CORRELATION BETWEEN DIFFERENTLY SITUATED WHORLS. 93 



THE CORRELATION BETWEEN DIFFERENTLY SITUATED WHORLS IN 

 RESPECT TO LEAF-NUMBER. 



In the preceding section we have examined the correlation existing 

 between leaf-number and position of the whorl on the axis, and in that 

 way determined the law according to which the size of whorls changes 

 with different positions on the branch. We may now consider the 

 further problem of how the absolute sizes of different whorls are cor- 

 related together. Especially it is desirable to determine to what degree 

 the first, whorl on a branch is correlated with whorls farther out. In 

 this way we shall see whether a particular branch has as a whole a 

 definite tendency or *'set" towards a relatively large (or small) absolute 

 leaf-number for all its whorls. It will be seen that this problem is quite 

 distinct from that considered in the last section. We are not now con- 

 cerned with the law of change with growth, but rather with absolute 

 sizes. All the whorls on a given branch may be relatively large or rela- 

 tively small and still have been differentiated according to our logarithmic 

 law. The question, then, with which this section has to do may be 

 stated in this way: If the first whorl on a branch has more than the 

 average number of leaves, will the succeeding whorls on the same branch 

 also tend to have in each case more than the average number of leaves 

 for their respective positions? In order to test this question we have 

 to determine individually the correlation between the first and each 

 successive whorl on the branch. On account of lack of material I have 

 not been able to carry the correlations beyond the tenth whorl. For 

 the same reason it is necessary to confine the discussion to primary- 

 branch whorls. We may first examine the results from the data of 

 Series I, II, and III combined. In table 47, page 94, is given the raw 

 material. It may be noticed that the totals of these tables do not 

 agree with those for the corresponding whorls in table 32, because in 

 that table every unmutilated whorl is included, while here we have, of 

 course, been restricted to every unmutilated pair of whorls. Naturally, 

 a great many broken whorls pair with unmutilated ones which appear 

 in the earlier tables, but not in these. 



The coefficient of correlation was determined for each of these tables 

 in the ordinary way. The values so obtained, together with their prob- 

 able errors, are given in table 48, page 95. 



There is clearly a very distinct correlation between the first and 

 second and first and third whorls. As we go farther out on the branch 

 the correlation steadily decreases, till finally at the ninth whorl it 

 becomes sensibly zero. There is apparently a rise in the correlation at 

 the eighth whorl, but this is probably a purely accidental result arising 

 from the fact that the number of pairs is getting too small to depend 



