44. BULLETIN OF THE 
ter | 1. 1-8 IV. (an outer individ.) gives rise to 8 branches and 34 individ, 
2. 9-12 IV. (an inner Cine) ee ed Ter at 
md 8. 13-16 IV. (an inner K adres ee re Katkin aai 
l4. 17,18 IV. (asubouter “ ET TO Kr e > 
Tara, | 5. 19-22 IV. (arshouter “ jJ «€ er! bi REN 
6. 23-26 IV. (ar ‚ner Sie S ei! ki ier en 
Oren § 7. 27-80 IV. (an inner BR EH Eee i megg st 
(8, 81-44 IV. (an outer Mishel ef ld rs 700 4 
According to the rule that inner branches are slightly prolific, we should 
expect cases numbered 4 and 5 in the above table to contain the fewest 
branches and individuals; in accordance with the rule that marginal 
branches even of subfans are more prolific, we should expect them, on 
the contrary, to contain more branches and individuals than cases num- 
bered 3, 6, ete. The result is usually a condition intermediate between 
that of the middle and outer branches, such as is partially realized in 
case number 5, Case number 4 seems to present an unusual condition, 
which may be correlated with the fact of its close approximation to 
number 5. (See Fig. 64, 17-20.) From the consideration of this and 
other cases, I think this conclusion may fairly be drawn: (6) Of the 
Jour proximal individuals from which a fan arises, the outer two will bear 
the greater number of individuals, the inner two the lesser. 
Since from rule 2 median individuals (ancestral branches) occupy the 
margins of fans (or subfans of any degree) and the lateral branches are 
intermediate, it follows, as a corollary to rule 5, that, in general, the an- 
cestral branches are the shorter, the lateral branches the longer; and, as 
a corollary to rule 6, that from any axil the ancestral branch will of the 
two give rise to the greater number of individuals; the lateral branch, 
conversely, to the less, other conditions being equal. 
We have deduced the laws of lateral budding on different parts of the 
circumference. We find also that there is a regular variation in the 
frequency of lateral budding, dependent upon the distance of the region 
from the primary individual of the fan. This rule, like any other, is not 
invariable, whatever the other conditions may be; but it is more or less 
dependent upon them. A small and regular fan having seven genera- 
tions gives this result. 
No. of Generation, Number of Individ. Increase per Cent. 
1 
