82 BULLETIN OF THE 



polypide. In Phylactolsemata the oral aspect of the polyplde is turned 

 towards the margin of the corni or the tip of the branching stock ; in 

 Gymnolsemata, on the contrary, the anal aspect is turned in that direc- 

 tion. This difference is a very striking and constant one. It is corre- 

 lated with another difference in the law of budding of the stock, which 

 will become evident upon comparing Formulas (4) and (5) on page 74, 

 of Phylactolsemata, with Formulas (1) on page 73 and (7) to (13). In 

 all of these the margin or tip of the stock is at the left, the centre at the 

 right. In the formulae of PhylactOjlsemata the budding is centrifugal, 

 new individuals being produced from the embryonic masses towards the 

 margin ; in the formulae of Gymnolaemata budding is centripetal, new 

 individuals being produced from the embryonic masses towards the 

 centre. In both Phylactolcemata and Gymnolcemata the anal asp)ect is 

 turned towards the gemmiferous region. 



Braem calls attention to one other difference, namely, that, in the case 

 of the retracted polypide, in Paludicella the rectum lies next the at- 

 tached surface of the stock ; in Phylactolseraata, the oesophagus. A 

 mechanical cause of this is suggested when this statement is put in other 

 words : the polypide in its retracted position is stored in both Phylac- 

 toljBmata and Gymnolsemata proximad of the atrial opening ; i. e. away 

 from the tip or margin, and towards the centre of the stock. May not 

 this be explained, in part at least, as an adaptation to room % 



I will here add four examples of regular budding taken from other 

 groups of animals, to illustrate the general applicability of this method 

 of representation. The first of these is that of the Siphonophore Hali- 

 stemma whose formula has been worked out by Chun ('88, p. 1169), and 

 expanded and illustrated by Korschelt und Heider in their recent text- 

 book (p. 39). It runs as follows : — 



(14) DcbaCdcbaBedcbaa^jSoA 



According to my interpretation of the case, this formula might be 

 written (15) : — 



-li;- D <;- c *b *a * C -^ d *c *b *a * B -$- *e *d *c *b *o *a *->' *J3 *o * A, 



in which the ^ behind B has been derived from the embryonic mass at 

 A, that behind C from B., etc. The -^'s represent embryonic masses 

 from which a, b, c, etc. are derived. 



If we assume that the terminal individual (A) has not been derived 

 from the primary embryonic mass, at the extreme left, but has had its 



