No. 408.] PECTINATELLA MAGNIFICA. 965 
perpendicularly to the surface of the statoblast. Between the 
cells are large water spaces, which may indicate that the hook- 
forming layer is turgescent, at least at the time of forming hooks. 
The first step in the formation of a hook is a fold (Fig. 7). 
As many folds arise at about the same time as there are hooks. 
Consequently the number of hooks is determined by the num- 
ber of folds, and the question of the cause of variability is 
transferred to the folds. I had thought at first that each fold 
might be derived from one cell, but since the hook-forming layer 
spreads over the forming float and consists already of numerous 
columnar cells, it would be difficult, if not impossible, to dem- 
onstrate this if it were so. The forming papilla is made up 
of 100 to 200 cells at its beginning. In its center is a core, 
filled with a secretion, which hardens to form the shaft of the 
hook. The prongs are secreted as a superficial cuticula at the 
apex of the papilla (Fig. 8). From this it will be seen that 
my hypothesis was incorrect, and I find in the embryology no 
ground for referring the number of hooks to a predetermining 
number of hook-forming Anlagen. 
It is possible that the number of papillae may be correlated 
with a variation in the perimeter of the statoblast, so that the 
number of hooks per unit of perimeter is constant. To settle 
this question, I measured the perimeter! of 125 statoblasts. 
I found these measurements interesting in themselves. The 
modal perimeter of the statoblasts was about 3.3 mm. The 
average was 3.319 ; o = .06649 mm. ; and c = 2.00, a remarkably 
low variability, almost one-fifth that of the number of hooks. 
By the use of the Galton-Pearson-Duncker? method of calculating 
1 The perimeter was measured by finding the length of a camera outline by 
means of the map-measure described in my Statistical Methods (New York, John 
Wiley & Sons, 1899). 
2 The reviewer of my Statistical Methods, in Nature, Dec. 14, 1899, says : “ On 
p. 33 we notice a lengthy method, quoted from Duncker, given for reducing the 
product sum; this should be replaced by the ordinary straightforward process of 
reduction to the mean.” Although I have been satisfied of the correctness of 
Duncker’s formula, which is got from Pearson’s by a process of simplification, I 
calculated » by Pearson's method. Using logarithms, this took about four hours ; 
whereas to calculate » by Duncker’s method took in this case about twenty min- 
utes. The results differed by .oor. The length of Pearson's process is a great 
obstacle to its use. 
