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Closely related to candle-power is mean spherical candle-power. The mean spherical candle-power of a lamp is simply the average of all the candle-powers in all directions about that lamp.
The Lumen.
We have seen that candle-power alone gives no indication of quantity* of light. It is necessary, therefore, for us to develop a unit whereby we can measure the quantity of total flux of light emitted by a source.
For this purpose let us assume a source giving one candle in every direction, and that this source is placed at the center of a sphere painted black on the inside and having a radius of, say, i foot.
/^ 3
Fig. 3 .
Opening OR has area of i square foot and emits i lumen; B One lumen falls on surface OP^R
(Sketch A, Fig. 3) OR represents an opening in the sphere through which some of the light may escape. The quantity of light allowed to escape may be varied by varying the size of the opening, with the candle-power of the source and the radius of the sphere remaining fixed; if we decide on some definite size of opening at OR we shall have a definite quantity of light which we can use as our unit for measuring quantity. The simplest area or unit to assume for OR is i square foot, and if we do make this opening of an area of i square foot, the amount of light that escapes is considered to be the unit of quantity, and is called a lumen. fThus we have established a permanent unit for the measurement of quantity of light; the mathematical relations used to fix it serve only the same purpose as two scratches on a platinum-iridium bar in the International Bureau of Weights and Measures, the distance bweteen which at a definite temperature is called a meter.
If the area of OR is made }i square foot, the light escaping will amount to J4 lumen; if the area of OR is doubled, the light escaping will be 2 lumens. On the other hand, if we have a uniform source of 2 candles instead of i, 2 lumens will be emitted through an opening of i
* Quantity is here used in the sense that it indicates only a summation of flux as throughout a given solid angle about the source, and over a given area illuminated to some average value. Quantity in a more precise sense is a summation over a period of time and is measured in lumen-hours.
t We could choose a sphere of any radius we cared to, as long as we kept the proportions the same by making the size of the opening such that its area would be equal to the square of the radius. The quantity would still be one lumen.
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