The Lumen.
—A light giving 1 candlepower, placed in the center of a sphere of 1 foot radius illuminates a sphere, the area of which is 4 × 3.1416 or 12.57 square feet. The intensity of light on each square foot is denoted as a candle-foot. The candle-foot is the standard of illumination on any surface. The quantity of light used in illuminating each square foot of the sphere is called a lumen. A light of 1 candlepower will therefore produce an intensity of 1 candle-foot over 12.57 square feet and give 12.57 lumens. Therefore, if all of the light is effective on a plane to be illuminated, a lamp rated at 400 lumens would light an area of 400 square feet to an average intensity of 1 candle-foot.
To find the number of lamps required for lighting any space, the area in square feet is multiplied by the required intensity in foot-candles, to obtain the total necessary lumens, and the amount thus obtained is divided by the effective lumens per lamp.
The bulletins of the Columbia Incandescent Lamp Works gives the following method of calculating the number of lamps required to light a given space:
Number of lamps = (S × I)/(Effective lumens per lamp)
S (square feet) × I (required illumination in foot-candles) = total lumens.
The total lumens divided by the number of effective lumens per lamp gives the number of lamps required. In using the formula the effective lumens per lamp is taken from the following table:
| Watts per lamp | 25 | 40 | 60 | 160 | 150 | 250 |
| Effective lumens per lamp | 95 | 160 | 250 | 420 | 630 | 1090 |
| Lumens per watt | 3.8 | 4.0 | 4.2 | 4.2 | 4.2 | 4.3 |
The size of the units is a matter of choice since six 400-lumen units are equal to four 600-lumen units in illuminating power, etc. In deciding upon the proper size of lamps to use, consideration must be taken of the outlets if the building is already wired. In general the fewest units consistent with good distribution will be the most economical. The table shows the lumens effective for ordinary lighting with Mazda lamps and clear high-efficiency reflectors with dark walls and ceiling. Where both ceiling and walls are very light these figures may be increased by 25 per cent.
To illustrate the use of the table, take an average room 16 by 24 to be lighted with Mazda lamps to an intensity of 3.5 foot-candles. If clear Holoplane reflectors are used, the values for lumens effective on the plane may be increased 10 per cent. due to reflection from fairly light walls. The lamps in this case are to be of the 40-watt type which in the table are rated at 160 lumens. To this amount 10 per cent. is added on account of the reflectors and walls. This data applied to the formula gives:
s = 16 by 24 feet
I = 3.5
Lumens per lamp = 160
((16 × 24) × 3.5)/176 = eight 40-watt lamps.
Fig. 219.