Rumford's Photometer

The apparatus for making the comparison consists simply of a bar, at the end of which a ground glass or paper screen is fixed, and on which a support is made to slide, carrying the gas jet or other source of light.

On the bar, and in. front of the screen, is placed a wooden rod, about 3 inches from the screen. The two lights to be compared are placed one on the sliding support and the other on the table at a fixed distance (taking care that both are the same height), the positions being so adjusted that the two shadows of the rod thrown on the screen are just in contact with each other without overlapping. The screen must be turned so that it makes equal angles with the direction of the light from each source. The distance of the sliding light has to be adjusted so that the two shadows are of the same depth.

Consider a unit of area, e.g. a square centimetre, of each shadow A and B; let the distance of the unit of area of A from the two sources of light be x, X, and let the distance of the unit of area of the shadow B from the same sources be y, Y respectively. Then the unit of area of A is illuminated only by the one source of light, distant X from it, and therefore its illumination is I/X², where I is the illumination per unit area at unit distance from the source. The unit of area of B is illuminated only by the source of light at distance y, and the illumination therefore is I'/y², when I' is the illumination per unit area at unit distance from the second source.

Hence, since the illuminations of the shadowed portions of the screen are equal,

If the two unit areas considered be immediately adjacent to the line of junction of the shadows, then we may measure x and y from the same point. Hence the ratio of the intensities of the two sources is the square of the ratio of the distances of the two sources from the line of contact of the shadows. The method has the advantage that the observations do not need a dark room.

The shadows may be so arranged that the line of contact is on the middle line of the bar on which the one source slides, and accordingly the distance may be measured along the bar. The other distance may be measured by a tape.

The arrangements necessary for determining the rate at which the gas is being burnt or the quantity of wax consumed are described in section 45.

Experiment. - Compare the illuminating power of the gas-flame and standard candle.

Enter results thus: -