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be inversely as the square of that distance. Let A and B be the two bodies : let o be the intensity of B, and y that of A; and let P represent the point at which the rays proceeding from A and B meet and are found to be of equal density : then if the distance of A from P be m, and that of B from the same part n, the intensity of the light of A at P is equal to and that of B=m; and since = īs we shall have x:y:: m2:n'.
There are many circumstances to which we ought to attend in experiments of this kind, or very fallacious conclusions will be deduced from them. After all, it will not be easy to select similar lights, and to judge, with sufficient precision, by the eye, concerning the densities of the shadows occafioned by them; and it is obvious that a small difference in this respect will produce a considerable error in estimating their comparative intensities.
By experiments conducted on the general principles which we have ftated, the author was led to the construction of an apparatus to which he has given the name of Photometer, and which seems to be well adapted to the purposes to which it is applied. This apparatus consists of a wooden box, 71 inches wide, 10 inches long, and 31 inches deep; the inside of which is painted black, and has a groove at the back part of it, which receives a small pane of ground glass, on which is pafted the white paper that forms the field of the instrument. The box is supported on a stand by means of a ball and socket, and the lid of it is made to rise on hinges. The front of it is closed; and the light is admitted through two horizontal tubes, which are placed so as to form an angle of 60', and with their axes meeting at the centre of the field. This field is viewed through an opening in the middle of the front of the box between these tubes. Instead of a fingle cylinder, which the author used in his first experiments, he now makes use of two cylinders; which are fixed perpendicularly in the bottom of the box, in a line parallel to the back of it, and distant from it 2 inches, and from each other 3 inches: the distances being measured from the centres of the cylinders. When the lights, which are the fubjects of examination, are properly placed, these two cylinders project 4 shadows on the paper called the field of the inftrument; and of these thadows, the two which are in contact precisely in the middle of this
field are only to be regarded. The Other (hadows are rendered invisible by contracting the field and caufing them to fall without it on a black surface. For cylinders of an inch in diameter and 21 inches in height, a field 21 inches wide will be sufficient, and it should not be more than is of an inch higher than the tops of the cylinders.
The covered glass, which we have already mentioned, is si inches long, and as wide as the box is deep; and the field is reduced to its proper, size by a screen of black pasteboard, in the middle of which is a hole, in the form of an oblong square, 1 inch wide and 2 inches high, which forms the boundaries of the field. Instead of this screen, the author sometimes uses another, which has a circular hole 1; 6 inch in diameter. By means of this the shadows are increased in width, so as completely to fill the field, and they appear under the form of two half disks, touching each other in a vertical line. The cylinders of this inftrument are moveable about their axes; and to each of them is added a vertical wing ts of an inch wide, tá of an inch thick, and of equal height with the cylinder itself. This wing commonly lies in the middle of the shadow of the cylinder, and it has then no effect : but, when it is necessary to enlarge the diameter of one of the shadows, the corresponding cylinder is moved about its axis, till the wing is made to intercept a portion of the light, and to render the projected fhadow on the field of the required magnitude. The cylinder must be turned outwards ; so that the augmentation of the fhadow may be on that side of it which is opposite to the shadow corresponding to the other light. The cylinders are turned by their lower ends, which pass through holes in the bottom of the box. They are made of brass, and fixed to a plate of brass, secured to the bottom of the box. By this precaution, they are always kept parallel to each other, and by other contrivances they are preserved firmly in their vertical positions. The cylinders, and every other part of the instrument, except the field, should be painted of a deep black dead colour.
In order to place the lights properly, 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 cylinder. When the tops of the shadows touch this last-mentioned line, the lights are at a proper height; and when the shadows are in contact with each other in the middle of the field, the lights are in their proper direction. In order to move the lights to and from the photometer, and to adjust their height, with the greater precision, the author has provided a very simple and convenient apparatus, which we have not room to describe.
In the use of this inftrument, it is necessary to assume some Iteady light of a proper degree of strength for the purpose as a Atandard, by which others may be compared. With this view the author selected an Argand's lamp; which, when properly adjusted, continues to emit light more equally for a conliderable time than any other lamp, and much more than any candle Rev. FEB. 1795
whatever. Having thewn how to adjust this lamp, and how to abridge the calculations that occur in the course of his experiments, he proceeds to investigate the truth of the law, by which the intensity of the light emitted by luminous bodies is efti. mated, viz. that it is every where as the squares of the distances from the luminous body inversely. This inquiry is naturally connected with another; and that is, whether the air is perfeetly transparent, or to what degree it resists the passage of light. Having selected two equal wax.candles, well trimmed, and which were found to burn with equal brightness, our author placed them together on one fide of the photometer, and counterbalanced their united light by an Argand's lamp placed on the other side over against them. The lamp was placed at the disa tance of 100 inches from the field of the instrument, and it was found that the light of the two candles is equivalent to that of the lamp at the field, when they were situated at the distance of 60.8 inches from that field. The light of one of the candles, when the other was extinguished, counterbalanced that of the lamp at the diftance of 43.4 inches. From this experiment it appears that, as the intensity of the disunited light of two candles is to that of one of them as-2 to 1, the square of their distances, in order to verify the assumed theory, ought to be in the same proportion. The distances are 60.8 and 43.4, and their squares, viz. 3656.64 and 1883.56, are to one another as 2 to i very nearly. The same conclusion was deduced from the mean result of this and three other similar experiments. The author varied his experiments by subftituting lamps for candles, and obtained the same general result. He also used lamps emitting light of very different degrees of brightness, and paid every porn fble attention to the experiments which he performed with them; and they all conspired to thew that the resistance of the air to light, in any distances to which bis trials extended, is too inconfiderable to be perceived, and that we may depend on the affumed law of the diminution of the intensity of light, without any material error. He apprehends, however, that means may be found for rendering the resistance of air to light apparent, and for measuring the degree of that resistance with tolerable accuracy. This, he conceives, might be discovered by an accurate determination of the relative intensity of the sun's of moon's light, when seen at different heights above the horizon, or when seen from the top and from the bottom of a very high mountain in very clear weather.
The next subject of inquiry was the loss of light in its para sage through plates or panes of different kinds of glass. In his experiments on this subject, our author provided two equal Argand's lamps, A and B, and placed them over against each other
at the diftance of 100 inches from the field of the instrument; and the light of B was rendered of the same intensity with that of A, or the shadows were reduced to the same density, by lengthening or shortening the wick of B as occasion required. In these circumstances, a pane of clear, transparent, well-polished glass, 6 inches square, was placed vertically on a stand and interposed before the lamp B, at the distance of about 4 feet from it, and in such a situation that the light of the lamp paffed per. pendicularly through the middle of the pane, before it arrived at the field of the instrument. The light of B being thus weakened, the illuminations of the shadows were no longer equal : but the shadow corresponding to the lamp A was less enlightened by the light of the lamp B, than the shadow corresponding to B by the undiminished light of A. In order to determine the amount of this diminution, the lamp B was brought nearer to the field of the instrument; till its light, passing through the glass, counterbalanced the direct light of the lamp A, or till the shadows were rendered equally dense. This effect was produced, when the lamp B was removed from the distance of 100 inches to that of 90.2 from the field. Hence we may infer, the intenfities of the lights being as the squares of their distances, when their illuminations on the field are equal, that the light of the lamp B was diminished in its pafiage through the pane of glass in the ratio of 100/2 to 90.2), or as I to .8136; so that no more than .8136 parts of the light, which impinged against the glass, found their way through it; the other .1864 parts being dispersed and loft.
This curious experiment was repeated no less than ten times, and the light loft by a mean of all these trials was .1973 parts of the whole quantity that impinged against it; the variations in the results of the several experiments being from .1720 to 2108. In four experiments with another pane of the fame kind of glass, the mean loss of light was .1869. When the two panes of glass were placed, without touching each other, before the lamp B at the same time, the loss of light by its paffage through both of them was at a mean .3184. another pane of thinner glass, the mean lofs of light in four experiments was 1813. With a very thin clean pane of clear colourless window.glass, not ground, the mean loss of light in four experiments was.1 263. When the experiment was repeated with this pane, a little dirty, the loss of light was more than doubled. The author suggests that experiments of this kind might be usefully employed by the optician, in order to deter. mine the degree of transparency of glass, and to direct his choice of this article.
By similar experiments, the author estimated the loss of light in its reflection from the surface of a plane glass mirror. From the mean of five experiments, which he has arranged in a table, noting the several circumstances attending them, it appears that the loss of light by reflection from a small but very excellent glass-mirror, made by Ramsden, was .3491; so that more than į part of the light, which falls on the best glass-mirror that can be constructed, is lost in reflection. In mirrors of inferior quality, the loss is more considerable. In a bad common looking-glass, it appeared to be .4816 parts, in another .4548 parts, and in a third .4430 parts. 'The author observes that the difference of the angles of incidence at the surface of the mirror within the limits specified in his experiments, and from 45° to 85°, did not appear to affect, in any sensible degree, the result of them.
The next object to which our author directed his attention was an estimate of the relative quantities of oil consumed and of light emitted by an Argand's Jamp, and by one on the common construction with a ribband wick. Having placed two lamps, one by Argand, and another of the common fort but excellent in its kind, before the photometer, the intenfities of the light emitted by the two lamps were found to be to each other as 17956 to 9063; the densities of the shadows being equal when Argand's lamp was placed at the distance of 134 inches, and the common lamp at the distance of 95.2 inches, from the field of the initrument. When both lamps had been made to burn with the same brilliancy for 30 minutes, it was found, by the difference of their weights before the commencement and at the close of the experiment, that the Argand's lamp had consumed it and the common lamp sitta of a Bava. rian pound of oil. By comparing the results of the intensities of the light of the two lamps with the quantities of oil consumed by them; i.e. .17956 to 9063 or 287 to 100, and 253 to 163 or 155 to 100; we shall perceive that the quantity of light, produced by the combustion of a given quantity of oil in Argand's lamp, is greater than that produced by burning the fame quantity in a common lamp, in the ratio of 187 to 155, or 100 to 85. Hence it appears that the saving of oil in the use of Argand's lamp cannot amount to less than 15 per cent. The author, however, does not pretend to decide whether this saving may not be counterbalanced by inconveniences that may attend the use of this improved lamp.
From other experiments, it appears that a common Argand's lamp, burning with its usual brightness, gives about as much light as nine good wax-candles; or by a more definite conclusion, it