be inversely as the square of that distance. Let A and B be the two bodies: let 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 denfity: then if the diftance of A from P be m, and that of B from the fame part n,

X

the intensity of the light of A at P is equal to and that of

m

2

we fhall have x ¦ y : : m2 : n2.

There are many circumftances to which we ought to attend in experiments of this kind, or very fallacious conclufions will be deduced from them. After all, it will not be eafy to felect fimilar lights, and to judge, with fufficient precifion, by the eye, concerning the denfities of the fhadows occafioned by them; and it is obvious that a small difference in this refpect will produce a confiderable error in eftimating their comparative intenfities.

By experiments conducted on the general principles which we have ftated, the author was led to the conftruction of an apparatus to which he has given the name of Photometer, and which feems to be well adapted to the purposes to which it is applied. This apparatus confifts of a wooden box, 7 inches wide, 10 inches long, and 3 inches deep; the infide 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 inftrument. The box is fupported on a ftand by means of a ball and focket, and the lid of it is made to rife 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 thefe tubes. Instead of a fingle cylinder, which the author used in his first experiments, he now makes ufe of two cylinders; which are fixed perpendicularly in the bottom of the box, in a line parallel to the back of it, and diftant from it 2,2 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 fhadows on the paper called the field of the inftrument; and of thefe fhadows, the two which are in contact precisely in the middle of this field are only to be regarded. The other thadows are rendered invisible by contracting the field and caufing them to fall without it on a black furface. For cylinders of an inch in diameter and 2 inches in height, a field 21% inches wide will be fufficient; and it fhould not be more than of an inch higher than the tops of the cylinders.

The

The covered glafs, which we have already mentioned, is 5 inches long, and as wide as the box is deep; and the field is reduced to its proper, fize by a fcreen of black pasteboard, in the middle of which is a hole, in the form of an oblong fquare, 1inch wide and 2 inches high, which forms the boundaries. of the field. Inftead of this fcreen, the author fometimes uses another, which has a circular hole 1 inch in diameter. By means of this the fhadows are increased in width, fo as completely to fill the field, and they appear under the form of two half difks, 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 of an inch wide, of an inch thick, and of equal height with the cylinder itself. This wing commonly lies in the middle of the fhadow of the cylinder, and it has then no effect: but, when it is necessary to enlarge the diameter of one of the fhadows, 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 shadow on the field of the required magnitude. The cylinder. must be turned outwards; fo that the augmentation of the fhadow may be on that fide of it which is oppofite to the fhadow correfponding to the other light. The cylinders are turned by their lower ends, which pafs through holes in the bottom of the box. They are made of brafs, 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 preferved firmly in their vertical pofitions. The cylinders, and every other part of the inftrument, except the field, fhould 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 fhadows touch this laft-mentioned line, the lights are at a proper height; and when the fhadows 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 precifion, 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 neceffary to affume some fteady light of a proper degree of ftrength for the purpose as a ftandard, by which others may be compared. With this view the author felected an Argand's lamp; which, when properly adjufted, continues to emit light more equally for a confiderable time than any other lamp, and much more than any candle REV. FEB. 1795. whatever.

L

whatever. Having fhewn 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 intenfity of the light emitted by luminous bodies is eftimated, viz. that it is every where as the fquares of the distances from the luminous body inverfely. This inquiry is naturally connected with another; and that is, whether the air is perfely tranfparent, or to what degree it refifts the paffage of light. Having felected 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 fide over against them. The lamp was placed at the dif tance of 100 inches from the field of the inftrument, and it was found that the light of the two candles is equivalent to that of the lamp at the field, when they were fituated at the distance of 60.8 inches from that field. The light of one of the candies, when the other was extinguifhed, counterbalanced that of the lamp at the distance of 43.4 inches. From this experiment it appears that, as the intenfity of the difunited light of two candles is to that of one of them as 2 to 1, the fquare of their distances, in order to verify the affumed theory, ought to be in the same proportion. The diftances are 60.8 and 43.4, and their squares, viz. 3696.64 and 1883.56, are to one another as 2 to 1 very nearly. The fame conclufion was deduced from the mean refult of this and three other fimilar experiments. The author varied his experiments by fubftituting lamps for candles, and obtained the fame general refult. He alfo ufed lamps emitting light of very different degrees of brightness, and paid every poffible attention to the experiments which he performed with them; and they all confpired to fhew that the refiftance of the air to light, in any diftances to which his trials extended, is too inconfiderable to be perceived, and that we may depend on the affumed law of the diminution of the intenfity of light, without any material error. He apprehends, however, that means may be found for rendering the refiftance of air to light apparent, and for meafuring the degree of that resistance with tolerable accuracy. This, he conceives, might be discovered by an accurate determination of the relative intenfity of the fun's or moon's light, when feen at different heights above the horizon, or when feen from the top and from the bottom of a very high mountain in very clear weather.

The next fubject of inquiry was the lofs of light in its paffage through plates or panes of different kinds of glass. In his experiments on this fubject, our author provided two equal Argand's lamps, A and B, and placed them over against each other

at

at the diftance of 100 inches from the field of the inftrument; and the light of B was rendered of the fame intenfity with that of A, or the shadows were reduced to the fame denfity, by lengthening or fhortening the wick of B as occafion required. In thefe circumstances, a pane of clear, transparent, well-polished glaís, 6 inches fquare, was placed vertically on a stand and interpofed before the lamp B, at the distance of about 4 feet from it, and in fuch a fituation that the light of the lamp paffed perpendicularly through the middle of the pane, before it arrived at the field of the inftrument. The light of B being thus weakened, the illuminations of the fhadows were no longer equal: but the fhadow correfponding to the lamp A was lefs enlightened by the light of the lamp B, than the fhadow correfponding 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 inftrument; till its light, paffing through the glafs, counterbalanced the direct light of the lamp A, or till the shadows were rendered equally denfe. 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 fquares of their distances, when their illuminations on the field are equal, that the light of the lamp B was diminished in its paflage through the pane of glass in the ratio of 1002 to 90.2), or as I to .8136; fo that no more than .8136 parts of the light, which impinged against the glafs, found their way through it; the other .1864 parts being difperfed and loft.

This curious experiment was repeated no less than ten times, and the light loft by a mean of all thefe trials was .1973 parts of the whole quantity that impinged against it; the variations in the results of the feveral experiments being from .1720 to .2.108. In four experiments with another pane of the fame kind of glass, the mean lofs of light was .1869. When the two panes of glafs were placed, without touching each other, before the lamp B at the fame time, the lofs of light by its paffage through both of them was at a mean .3184. With another pane of thinner glass, the mean lofs of light in four experiments was .1813. With a very thin clean pane of clearcolourless window-glafs, not ground, the mean lofs of light in four experiments was.1263. When the experiment was repeated with this pane, a little dirty, the lofs of light was more than doubled. The author fuggefts that experiments of this kind. might be usefully employed by the optician, in order to determine the degree of tranfparency of glafs, and to direct his choice of this article.

By fimilar experiments, the author eftimated the lofs of light in its reflection from the furface of a plane glass mirror. From the mean of five experiments, which he has arranged in a table, noting the feveral circumftances attending them, it appears that the lofs of light by reflection from a fmall but very excellent glafs-mirror, made by Ramfden, was .3494; fo that more than part of the light, which falls on the best glafs-mirror that can be constructed, is loft in reflection. In mirrors of inferior quality, the lofs is more confiderable. In a bad common looking-glafs, 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 furface of the mirror within the limits fpecified in his experiments, and from 45° to 85°, did not appear to affect, in any fenfible degree, the refult of them.

The next object to which our author directed his attention was an estimate of the relative quantities of oil confumed and of light emitted by an Argand's lamp, 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 denfities of the fhadows being equal when Argand's lamp was placed at the distance of 1341 inches, and the common lamp at the diftance of 95.2 inches, from the field of the inftrument. When both lamps had been made to burn with the fame 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 confumed and the common lamp of a Bavarian pound of oil. By comparing the refults of the intensities of the light of the two lamps with the quantities of oil confumed by them; i. e. .17956 to 9063 or 187 to 100, and 253 to 163 or 155 to 100; we fhall perceive that the quantity of light, produced by the combuftion 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 faving of oil in the ufe of Argand's lamp cannot amount to lefs than 15 per cent. author, however, does not pretend to decide whether this faving may not be counterbalanced by inconveniences that may attend the use of this improved lamp.

16

The

From other experiments, it appears that a common Argand's lamp, burning with its ufual brightness, gives about as much light as nine good wax-candles; or by a more definite conclufion, it

affords