192 Dr. Honstoun and Miss Dunlop on a Statistical 



numbers were determined for all the observers. The results 

 of the tests are given in the preceding table and are repre- 

 sented in figs. 5 to 10. We learn, for example, from the 

 table that 68 men recognized the black disks between 10 

 and 11 mm. from focus, the range including 10 mm. itself 

 but stopping short of 11 mm., and that 21 women recognized 

 the same disks within the same range. 



The question naturally arises, as to how T far the readings 

 taken with the microscope can be regarded as a reliable test 

 of colour vision. They were checked to some extent by 

 Dr. Edridge-Green's bead test. In this test the observer is 

 provided with a number of coloured beads and four little 

 boxes labelled red, yellow, green, and blue, and is asked to 

 put the beads into the appropriate boxes : once the bead goes 

 through the hole in the box, it is lost from view. There is 

 no doubt that this is a very effective test, not so much by 

 reason of what the observer does eventually, as by how he 

 does it ; if he hesitates long with a pink over the mouth of 

 the hole marked blue, his colour vision cannot possibly be 

 normal. Generally speaking the two methods agreed: if an 

 observer could not distinguish red from green w T ith the 

 microscope except close up, he put some beads in the wrong- 

 holes and vice versa. But there were exceptions : one man 

 whose mean distance for distinguishing red from green was 

 2*99 mm. appeared quite normal under the bead test, and 

 another who distinguished red from green at 12*5 mm. put 

 a brioht red into the green hole. This man was examined 

 by the bead test at his own request. 



Prof. Karl Pearson has established a system of formulae 

 for representing frequency distributions. A short account 

 of these formulae is given in his " Tables for Statisticians 

 and Biometricians," p. Ix, and a fuller account together 

 with the method of deriving their constants by means of the 

 moments of the distributions together with worked examples 

 is given in Elderton's " Frequency Curves and Correlation." 

 In figs. 5 to 10 the area of each rectangle represents the 

 number of observers in one group. If the number of 

 observers was increased to many thousands and the number 

 of groups also increased, the rectangles would become 

 narrower, until finally in the limit the steps would disappear 

 altogether, and the frequency distribution would be repre- 

 sented simply by a smooth curve. The frequency distri- 

 butions are not smooth curves because the observations are 

 not numerous enough. Are they reasonable approximations 

 to Pearson's types, considering the limitations of the 



