MUSEUM OF COMPARATIVE ZOOLOGY. 85 



giving rise to the phenomena of young individuals interpolated between 

 older ones. Representing, then, individuals by the budding zones from 

 which they have arisen, we may convert the following formula of Semper 

 into one based on our own nomenclature : 



E DH BG CF A 



az.-3 + O-O 4 + 0-1 + 0-0 4 + 1-1 + 0-0 4 + 0-2 + 0-0 4 + 1 



in which the succession of generations of zooids is 



... 5, 4, 8, 2, 7, 3, 6, 1. 



In the above formula A, B, C, etc. represent zooids; the numerals 

 below the letters, the number of metameres of which each is composed ; 

 0, an incomplete metamere about to be derived from a budding zone ; 

 az., the anal zone. Written in accordance with my conception of the 

 facts, this formula would read : 



(20) -:■> D (*) * C (*) * a (*) * B (*) * b (*) * a (*) * a' (*) * A, 



which somewhat resembles P'ormula (15) of Halistemma, and signifies 

 that two embrj'onic masses are left behind by the anal zone, of which 

 the one anterior to the zooids proper (represented by letters) goes merely 

 to form the head parts, and is represented parenthesized. The second 

 is caudad the zooid, and may form a secondai-y " anal zone " giving rise 

 to new zooids. From one zooid two or more anal zones may take their 

 origin. Thus, from the embryonic mass caudad of A there have arisen 

 that caudad of b, which has given rise to b (*) * a (*), and that caudad 

 of a', which has given rise to a' (*)^ 



The most general fornmla given on page 81 undergoes many modi- 

 fications in the difterent groups, but in the midst of these modifications 

 certain laws are to be discerned, to some of which I have already called 

 attention. I will now proceed to a discussion of the significance of 

 these laws. 



The quincunx arrangement of individuals, which is so noticeable in 



1 From a study of surface views of many specimens of Autolytns collected 

 at Newport during June, 1891, I am convinced that the sexual individuals are 

 produced by proliferation of cells in the metamere XIII. or XIV. of " parent 

 form," — the last which remains behind after breaking off of sexual form. Kep- 

 resenting the proliferating metamere by (S-), we may write the budding formula 

 of Autolytus thus : 



(20a) A E (*) D (*) C (*) B (*) A (*) 



in which the parenthesized asterisks indicate the proliferating, but not gemmif- 



erating anal metameres of the sexual form. (Cf. A. Agassiz, '63, pp. 397-400.) 



