152 SIDNEY F. HAEMER. 



That there are exceptions to this rule has been shown above 

 by the description of odd-numbered branchless internodes ; but 

 it must be remembered that these cases are rare. 



From what has already been said of the laws which regulate 

 the growth of Crisia, it is obvious that a representation of a 

 colony can easily be reconstructed from a formula of the cha- 

 racter introduced by Smitt; and no further justification is 

 required for the use of such formulae. 



In some specimens of C. denticulata the average number 

 of zocecia in an internode may be higher than in the one de- 

 scribed; and the numbers 13^ 15, 17, and even 19 are by no 

 means uncommon. It may often be noticed that, although inter- 

 nodes consisting of any given number of zooecia do not seem 

 to be arranged in any definite order in the colony, an indivi- 

 dual colony may be characterised by the frequent occurrence of 

 internodes with that number of zooecia. Thus if the dominant 

 number, in any particular case, be 11 — and this seems to me 

 the most common case — variations in the number of zooecia in 

 the internodes of that colony will apparently take place about 

 the number 11 as a mean ; so that, although internodes of 9 or 

 13 zooecia are common, there may be none of so many as 15 

 zocEcia. But if the colony have many internodes of 15 zooecia, 

 for instance, then it will probably be found that some of the 

 other internodes have 1 7 or 19. 



If the growth of the branch be complete, so that no more 

 axial joints are to be formed, the terminal internodes, and 

 especially those which have produced ovicells, may have a 

 larger number of zooecia than the internodes of the rest of 

 the colony; and the number of zooecia formed before the 

 growing-point exhausts its activity does not appear to be 

 regulated by the laws which govern those internodes which 

 are not terminal. But even the terminal internodes normally 

 produce no more than a single branch (cf. C. aculeata and 

 C. ramosa), the cases mentioned on p. 149 being the only 

 ones in which two branches were noted to come off from the 

 same internode. 



The articulations of the lateral branches of this species are 



