C. A. BARBER 169 



the first and second classes and the third and fourth would overlap and, when 

 there are 323, the second and third only, in each case bringing the classes each 

 to 81 seedlings. This method does away with the fraction which introduces 

 difficulties in calculation and, in dealing with large numbers, has no advantage. 

 By using the method of overlapping, in classes of equal numbers there will 

 never be an excess of seedlings over the actuals of more than three. 



In the second method, that of dividing the list into classes with equal 

 differences in leaf width, on the other hand, the matter is not so simple. If 

 overlapping is resorted to, it will not be of individuals but of classes and the 

 number of seedlings will sometimes be considerably increased, according to 

 the numbers in the repeated classes. The number of classes in the general 

 list of Karun seedlings is 20, but we cannot simply divide these into four 

 classes of five each because they are not of equal leaf width difierences. The 

 extremes are 1-5" and 3-6", thus making 22 classes separated by one-tenth 

 inch in leaf width, the two classes 3*4" and 3-5" having no representatives. 

 In dividing these into four classes according to leaf width, two must overlap, 

 giving the four groups 1-5— 2-0", 2-0-2-5", 2-6— 3-1" and 3-1— 3-6". It is 

 obvious that there are objections to this overlapping, but the method 

 appears, on the whole, to work satisfactorily. The two classes which are 

 repeated have, between them, 24 seedlings, and the number of seedlings in 

 the four classes is thus 346 instead of the correct number 322. It all 

 depends on whether the repeated classes are likely to alter the general results, 

 and this is one reason for the inclusion of the division into two classes as well, 

 for then the class repeated, if there is one, will be a different one. In the case 

 in point, class 2-0" (with 20 seedlings) has 14-96 sucrose, which is fairly average, 

 but class 3-1" (with 4 seedlings) is distinctly low, but there are too few seedlings 

 in the latter class to make much difference. Each case must be thus judged 

 on its merits, and one is given on p. 189, where the repetition of classes has 

 introduced a discrepancy, because the classes repeated are both exceptional 

 and of sufficient size to influence the results. This is at once checked by 

 the divisions into two classes and such cases give additional weight to the 

 advisability of studying these correlations by the two methods described 

 above. 



From a consideration of the table of Karun seedlings, it is seen that there 

 is a distinct tendency for the narrow leafed forms to have richer Juice (as 

 judged by the sucrose contained) than the broader leafed forms, in other 

 words, that there is a negative correlation between leaf width and sucrose. 

 But this by no means excludes the occurrence of good seedlings among the 



