86 University of California Publications in Zoology. [Vol. 6 



stigmata vary from "short" to "long." Figures 15, 16, and 17 

 illustrate this. It has also been shown that these form varieties 

 are correlated with the size and at least to some extent with the 

 age of the individual animals. Of course the individual stigmata 

 develop. This latter fact is so obvious as to seem too trivial to 

 mention. Yet from our present standpoint it is of real interest 

 and demands special attention, for see what questions we may 

 ask in consistency with the perceptions of multiplicative rules 

 already reached. Recalling what has been noted about the ma- 

 terial basis of the stigmata, namely, that this is the row of 

 ciliated cells bordering the orifice, it will be seen that the devel- 

 opment of the stigmata is dependent upon the multiplication of 

 these cells. Is it not probable then that the various forms of the 

 ellipse passed through by a particular stigma in the course of 

 its development is determined by the rate of multiplication of 

 the cells and the size of these in the different parts of the circum- 

 ference, and is it not further probable that this rate of multi- 

 plication and cell-size are in turn dependent upon the distance 

 in both time and locality of the cells from the initial "germ 

 mass" of the stigmata to which attention was above called. 

 Again, is it not probable that a diminishing rate of both cell- 

 size and cell-multiplication occurs in the different time and 

 locality parts of the border, so that, however long continued the 

 development of tin.' stigma, its sides would never become truly 

 parallel; in other words, that its ellipsoid form would be retained 

 throughout, though with ever increasing ratio of long to short 

 axis .' 



Still further, is it not probable that the rule of diminution 

 in multiplication and enlargement likewise holds as to the pro- 

 duction of new stigmata so that in every branchial sac, to how- 

 ever vigorous and large-grown an animal it may belong, a defi- 

 nitely graded series of sizes and shapes of stigmata must theoret- 

 ically and to some extent practically occur? 



I conclude this section with the remark only incidental to the 

 present "inquiries" though fundamental to possible future ones, 

 that further mere inspectional study in the directions here blazed, 

 if carefully prosecuted on this and other species of simple aseid- 



