76 Messrs. Paterson and Dudding on the 



when any one observer's differences for the five steps of the 

 cascade are added together, the total difference does not 

 entirely accord with the results of that observer's direct 

 comparison through the large colour step. (Compare the 

 last two lines of the table.) For observers E and F the 

 sum of the differences for the five small steps gave, it is 

 true, nearty the same figure as for the one large step, but 

 in all other cases the differences were appreciable, observers 

 B and D especially showing unexpected results in the direct 

 comparison. This illustrates what was stated earlier as to 

 the more erratic nature of results obtained with large colour 

 steps. The experience obtained with these and other com- 

 parisons is that whereas an observer may be relied upon 

 for constancy of judgment in measuring with small colour 

 differences, the same constancy of judgment is not obtainable 

 with large ones. 



Efforts were made to obtain a comparison between sets 1 

 and 6 by means of the flicker method. Several flicker 

 photometers were tried by four of the observers, but the 

 precision of the measurements was found to be so inferior 

 to that obtainable with the Lnmmer-Brodhun photometer 

 that after much time had been spent the attempt was 

 abandoned. The authors were unable to experience the 

 sensitivity claimed for the flicker photometer by some other 

 experimenters, and the results they obtained with it were of 

 ■quite a different order of accuracy from those forming the 

 subject of this paper. Moreover, it is found that the fatigue 

 occasioned by continuous photometric observation throughout, 

 a whole day necessitated by these standardizations was very 

 serious with the flicker photometer, and tended still further 

 to diminish the sensitivity. 



2. Probable Error of the Results. 



In computing the probable error in the value attributed 

 to a lamp by a set of observations, the error may be 

 regarded as arising from three distinct causes. 



First, there is the error due mainly to the lack of 

 sensitivity of the photometer, resulting in a succession 

 of readings being obtained which differ slightly amongst 

 themselves — all other variables being constant for the short 

 period during which the lamp is being photometered. Five 

 or more photometric settings have always been made by 

 each observer on each occasion on which the lamp is tested. 

 The usual probable error in the arithmetical mean of these 



