accordingly, after many trials, he found that the moment of disappearance can be observed with much greater accuracy when a black object

object is placed on a white ground, than when a white object is placed on a black ground; that the accuracy was still greater when the observation was made in the sun than in the shade; and that even a still greater degree of accuracy was obtained, when the white space surrounding a black circle, was itself surrounded by a circle or ground of a dark colour. This last circumstance was particularly remarkable, and an observation quite new.

If a circle totally black, of about two lines in diameter, be fastened on the middle of a large sheet of paper or pasteboard, and if this paper or pasteboard be placed in such a manner as to be exposed fully to the light of the sun, if you then approach it at the distance of three or four feet, and afterwards gradually recede from it, keeping your eye constantly directed towards the black circle, it will appear always to decrease in size the farther you retire from it, and at the distance of 33 or 34 feet will have the appearance of a point. If you continue still to recede, you will see it again enlarge itself; and it will seem to form a kind of cloud, the darkness of which decreases more and more according as the circumference becomes enlarged. The cloud will appear still to increase in size the farther you remove from it; but at length it will totally disappear. The moment of the disappearance, however, cannot be accurately ascertained; and the more experiments were repeated the more were the results different.

M. de Saussure, having reflected for a long time on the means of remedying this inconvenience, saw clearly, that, as long as this cloud took place, no accuracy could be obtained; and he discovered that it appeared in consequence of the contrast formed by the white parts which were at the greatest distance from the black circle. He thence concluded, that if the ground was left white near this circle, and the parts of the pasteboard at the greatest distance from it were covered with a dark colour, the cloud would no longer be visible, or at least almost totally disappear.

This conjecture was confirmed by experiment. M. de Saussure left a white space around the black circle equal in breadth to its diameter, by placing a circle of black paper a line in diameter on the middle of a white circle three lines in diameter, so that the black circle was only surrounded by a white ring a line in breadth. The whole was pasted upon a green ground. A green colour was chosen, because it was dark enough to make the cloud disappear, and the easiest to be procured.

The black circle, surrounded in this manner with white on a green ground, disappeared at a much less distance than when it was on a white ground of a large size.

If a perfectly black circle, a line in diameter, be pasted on the middle of a white ground exposed to the open light, it may be observed at the distance of from 44 to 45 feet; but if this circle be surrounded by a white ring a line in breadth, while the rest of the ground is green, all sight of it is lost at the distance of only 15$\backslash frac\{1\}\{2\}$ feet.

According to these principles M. de Saussure delineated several black circles, the diameters of which increased in a geometrical progression, the exponent of which was $\backslash frac\{1\}\{2\}$. His smallest circle was $\backslash frac\{1\}\{2\}$ or 0.2 of a line in diameter; the second 0.3; the third, 0.45; and so on to the sixteenth, which was 87.527, or about 7 inches 3$\backslash frac\{1\}\{2\}$ lines. Each of these circles was surrounded

by a white ring, the breadth of which was equal to the diameter of the circle, and the whole was pasted on a green ground.

M. de Saussure, for his experiments, selected a straight road or plain of about 1200 or 1500 feet in circumference, which towards the north was bounded by trees or an ascent. Those who repeat them, however, must pay attention to the following remarks: When a person retires backwards, keeping his eye constantly fixed on the pasteboard, the eye becomes fatigued, and soon ceases to perceive the circle; as soon therefore as it ceases to be distinguishable, you must suffer your eyes to rest; not, however, by shutting them, for they would when again opened be dazzled by the light, but by turning them gradually to some less illuminated object in the horizon. When you have done this for about half a minute, and again directed your eyes to the pasteboard, the circle will be again visible, and you must continue to recede till it disappear once more. You must then let your eyes rest a second time in order to look at the circle again, and continue in this manner till the circle becomes actually invisible.

If you wish to find an accurate expression for the want of transparency, you must employ a number of circles, the diameters of which increase according to a certain progression; and a comparison of the distances at which they disappear will give the law according to which the transparency of the atmosphere decreases at different distances. If you wish to compare the transparency of the atmosphere on two days, or in two different places, two circles will be sufficient for the experiment.

According to these principles, M. de Saussure caused to be prepared a piece of white linen cloth eight feet square. In the middle of this square he sewed a perfect circle, two feet in diameter, of beautiful black wool; around this circle he left a white ring two feet in breadth, and the rest of the square was covered with pale green. In the like manner, and of the same materials, he prepared another square; which was, however, equal to only $\backslash frac\{1\}\{2\}$ of the size of the former, so that each side of it was 8 inches; the black circle in the middle was two inches in diameter, and the white space around the circle was 2 inches also.

If two squares of this kind be suspended vertically and parallel to each other, so that they may be both illuminated in an equal degree by the sun; and if the atmosphere, at the moment when the experiment is made, be perfectly transparent, the circle of the large square, which is twelve times the size of the other, must be seen at twelve times the distance. In M. de Saussure's experiments the small circle disappeared at the distance of 314 feet, and the large one at the distance of 3,88 feet, whereas it should have disappeared at the distance of 3768. The atmosphere, therefore, was not perfectly transparent. This arose from the thin vapours which at that time were floating in it. M. de Saussure, as we have observed, calls his instrument a diaphanometer; but as it answers one of the purposes of a photometer, we trust our readers will not consider this account of it as a digression.

To return to Count Rumford. From a number of experiments made with his photometer, he found that, by passing through a pane of fine, clear, well polished glass, such as is commonly made use of in the construction of looking-glasses, light loses, 1973 of its whole quantity,

quantity, i. e. of the quantity which impinged on the glass; that when light is made to pass through two panes of such glass standing parallel, but not touching each other, the loss is, 3184 of the whole; and that in passing through a very thin, clear, colourless pane of window-glass, the loss is only, 1263. Hence he infers, that this apparatus might be very usefully employed by the optician, to determine the degree of transparency of glass, and direct his choice in the provision of that important article of his trade. The loss of light when reflected from the very best plain glass mirror, the author ascertained, by five experiments, to be $\backslash frac\{1\}\{2\}$d of the whole which fell upon the mirror.