92 



TABLE 67.— VISUAL RANGE OF WHITE LIGHTS 2 " 



Candlepower c candles at visual threshold of steady point source of white light seen 

 against white hack-ground brightness b millimicrolanihert (ni/tiL) at range r sea miles 

 through an atmosphere of attenuation a per sea mile is given by 



C = 3.7X 10 :, ( 1 +/0'r-V r , 



which is valid within a factor of 3 for b from total darkness to full daylight. For practical 

 signaling or navigation multiply c by at least 100. 



Threshold r candles, b = 100 m/i L, at night 



Kange r , A 



sea mile a — 1 a = 0.8 a = 0.6 



1 04 .05 .06 



2 15 .23 .41 



3 33 .65 1.5 



5 91 2.9 12 



7 1.8 8.6 ■ 62 



10 3.6 34 610 



a — 0.4 

 .09 



.9 



5.2 

 90 

 1100 

 35000 



«• Knoll, H. A., Tousey, R.. ami Hulburt, E. O., Journ. Opt. Soc. Amer., vol. 36, p. 480, 1946. 



TABLE 68.— THE BRIGHTNESS OF THE SUN 



From the definition of a lumen, the lumen output from a point source within a unit solid 

 angle is numerically equal to the candlepower of the source. This also holds for any 

 radiating source that behaves as a point, such as a spherical blackbody,* or any spherical 

 radiator of uniform brightness that obeys the Lambert cosine law of radiation, providing 

 the measurements are made at such a distance from the source that the inverse square 

 law is obeyed. (See Table 74.) As an example of this, consider the brightness of the sun. 

 The sun when directly overhead on a clear day gives an illumination of about 10,000 foot- 

 candles. This is equal to 10,000 lumens per ft. 2 (See Table 73.) To change this to lumens 

 for a unit solid angle, multiply by the radius of the earth's orbit squared (i.e., 2.41 X 10 23 

 ft 2 ). Thus, the candlepower of the sun is 2.41 X 10 27 . To get the brightness per cm 2 divide 

 this by the projected area of the sun in cm 2 (i.e., 1.52 X 10 22 ), which gives about 160,000 

 c/cnf for the brightness of the sun as observed at the earth's surface. This, of course, 

 assumes that the sun's surface is of uniform brightness and that its radiation obeys the 

 Lambert cosine law. The data (Table 813) on the distribution of energy of the solar 

 spectrum give a brightness of the sun of 146,000 c/cm 2 . 



* The lumens within a unit solid angle around the normal from a plane blackbody is equal to 0.92 

 times the normal intensity. 



TABLE 69.— SOME OBSOLETE PHOTOMETRIC STANDARDS 



(In use prior to 1948.) 



In Germany the Hefner lamp was most used ; in England the Pentane lamp and sperm 

 candles ; in France the Carcel lamp was preferred ; in America the Pentane and Hefner 

 lamps were used to some extent, but candles were largely employed in gas photometry. For 

 the photometry of electric lamps, and in accurate photometric work, electric lamps, stand- 

 ardized at a national standardizing institution, were employed. 



The "international candle" designated the value of the candle as maintained by co- 

 operative effort between the national laboratories of England, France, and America ; and 

 the value of various photometric units in terms of this is given in the following table 

 (Circular No. 15 of the Bureau of Standards) : 



1 international candle = 1 Pentane candle. 

 1 international candle = 1 Bougie decimale. 

 1 international candle = 1 American candle. 

 1 international candle = 1.11 Hefner unit. 

 1 international candle = 0.104 Carcel unit. 



1. Standard Pentane lamp, burning pentane 10.0 candles. 



2. Standard Hefner lamp, burning amyl acetate 0.9 candles. 



3. Standard Carcel lamp, burning colza oil 9.6 candles. 



4. Standard English sperm candle, approximately 1.0 candles. 



The international candle was in reality taken from the candlepower of a number of in- 

 candescent lamps, operated under definite conditions and kept at the standard laboratories 

 of France, Britain, and the United States. 



SMITHSONIAN PHYSICAL TABLES 



