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Table I Reflection Factors by Three Methods of Measurement.

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F = c m F + π b o c
π b o a m + F
( 1 m ) [ π b o a m + F ]
π b o c + c m F + ( 1 m ) [ π b o a m + F ) ] = F
b o = m 2 F ( 1 c ) π [ m c + a ( 1 m ) ] = m 2 F a π [ m c + a ( 1 m ) ]
( 1 m x ) ( π b x c + c m F ) + ( 1 m ) [ π b x a m + F ] = F
b x = m 2 F ( a + c m x ) π [ c m ( 1 m x ) + a ( 1 m ) ]
b = m 2 F ( a + c m ) π [ ( 1 m ) ( c m + a ) ]
Let b b o = K and b x b o = K x
K = m 2 F ( a + c m ) π ( 1 m ) ( c m + a ) m 2 F a π [ m c + a ( 1 m ) ] = ( m c + a ) [ m c + a ( 1 m ) ] a ( m c + a ) ( 1 m )
m 2 [ c ( c a ) + K a c ] + m a [ c + ( c a ) ( 1 K ) ] + a 2 ( 1 K ) = O .
K x = m 2 F ( a + c m x ) π [ c m ( 1 m x ) + a ( 1 m ) ] m 2 F a π [ m c + a ( 1 m ) ] = ( a + c m x ) [ m c + a ( 1 m ) ] a [ m c ( 1 m x ) + a ( 1 m ) ]
m x = a ( K x 1 ) [ c m + a ( 1 m ) ] a c ( 1 m ) + m c ( c + K x a )
Let c , c , a , m , m x and F have the same meaning as before . b = brightness of sphere surface when the hole is covered with a test surface of factor m x . R = value of b when hole is covered with surface m value of b when hole is covered with surface m .
( 1 m ) π b a m + ( 1 m x ) ( F + c π b ) = F
b = m m x F π [ a ( 1 m ) + c m ( 1 m x ) ]
R = m m F π [ a ( 1 m ) + c m ( 1 m ) m m F π [ a ( 1 m ) + c m ( 1 m ) ] = m [ a ( 1 m ) + c m ( 1 m ) ] m [ a ( 1 m ) + c m ( 1 m ) ]
m = m x = R m [ a ( 1 m ) + m c ] ( 1 m ) ( a + c m ) + R m 2 c