The difficulty of constructing a sphere has led to the frequent adoption of a cube as a sufficiently near approximation for work of moderate accuracy. When a cube is used, the light source should be placed in the centre, with its axis of symmetry perpen dicular to the line joining it to the window, the latter being in the centre of one face of the cube. It is clear a priori that, if the light distributions from the sources to be compared are exactly the same, the form of the enclosure employed is immaterial. So long, therefore, as the distributions do not differ too much, a cube gives quite satisfactory results.
The most natural form of instrument is one in which the in verse square law is used to obtain the necessary variable bright ness. Such an instrument consists, generally, of a long tube black ened internally and containing a lamp in a small diaphragmed en closure. This enclosure is attached to a rod moved by a rack and pinion so that the lamp may be brought towards or away from a piece of opal glass placed near the end of the tube. The brightness of the opal glass is compared with that of an external test sur face by means of a small Lummer-Brodhun cube viewed through an eyepiece attached to the side of the tube. An inverse square scale is attached to the rod and the constant of this scale is adjusted to unity by previous calibration.
An instrument in which the inverse square law is not employed is the Holophane lumeter, shown in fig. 9. The lamp L is en closed in a whitened box of shallow cylindrical form. This box is provided with a window of diffusing glass W, the light from which illuminates the opaque outer parts of the comparison screen S. The eye views the test surface T through the central transparent part of S, and the two parts of the field are adjusted to equality by altering the exposed area of W. This is achieved by means of a cylindrical shutter which can be rotated about the lamp enclos ure by means of the handle H. The shutter is provided with an opening of the form shown in the figure. It will be clear that if W is uniformly bright, the scale of the instrument will consist of two parts, one corresponding to each of the breadths of opening, the scale being even within each part.
In most illumination photometers the scale of the instrument may be extended by the provision of neutral glass screens with transmission factors of one-tenth. If these are inserted between the test surface and the eye, the scale is extended upwards, the instrument reading having to be multiplied by io or roo according as one or both of these screens is inserted. If the screens are inserted between the internal lamp and the comparison surface, the instrument reading must be divided by the appropriate factor. The lamp is supplied from some form of portable battery, pref erably, an "accumulator." A rheostat and a voltmeter or am meter are provided for adjusting the current through the lamp to the value at which the instrument was calibrated. This adjust ment has to be made with the greatest possible care since, owing to the characteristics of the small battery lamps which have to be used, an error of 1% in the current setting may result in an as much as '0% in the readings.
The calibration of every portable photometer should be checked at frequent intervals. This may be done by setting up the test surface at the zero point of a photometer bench and placing a sub-standard of known candle-power at convenient distances from it so as to give even values of illumination at the surface. The test surface should approximate as closely as possible to a perfect diffuser. Ground opal glass or sandblasted opaque white celluloid are frequently used.
Measurement of Brightness and Reflection Factor.—Any illumination photometer which employs a detached test surface may be used for measuring the brightness of a surface, or its reflection factor if it is not self-luminous. This will be made clear by means of an example. When the instrument is set to a reading of, say, E foot-candles, a balance is obtained when the illumination of the test surface has this value. If, now, the reflection factor of this surface be p, its brightness under these conditions is Epir candles per square foot, or Ep foot-lamberts. Hence if, when the photometer is sighted on any other surface, a balance is obtained at the mark E on the instrument scale, the brightness of this surface must be Ep/7r candles per square foot. Thus to convert the scale of illumination on the instrument to a scale of brightness it is only necessary to multiply by the constant factor p/r. Similarly, it is clear that, if two surfaces be equally illumi nated, their brightnesses are proportional to their reflection factors. It, therefore, a surface of reflection factor p' be sub stituted for the test surface of an illumination photometer, the reading obtained will bear to the actual illumination the ratio p'ip where p is the reflection factor of the test surface.