130 SIDNEY F. HAEMBE. 



the internode below it and in the internode above it on the 

 stem. 



But if an even-numbered internode is developed (fig. 2), 

 its last zooecium will of course be on the same side of the stem 

 as the last zocEcium of the preceding internode ; and conse- 

 quently the basal zooecium and the branch of the internode 

 above it will be on the same side as its own basal zooecium, 

 and on the opposite side to the branch next below it ; or, illus- 

 trating this by a formula, we shall, as a rule, find cases like 

 (IS + r-g) +(8) + (7 + 2r), as shown in fig. 3. 



Thus, stating the same fact in another way, an even- 

 numbered and branchless internode may be intercalated in the 

 stem without disturbing the alternate origin of the branches 

 on opposite sides. The same is true of those cases where two 

 even-numbered internodes occur consecutively on the same 

 axis. 



The more closely one investigates unusual methods of 

 branching in this species, the more obvious does it become 

 that the growth of the colony is regulated by some well-defined 

 law, which finds one of its expressions in the preceding rule. 



Thus it will be seen, by reference to figs. 2, 4, 6, and 11, 

 that the basal zooecium of a lateral branch is on the abaxial 

 side of the latter in all the four species referred to; and 

 further, that the branch given ofi' by the basal internode of an 

 axis is also on the abaxial side. This is obvious enough for 

 C. denticulata, from the formula on p. 146, where it will 

 be noticed that, in the one case in which the basal internode 

 has an even number of zooecia, the second internode develops 

 the first branch, and that that branch (and of course the basal 

 zooecium) is on the abaxial side. 



On two occasions abnormal branching of the type (9 + ^r) + 

 (13) + (11 +^r) was noticed. Here an odd-numbered branch- 

 less internode occurs ; but such cases seem to be rare. Since 

 the number of zooecia in the branchless internode is odd, it 

 follows that the basal zooecium, and consequently the branch, 

 of the third internode will be on the same side as in the first 

 internode, 



