Transactions of the Society of Motion Picture Engineers (1916)

square foot in this particular sphere. \Ye know by arithmetic that the total surface of the sphere having a radius of i foot is 12.57 square feet. In other words, removing the sphere entirely, we would have the equivalent of 12.57 openings the size of OR; that is, if the candle gives I candle in every direction, with the sphere removed it would give 12.57 lumens. This means that if we know the mean spherical candlepower of a source by multiplying this value by 12.57 we obtain the number of lumens emitted by that source. A lumen may also be defined as being equivalent to the quantity of light intercepted by a surface of I square foot every point of which is at a distance of i foot from a source of i candle. (Fig. 3, Sketch B). While the foregoing definitions establish definitely the quantity of light that we use as our basic unit, it must be remembered that a lumen, in order to be a lumen, need not necessarily conform with these specifications if the quantity of light represented is equivalent to that prescribed by the definition. A bushel might be defined as the quantity of any commodity contained in a cylindrical measure having a diameter of 13/4" and a height of 8''; however, a bushel of potatoes spread out in the field is just as much a bushel as though the shape of the pile conformed in every respect to the dimensions just mentioned. A conception of the relations just discussed may be obtained from the following simple analogy: Suppose that we have a pool of water of unknown depth, whose area has been found to be 5000 square inches, and it is desired to obtain a measurement of the quantity of water in the pool. At first thought, one might be tempted to measure the depth at some point by means of a yardstick. If, for example, the depth at this point were found to be 6 inches, he might say that the pool contained 6 inches of water. Obviously, such a measurement would be practically useless. A measurement of this sort corresponds to the measurement of the quantity of light given off by an illuminant as determined by its candle-power in a single direction. On second thought, the investigator might make determinations of depth at regular intervals along a straight line through the center of the pool from edge to edge and find the average depth along this line to be, say, 4 inches. To say that the pool contains 4 inches of water would hardly be more conclusive than the first determination. Such a measurement would correspond to the mean horizontal candle-power of a light source. If the surface of the pool were divided into a large number of equal squares and measurements of depth made at the center of each square, the average depth thus found would give a definite idea of the quantity of the water in the pool since the surface area is already known. This determination corresponds to mean spherical candlepower. Now, if the average depth of the pool as just determined, is, say, 4>2 inches, the quantity of water in the pool is 4^^ times 5,000 or 22,500 cubic inches. .To say that the pool contains 22,500 cubic inches of water is definite and positive, and this measurement corresponds to the number of lumens given off by a light source. The average depth of the pool corresponds in this analogy to the average intensity of the light source in all directions and the area of the pool corresponds to the area of the imaginary sphere about the light source. It might be said that the above method would be a very awkward 78