MUSEUM OF COMPARATIVE ZOOLOGY. 43 



generations (24 X., 25 IX.). This may be expressed by saying branches 

 are given off on the side towards the axils. 



By consulting Figure 64* and tracing out the finely dotted lines which 

 connect the second, third, etc. axils of all branches counting from the 

 proximal end of the fan, it will be seen that (3) lateral buds tend to arise 

 on two closely related branches in the same generation. There are several 

 slight deviations from this rule. The less closely related the branches, 

 the less marked the tendency, although it is still discernible. (Cf. 

 branches 9-16, 23-30.) 



This rule does not hold, however, so well on the margins as in the 

 middle region of the fan, for here another and a superior rule seems to 

 obtain. This is that (4) lateral budding occurs more frequently at the 

 margins of " fans" than elsewhere. Thus in Figure 64* there is at the 

 margins, on the average, 1 case of lateral budding to 4.3 cases of median 

 budding. Elsewhere the average is as 1 to 6.5. In larger fans the 

 difference is even more pronounced. This is true not only for the 

 "fans," but also, to a less degree, for the two "subfans" which arise re- 

 spectively from the two individuals of generation II. (but 17, 18 is very 

 anomalous in this respect). In general, any rule deduced for the mar- 

 gin of the fans holds true also for subfans to any degree of subdivision ; 

 but the less perfectly, the higher the degree. 



By consulting again the diagram, it will be seen that the branches 

 have attained different lengths. Thus 9, 10, 29, and 30 contain repre- 

 sentatives of generation XIII., while the terminal individual of branch 1 

 is of generation X., and those of branches 35-44 are of generation XI. 

 So the curve which connects the tips of the branches (see dot-and- 

 dash line, Fig. 64*) would rise from 1 to 9-10 as a maximum, and fall 

 again till it reached the margin of the first subfan ; then rise again, 

 reaching a second maximum in the middle at 29-30, and finally fall 

 again to the other margin. In general, then, (5) the marginal branches 

 are shortest, the intermediate ones longest, i. e. give rise to the greatest 

 mimber of generations. 



Although the marginal individuals of say genei'ation Til., IV., or V. 

 do not support branches with so many generations as the intei'mediate 

 ones, yet they are not therefore necessarily less prolific in individuals, 

 because the number of branches arising distally of such individuals is 

 greater according to rule 4 than the number arising distally of the 

 intermediate ones. Thus, if we count the number of individuals borne 

 on each of the eight individuals of the fourth (IV.) generation of 

 Figure 64, we find in the given case : — 



