82 BULLETIN OF THE 
polypide. In Phylactolemata the oral aspect of the polypide is turned 
towards the margin of the corm 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 Phylactolemata, 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 formule of Phylactolemata the budding is centrifugal, 
new individuals being produced from the embryonic masses towards the 
margin; in the formule of Gymnolemata budding is centripetal, new 
individuals being produced from the embryonic masses towards the 
centre. In both Phylactolemata and Gymnolemata the anal aspect 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 Phylactolemata, the œsophagus. 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- 
tolemata and Gymnolemata 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 Halı- 
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) DO ba Oo 4d. ¢ b BL do brava y 8 aA 
According to my interpretation of the case, this formula might be 
written (15) :— 
%#D sc xb xa xC 3d #c xb xa xB ae xe xd xc xD xa xa ey #B ra % 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 
