The most obvious method of comparing the candle-powers of two sources on the bench would be to place them one on each side of the photometer head, and adjust their positions until a balance was obtained. On the assumption that equality of brightness of the two surfaces in the photometer head implied a similar equality of illumination, the candle-powers of the sources, and and their respective distances d and d' from the photometer would then be related thus This assumption, although plausible, is never safe in practice and in all accurate photometry at the present time the substitution method is employed.
The Substitution Method.—A "comparison" lamp of con stant, but not necessarily known, candle-power is placed in the carriage at one end of the bench, and this carriage is rigidly attached, by means of a rod, to the carriage holding the photom eter head so that the two carriages move on the bench as one unit. Thus one side of the photometer field has a constant bright ness. Other lamps can now be placed in turn at the other end of the bench, and the distances can be found at which the illumina tions they produce at the photometer will give a balance with this constant brightness. These illuminations must, then, be equal to each other so that, if the candle-powers of the lamps be etc., and their respective distances from the photometer head at the position of balance, etc., it follows that . . . . Thus if one of the lamps be a sub-standard of known candle-power, the candle-powers of the other lamps are found at once. In all photometry it is most important that only the light directly emitted by the sources to be compared shall reach the photometer head, and stray light from external sources, or that reflected from objects in the room, must be shut off by means of suitably placed black screens.
Although, owing to its convenience, the inverse square law is that most commonly used as the law governing the illumination of one of the comparison surfaces of a photometer head, there are other laws which are adopted, for special reasons in certain types of instruments. The cosine law is seldom employed, but the proportionality between luminous intensity and area in the case of a surface of uniform brightness is sometimes used to provide what is, in effect a comparison source of variable candle-power. The reduction of intensity of a polar ized beam by the rotation of a nicol prism placed in its path (see LIGHT) is a favourite device in spectrophotometry (see p.
844), while a transparent plate of graduated transmission factor (e.g., a small-angle wedge of neutral glass), is also useful for
special purposes.
The Sector Disc.—A very accurate method of controlling the illumination of a surface is to interrupt the light reaching it at regular and frequent intervals. It has been found that the ap parent brightness of a surface intermittently illuminated bears to the actual brightness when steadily illuminated, the ratio of the time of exposure to the total time, provided the intermittency is sufficiently rapid to avoid any appearance of flicker. This law is known as Talbot's law and, though it has no theoretical founda tion, it has been proved experimentally that it holds with great accuracy for all ratios down to 3% or less. The law may be ap plied by placing in the path of the light to be reduced an opaque disc having a radial slot cut in it, so that the light only reaches the photometer as the slot passes between it and the lamp. If, for instance, there are three slots in the disc, each 6° in breadth, the ratio of reduction is 1/20. Such discs are exceedingly valuable as auxiliaries to other photometric apparatus, but it will be clear that, as their reduction ratio is fixed, they cannot themselves be used to produce the variation of illumination needed in a pho tometer. For this purpose some form of disc with variable sectors is needed, and many attempts have been made to produce satis factory apparatus of this kind.
The mechanical difficulties are, however, very great and prob ably the most satisfactory type of variable sector disc is that in which the disc remains stationary while the beam of light rotates. Fig. 6 shows the principle of the apparatus. The light from the lamp is reflected twice, as shown by the fine line, traverses the slot in the disc S and is again reflected so that it resumes its origi nal direction. The reflecting surfaces may be mirrors or, prefer ably, the surfaces of rhomboidal prisms as illustrated. In any case the four surfaces are rigidly fixed to one another in the relative positions shown, and the combination is rotated about its horizontal axis. It will be seen that the effect at the photometer surface P is precisely equivalent to that which would be produced by lowering the disc and spin ning it in the usual way. As, however, the disc remains stationary, there is no diffi culty whatever in making it easily adjustable by the observer, while a setting can be at once read off by having a scale on one disc and an index line on the other.