Unit of Candle-power in White Light. 77 



five settings in any step of the cascade is 0*2 per cent. in. 

 candle-power, whilst for the direct step with the large colour- 

 difference it is 0*3 per cent. The ultimate probable error in 

 the unit of candle-power held in a batch of lamps due to 

 this cause is, however, very small, being reduced approxi- 

 mately in proportion to the square root of the total number 

 of measurements made. This number being very great the 

 error becomes entirely negligible. 



The second source of error, called here the " day-to-day 

 error," produces differences in the value obtained for the 

 same lamp as measured from day to day. These dis- 

 crepancies may be ascribed to the slight differences in the 

 mechanical or electrical adjustments of the lamps, to small 

 changes in the lamps themselves, or to variations of the 

 observers' judgment due to physiological or psychological 

 causes. The probable error due to these causes is kept 

 small by each observer making his measurements on a 

 sufficient number of different days. It may amount to 

 O0 4 per cent, for the determination of the values of one 

 set of lamps in terms of an adjacent one in the cascade 

 series. In computing this error it would not be right to 

 regard the causes as entirely mechanical in character. If 

 they were, the probable error would be much reduced by the 

 fact that there were at least 10 lamps in each set. It is 

 necessary to regard at least a portion of the error as due 

 to physiological causes the effect of which is not reduced 

 by having a number of lamps, but only by increasing the 

 number of observers. \n order to avoid too sanguine a figure 

 for the " day-to-day " error, its value has been computed on 

 the assumption that errors under this section are entirely 

 physiological in origin. 



The third and ino&t important source of error lies in the 

 consistent differences which exist between various observers, 

 due to colour differences. In the cascade method of bridging 

 the step from the lowest to the highest efficiency standards 

 the errors are additive from one step to the next, and the 

 final probable error has been calculated from the final 

 differences tabulated in line 7, Table IV. 



The amount of the probable errors ascribed to each cause 

 for each step of the cascade is given in Table V. It will be 

 seen that the probable error of the final result — viz., of the 

 unit represented by set (> in terms of set No. 1 — is of the 

 order of 0*3.-, per cent, both by the cascade and by the direct 

 methods. 



