74 



Messrs. Paterson and Dud ding on the 



compared set 2 against set 1 about eight times, and obtained 

 a value of 99* 5 5 for set 2 as compared with a mean value for 

 all observers of 100. He then compared 3 against 2, as- 

 suming his own value of 99*5 5 for set 2. In the same way 

 4 is compared against 3, and so on to set 6. The bottom 

 line, therefore, gives the values which each observer obtains 

 for set 6 in terms of set 1 as a result of his own inde- 

 pendent descent through the intermediate steps of the 

 cascade. 



Table III. gives the value which each observer obtains 

 for set 6 when compared in one step against set 1 with the 

 Lummer-Brodhun photometer. It will be seen in the last 

 column that this direct comparison of set 6 with set 1, 

 entailing the full colour difference, yielded as the mean of 

 all observers a result differing by a little less than 0'3 per 

 cent, from the comparison by the cascade method (Table II.) . 

 By reference to Table Y. it will be seen that this is the order 

 of the probable error of either result. 



Table III. — Summary of Direct Comparison of Set 6 

 against Set 1 by each Observer. 



Observer. 



A. 



B. 



C. 



D. 



E. 



F. 



Average. 



Set 6 



99-0 8 



99-5 5 



98-9 5 



99-3- 



100-9 G 



100-4! 



99-7 2 



Judged from the physiological standpoint, it cannot be 

 said with certainty that the cascade method (Table II.) 

 should give a result which is more absolutely rigorous than 

 the direct method (Table III.). The case is, however, some- 

 what analogous to the comparison of a low with a high 

 resistance direct, and through the medium of a series of 

 resistances with intermediate values. The authors place 

 more reliance on the cascade method because of the less 

 consistent manner in which observers by the direct method 

 have been found to repeat their individual readings over 

 considerable intervals of time. This lack of consistency has 

 not been found where the small colour differences of the 

 cascade method are concerned. All the measurements with 

 the direct step were taken over a relatively short period of 

 time, whilst those included in the cascade method extended 

 over several years. The experience of the authors where 

 larger colour intervals are concerned does not afford an 

 assurance that the "day to day" probable error of the 



