Form the same curve

marked by eight half ovals. It will be noticed that the points touched are necessarily at rest, and hence lie on the nodal lines. By using the three plates of the same form, some of the laws of the vibrations of plates may be proved. 1st. The number of vibrations is proportional to the thickness. on the two plates, of which one is double the thickness of the other, and it will be noticed that the pitch is always an octave higher. 2d. In similar plates of equal thickness, the number of vibrations is inversely as the square of the homologous parts. Hence the small plate gives a note two octaves above the large one of the same thickness.

LIGHT.

67. PHOTOMETER FOR ABSORPTION.

Apparatus. In Fig. 59, A is the source of light, which may be a candle in a spring candle-stick, or a small gas jet. B and C are two mirrors set at such an angle that they will form images of A, just 50 inches apart, and making ABC a right-angled triangle. D is a Bunsen photometer disk, made by placing a circular piece of thick paper in a lathe, and painting all but the centre with the best melted sperm-candle wax. It then possesses the property when placed between two lights, of changing its appearance according as one or the other is the brighter. It is mounted on a slide and carries an index which moves over a graduated scale. F is a screen so placed as to protect D and the eyes of the observer from the direct light of A, while it leaves the scale illuminated so that it can be easily read. A stand with a graduated circle is also provided, on which one or more plates of glass may be set and inclined at any angle to the ray of light AB. Some observers prefer a disk with only the central part covered with wax, and instead of a circular spot use some other form. The great difficulty in these cases is to distribute the wax uniformly, and prevent its accumulating at the edges. Still another method is to punch figures in a sheet of thick paper, and cover both sides of it with tissue paper, taking care that no wrinkles remain. The whole apparatus must be used in a darkened room.

Experiment. The disk D possesses the curious property of appearing bright in the centre when

E

Fig 49.

a strong light is in front of it, but dark when the brighter light is behind. When placed between two lights there is therefore a certain position where the spot will disppear, in which case it is so much nearer the fainter light that the illumination on its two sides are equal. Their relative brightness may then be readily

132

determined from the law that the intensity is inversely as the square of the distance. Now the two images of A act like two precisely similar lights, any change in one affecting the other equally. By moving D the centre spot may be made either light or dark, and there will be a certain intermediate position in which it will disappear. The exact point of disappearance can be determined only by long practice, noticing that it varies with the position of the eye, and with the two sides of the disk. Find this point as nearly as possible, read the index, move D a short distance, set again and take the mean of several such observations. Compute the probable error in inches, and the result multiplied by 4 gives the error in percentage. Let x be the mean observed reading, or AB+BD. Then the distance of the other image of the light equals DC+ CA, or 50. Calling B and C their intensities at a distance unity, their intensities at the distance of or since these quantities are

B x2

the disk will be and

C
(50 - x) 2 ;

equal, their relative intensities I

B

Ꮯ

2

(50). Next place

a piece of plate glass carefully cleaned on the stand between A and B, and at right angles to the line connecting them. To make this adjustment remove D, and place the eye beyond the light. Then turn the stand until A, its reflection in the plate glass, and its reflection in B and C, all lie in the same straight line. Now set the disk as before, record the mean reading, and compute the relative intensities. Increase the number of plates one at a time, and compute the intensity in each case. This number divided by that when no plates were interposed, gives the percentage transmitted.

This same apparatus is well adapted to determine the amount of light transmitted at different angles of incidence, that cut off by ground glass, the effect of the snuff of a candle, or the overhanging portion of the wick, and the comparative brilliancy of the edge and side of a flat flame. In the last case it is only necessary to set the flame so that it shall shine edgewise, first into B and then into C, and compare the position of the disk in the two It will thus be found that the prevalent impression that flame is perfectly transparent, is erroneous.

cases.

68. DAYLIGHT PHOTOMETER.

Apparatus. In Fig. 50, AB is a box about six feet long, a foot wide, and a foot and a half high. It may be made of a light wooden frame covered with black paper or cloth. A circular hole about four inches in diameter is cut in the end B, and covered with blue glazed paper with the white side out, and made into a Bunsen disk by a drop of melted candle-wax in the centre. A long wooden rod rests on the bottom of the box, and has a standard wax candle, A, in a spring candle-stick attached to one end. The distance of the candle from the disk may thus be varied at will, and measured by a scale attached to the rod. The box should be ventilated by suitable holes cut in it, or the air will become so impure that the candle will not burn properly.

Experiment. This instrument is intended to compare the amount of light in different portions of a room, or its brightness

Fig. 50.

at different times. When the candle is placed at a distance from the photometer disk, the latter will appear dark in the centre, while by making AB very

small, so that the strongest light shall be inside, the centre will be bright. The color of the candle flame being of a reddish tint compared with daylight, is first passed through the blue paper, which thus renders the colors more nearly alike. When the distance of the candle is such that the illumination is equal on both sides of the disk, the spot will nearly disappear, and unity divided by the square of this distance gives a measure of the comparative brightness under various circumstances.

An excellent experiment with this instrument is to measure the fading of the light at twilight. Light the candle and place it at such a distance from the disk that the spot shall disappear, as in the last experiment. As the light diminishes, the distance AB must be increased. Take readings at intervals of one minute, and construct a curve with ordinates equal to one divided by the square of this distance, and abscissas equal to the time. The amount of light for different distances of the sun below the hori

zon may be obtained directly from this curve. In the same way the brightness of different parts of the laboratory may be measured, the effect of drawing the window curtains, and the comparative brightness of clear and cloudy days. This apparatus was used during the Total Eclipse of 1870, to measure the amount of light during totality, possessing the advantage that on returning, the precise degree of darkness could be reproduced artificially. Comparisons may also be made with moonlight, the light of the aurora or other similar sources of light.

69. BUNSEN PHOTOMETER.

Apparatus. A photometer room forms a most valuable addition to a Physical Laboratory, both on account of the great variety of original investigations which may easily be conducted in it by students, and also owing to the practical value of the instrument, and the excellent training it affords in the use of various forms of gas apparatus. If a separate room cannot be obtained, a part of the laboratory may be partitioned off by paper or cloth screens blackened on the interior, so as to leave a space about twelve feet long by five wide and eight feet high, which should be nearly dark, and supplied with some means of ventilation. In this is a table ten

C:

feet long, a foot and a half wide, and three high, and over its centre, at a height of five feet from the floor, the photometer bar, AB, Fig. 51, is placed. The latter is 100 inches in length, and divided on one side into inches and tenths, and on the other into candle powers. To make this graduation, calling x the distance from one end of the bar in inches, and Cthe corresponding candle power, we have, as will be seen below, x2: (100 x)2 = С: 1, or x = 100 1+ By making C=1, 2, 3, etc., the bar may be graduated as desired. At one end of the bar is placed a sperm candle, A, supported in a balance for determining its loss of weight as it burns. The best form is that invented by Prof. F. E. Stimpson, on the principle of the bent-lever balance, in which the motion of a long arm over a scale shows the number of grains consumed.

At the other end of the bar, gas is admitted, and its brightness when burned compared with that of the candle. The pipe supplying the gas passes through the meter F, which is of the form known as the wet meter, and indicates the volume to one thousandth of a foot. To read it, a separate burner E is provided, supplied with gas, which does not pass through the meter. course it is turned down when setting the disk. The gas passes from the meter to the regulator G, by which the pressure is rendered perfectly constant. This consists of a bell resting in water, like a gas-holder, with a long conical rod attached to its centre,

Of