62 MIDDLEKAUFF AND SKOGLAND : EQUATIONS 



corresponding to that color are computed from the voltage at 

 which the candlepower is known, this computation being made by 

 the use of the voltage-candlepower equation of the standards. 



In order fully to realize the advantages of this method in 

 practice, it was necessary, first, to measure a large variety of 

 tungsten lamps to find the relation of candlepower to voltage, and 

 then to calculate the equation which would express this relation 

 over a wide range of voltage or efficiency. The results were far 

 more satisfactory than was at first anticipated. 



It was found that all vacuum tungsten lamps, within a wide 

 range of wattage, have the same voltage-current-candlepower 

 characteristics regardless of the make or method of manufacture. 

 It was found also that, not only the voltage-candlepower relation, 

 but also the voltage-current, voltage-wattage, and voltage-watts 

 per candle, relations could be accurately expressed by one general 

 equation of the form y = Ax~ + B.t + C. In this equation 

 X = log voltage, y = log candlepower, log wattage, log current, 

 or log watts per candle, and A, B, and C are constants, the 

 values of which depend upon the significance of y. It is found 

 most convenient to express all these variables, except watts per 

 candle, in terms of the respective values of each at a chosen normal 

 efficiency. In this way the constant C disappears from the 

 equation except when y represents the watts per candle, in which 

 case C is the logarithm of the watts per candle chosen as normal. 



The above general equation applies very exactly over the 

 whole range investigated, namely, from 0.7-ivpc to S.3-ivpc, the 

 latter limit extending somewhat beyond the watts per candle 

 corresponding to color match with 4i-wpc carbon lamps. 



These equations are useful for two purposes. The international 

 candle is maintained at the Bureau of Standards by means of 

 4l-wpc carbon standard lamps. If for example it were desired to 

 establish a group of tungsten standards operating at 1.5 wpc. 

 these tungsten standards would be measured directly in terms 

 of the primary i-tvpc carbon standards with the voltage on the 

 tungsten lamps so adjusted as to bring them into color match 

 with the primary standards. Then, from the voltage and 

 corresponding efficiency of the tungsten lamps at this color, the 



