If a source of light has a luminous intensity of one candle in all directions, the illumination at a distance of one foot in any direction is said to be a foot-candle.  This is the unit of illumination intensity.  A lumen is the quantity of light which falls on one square foot if the intensity of illumination is one foot-candle.  It is seen that the area of a sphere with a radius of one foot is 4 pi or 12.57 square feet; therefore, a light-source having a luminous intensity of one candle in all directions emits 12.57 lumens.  This is the satisfactory unit, for it measures total quantity of light, and luminous efficiencies may be expressed in terms of lumens per watt, lumens per cubic foot of gas per hour, etc.

Of course, the efficiencies of light-sources are usually of interest to the consumer if they are expressed in terms of cost.  But from a practical point of view there are many elements which combine to make another important factor, namely, satisfactoriness.  Therefore, the efficiency of artificial lighting from the standpoint of the consumer should be the ratio of satisfactoriness to cost.  However, the scientist is interested chiefly in the efficiency of the light-source which may be expressed in lumens per watt, or the amount of light obtained from a given rate of consumption or of emission of energy.  This method of rating light-sources penalizes those radiating considerable energy which does not produce the sensation of light or which at best is of wave-lengths that are inefficient in this respect.  That radiant energy which is wholly of a wave-length of maximum visibility, or, in other words, excites the sensation of yellow-green, is the most efficient in producing luminous sensation.  Of course, no illuminants are available which approach this theoretical ideal and it is not likely that this would be a practical ideal.  Under monochromatic yellow-green light the magical drapery of color would disappear and the surroundings would be a monochrome of shades of this hue.  Having no colors with which to contrast this color, the world would be colorless.  This should be obvious when it is considered that an object which is red under an illuminant containing all colors such as sunlight would be black or dark gray under monochromatic yellow-green light.  The red under present conditions is kept alive by contrast with other colors, because the latter live by virtue of the fact that most of our present illuminants contain their hues.  It is assumed that the reader knows that a red object, for example, appears red because it reflects (or transmits) red rays and absorbs the other rays in the illuminant.  In other words, color is due to selective absorption reflection, or transmission.

Perhaps the ideal illuminant, which is most generally satisfactory for general activities, is a white light corresponding to noon sunlight.  If this is chosen as the scientific ideal, the illuminants of the present time are much more “efficient” than if the most efficient light is the ideal.