ACTINOZOA. 



175 



expected that for all corallites of this order having 

 a higher formula than S. 24, the number of new- 

 septa produced within each of the first formed 

 chambers would be represented by the successive 

 terms of the series 7, 15, 31, 63, &c., in which 

 each number is double plus unity of its antecedent. 

 Practically, however, we find that, as soon as the 

 formula S. 24 has been reached, only two septa 

 arise at the same time in each primary chamber, 

 or, in other words, the corallite developes simul- 

 taneously not more than twelve additional septa. 

 So that the simple expression n x 6 + 6 at once 

 determines the normal septal formula for all 

 Zoantharian corallites having twenty-four or more 

 septa. Here n is = the number of septa between 

 each primary pair, and corresponds to the succes- 

 sive terms of the arithmetical progression 5, 7, 9, 



11, 13, &c. 



Since, therefore, the Dumber of septa in process 

 of formation is often less than the number of 

 loculi, it becomes necessary to determine those 

 chambers in which the new septa first appear, and 

 the precise order of succession which they observe. 

 But first let us explain the few technical terms by 

 which the facts to be announced have been ren- 

 dered susceptible of definition. 



All septa which commence their growth simul- 

 taneously are said to be of the same order, while 

 those which divide chambers of equal size belong 

 to the same cycle. It is evident that septa of the 

 first three cycles must correspond to those of the 

 first, second, and third orders, respectively. But 

 the fourth cycle includes septa of the fourth and 

 fifth orders ; the fifth, of the sixth, seventh, eighth, 

 and ninth; and the sixth of the 10th, nth, 12th, 



