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. (Of. 
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 XII., 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 
number of generations. 
Although the marginal individuals of say generation II., IV., or V. 
do not support branches with so many generations as the intermediate 
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 :— 
