312 ELEMENTS OF ELECTRICAL ENGINEERING. 



Intensity of illumination. The amount of light per unit sec- 

 tional area of a beam, that is, the sectional intensity of the beam, 

 measures the intensity of illumination of a surface upon which 

 the beam falls perpendicularly. Therefore the intensity of illumi- 

 nation of a surface may be expressed in luxes. Thus the in- 

 tensity of illumination required for easy reading is the intensity 

 of illumination at a distance of one foot from a standard candle, 

 which intensity is sometimes called the " candle-foot," and it is 

 equal to i.i36/(o.3O5) 2 = 12.21 luxes according to equation (50). 



A complete statement of the various photometric units depends upon a clear under- 

 standing of what is called solid angle. Consider a cone, and a sphere with its center 

 at the apex of the cone. The solid or spherical angle of the cone is measured by the 

 ratio of the area of the portion of the spherical surface within the cone to the square 

 of the radius of the sphere. Thus the unit of solid angle is subtended by one square 

 centimeter of the surface of a sphere of one centimeter radius, and the complete sur- 

 face of a sphere represents 4^ units of solid angle. 



Consider a lamp placed at the center of a sphere of unit radius so that one unit of 

 area of this sphere may represent one unit of solid angle or one unit-cone. Imagine 

 the lamp to give one hefner of conical intensity of light in every direction. Then the 

 amount of light (light-flux) passing out in one unit-cone (through unit area of the 

 sphere) is called one lumen of light-flux. 



The given lamp emits one spherical -hefner (0.88 of a spherical-candle) of light-flux, 

 because the conical intensity is assumed to be the same in every direction ; but the 

 whole spherical surface represents 477 units of solid angle or 4?r unit cones. Therefore 

 the lamp emits 4?r lumens of light-flux. That is to say, a spherical-hefner of light- 

 flux is equal to 477 lumens. 



The lux, which is defined above as the intensity of illumination at a distance (hori- 

 zontally) of one meter from a Hefner lamp, represents of course a certain amount 

 of light flux falling upon each square centimeter of the illuminated surface. Now the 

 area of a sphere of one meter radius is 40,00077 square centimeters and if the lamp 

 gave out light equally in all directions, one spherical-hefner or 477 lumens would 

 pass out from it. Therefore one lux represents one ten -thousandth of a lumen per 

 square centimeter or ^-jj^Vffw ^ a spherical-hefner per square centimeter. 



As an illustration of the significance of the terms hefner, lumen and lux, consider a 

 beam of light emitted by a glow lamp. Let the conical intensity of this beam be 1 8. 2 

 hefners (16 candles). Let the solid angle of this beam be o.oi of a unit, that is to 

 say, the solid angle subtended by o oi of a square centimeter of the surface of a sphere 

 of which the radius is one centimeter. Then the number of lumens of light- flux in 

 the beam is 18.2 hefners multiplied by o.oi unit of solid angle, which is equal to 

 0.182 lumen. The sectional intensity of this beam at a distance of one meter from 

 the lamp is 1 8. 2 luxes. 



