an apparatus for measuring the intensity of light, and likewise the transparency of the medium through which it passes. Instruments for this purpose have been invented by Count Rumford, M. de Saufure, that eminent mathematician and philosopher Mr John Leslie, and others. We shall content ourselves with describing in this place the photometer of Count Rumford, and the instrument to which Saufure gives the name of diaphanometer. Mr Leslie's is indeed the simplest instrument of the kind of which we have anywhere met with a description; but it measures only the momentary intensities of light; and he who wishes to be informed of its construction, will find that information in the third volume of Nicholson's Philosophical Journal.

Count Rumford, when making the experiments which we have noticed in the article Lamp (Suppl.), was led step by step, to the construction of a very accurate photometer, in which the shadows, instead of being thrown upon a paper spread out upon the window, or side of the room (See page 64 of this volume), are projected upon the inside of the back part of a wooden box 7½ inches wide, 10½ inches long, and 3½ inches deep, in the clear. The light is admitted into it through two horizontal tubes in the front, placed so as to form an angle of 60°; their axes meeting at the centre of the field of the instrument. In the middle of the front of the box, between these two tubes, is an opening thro' which is viewed the field of the photometer (See fig. 1.). This field is formed of a piece of white paper, which is not flattened immediately upon the inside of the back of the box, but is palled upon a small pane of very fine ground glass; and this glass, thus covered, is let down into a groove, made to receive it, in the back of the box. The whole inside of the box, except the field of the instrument, is painted of a deep black dead colour. To the under part of the box is fitted a ball and socket, by which it is attached to a stand which supports it; and the top or lid of it is fitted with hinges, in order that the box may be laid quite open, as often as it is necessary to alter any part of the machinery it contains.

The Count had found it very inconvenient to compare two shadows projected by the same cylinder, as these were either necessarily too far from each other to be compared with certainty, or, when they were nearer, were in part hid from the eye by the cylinder. To remedy this inconvenience, he now makes use of two cylinders, which are placed perpendicularly in the bottom of the box just described, in a line parallel to the back part of it, distant from this back 2½ inches, and from each other 3 inches, measuring from the centres of the cylinders; when the two lights made use of in the experiment are properly placed, these two cylinders project four shadows upon the white paper upon the inside of the back part of the box, or the field of the instrument; two of which shadows are in contact, precisely in the middle of that field, and it is these two alone that are to be attended to. To prevent the attention being distracted by the presence of unnecessary objects, the two outside shadows are made to disappear; which is done by rendering the field of the instrument so narrow, that they fall without it, upon a blackened surface, upon which they are not visible. If the cylinders be each ¼ of an inch in diameter, and 2½ inches in height, it will be quite sufficient that the field be 2½ inches wide; and as an unnecessary height of the field is not only useless, but disadvantageous, as a large surface of white paper not covered by the shadows produces too strong a glare of light, the field ought not to be more than ¼ of an inch higher than the tops of the cylinders. That its dimensions, however, may be occasionally augmented, the covered glass should be made 5½ inches long, and as wide as the box is deep, viz. 3½ inches; since the field of the instrument can be reduced to its proper size by a screen of black palisado, interposed before the anterior surface of this covered glass, and resting immediately upon it. A hole in this palisado, in the form of an oblong square, 1½ inch wide, and two inches high, determines the dimensions, and forms the boundaries of the field. This screen should be large enough to cover the whole inside of the back of the box, and it may be fixed in its place by means of grooves in the sides of the box, into which it may be made to enter. The position of the opening above-mentioned is determined by the height of the cylinders; the top of it being ¼ of an inch higher than the tops of the cylinders; and as the height of it is only two inches, while the height of the cylinders is 2½ inches, it is evident that the shadows of the lower parts of the cylinders do not enter the field. No inconvenience arises from that circumstance; on the contrary, several advantages are derived from that arrangement.

That the lights may be placed with facility and precision, a fine black line is drawn through the middle of the field, from the top to the bottom of it, and another (horizontal) line at right angles to it, at the height of the top of the cylinders. When the tops of the sha-

Suppl. Vol. II. Part I. there is a straight groove, in which a sliding carriage, upon which the light is placed, is drawn along by means of a cord which is fastened to it before and behind, and which, passing over pulleys at each end of the table, goes round a cylinder; which cylinder is furnished with a winch, and is so placed, near the end of the table adjoining the photometer, that the observer can turn it about, without taking his eye from the field of the instrument.

Many advantages are derived from this arrangement: First, the observer can move the lights as he finds necessary, without the help of an assistant, and even without removing his eye from the shadows; secondly, each light is always precisely in the line of direction in which it ought to be, in order that the shadows may be in contact in the middle of the vertical plane of the photometer; and, thirdly, the sliding motion of the lights being perfectly soft and gentle, that motion produces little or no effect upon the lights themselves, either to increase or diminish their brilliancy.

These tables must be placed at an angle of 60 degrees from each other, and in such a situation, with respect to the photometer, that lines drawn through their middles, in the direction of their lengths, meet in a point exactly under the middle of the vertical plane or field of the photometer, and from that point the distances of the lights are measured; the sides of the tables being divided into English inches, and a vernier, showing tenths of inches, being fixed to each of the sliding carriages upon which the lights are placed, and which are so contrived that they may be raised or lowered at pleasure; so that the lights may be always in a horizontal line with the tops of the cylinders of the photometer.

In order that the two long and narrow tables or platforms, just described, may remain immovable in their proper positions, they are both firmly fixed to the stand which supports the photometer; and, in order that the motion of the carriages which carry the lights may be as soft and gentle as possible, they are made to slide upon parallel brass wires, 9 inches apart, about 1/4 of an inch in diameter, and well polished, which are stretched out upon the tables from one end to the other.

The structure of the apparatus will be clearly understood by a bare inspection of Plate XLI., where fig. 1. is a plan of the inside of the box, and the adjoining parts of the photometer. Fig. 2. Plan of the two tables belonging to the photometer. Fig. 3. The box of the photometer on its stand. Fig. 4. Elevation of the photometer, with one of the tables and carriages.

Having sufficiently explained all the essential parts of this photometer, it remains for us to give some account of the precautions necessary to be observed in using it. And, first, with respect to the distance at which lights, whose intensities are to be compared, should be placed from the field of the instrument, the ingenious and accurate inventor found, that when the weakest of the lights in question is about as strong as a common wax-candle, that light may most advantageously be placed from 30 to 36 inches from the centre of the field; and when it is weaker or stronger, proportionally nearer or farther off. When the lights are too near, the shadows will not be well defined; and when they are too far off, they will be too weak.

It will greatly facilitate the calculations necessary in drawing conclusions from experiments of this kind, if some steady light, of a proper degree of strength for that purpose, be assumed as a standard by which all others may be compared. Our author found a good Argand's lamp much preferable for this purpose to any other lamp or candle whatever. As it appears, he says, from a number of experiments, that the quantity of light emitted by a lamp, which burns in the same manner with a clear flame, and without smoke, is in all cases as the quantity of oil consumed, there is much reason to suppose, that, if the Argand's lamp be adjusted as always to consume a given quantity of oil in a given time, it may then be depended on as a just standard of light.

In order to abridge the calculations necessary in these inquiries, it will always be advantageous to place the standard-lamp at the distance of 100 inches from the photometer, and to assume the intensity of its light at its source equal to unity; in this case (calling this standard light A, the intensity of the light at its source \(= x = 1\), and the distance of the lamp from the field of the photometer \(= m = 100\)), the intensity of the illumination at the field of the photometer \((= \frac{x}{m})\) (See Lamp, p. 67. of this volume) will be expressed by the fraction \(\frac{1}{100^2} = \frac{1}{10000}\); 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 \(\frac{y}{n^2} = \frac{x}{m^2}\), as was shown in the article Lamp referred to; or, instead of \(\frac{n^2}{m^2}\), writing its value \(= \frac{1}{10000}\), it will be \(\frac{y}{n^2} = \frac{1}{10000}\); 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

\[ y = \frac{1}{10000} \]

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, \(z = \frac{a}{p}\); 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 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 this 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, \( \frac{60.8^2}{43.4^2} = \frac{3696.64}{1883.56} \approx 2 \) to 1 very nearly.

Again, in another experiment, the distances were,

With two candles = 54.6 inches. Square = 2916 With one candle = 39.7 = 1576.09

Upon another trial,

With two candles = 54.6 inches. Square = 2916 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,

| Squares of the Distances | |--------------------------| | With two Candles. With one Candle | | In the Experiment No. 1. 3696.64 — 1883.56 | | No. 2. 2916 — 1576.09 | | No. 3. 2916 — 1576.09 | | No. 4. 3410.56 — 1780.84 |

\( \frac{13004.36}{4} = 3251.09 \) and \( \frac{6730.45}{4} = 1682.61 \)

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 Photometer 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, p. 293, Suppl.

The ingenious author's experiments all conpired 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, so 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 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 1. His smallest circle was \( \frac{1}{2} \) 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 3½ 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 \( \frac{1}{4} \) 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 3188 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 4d of the whole which fell upon the mirror.