KOFOID: DEVELOPMENT OF LIMAX. 59 
the strict arithmetical series in that a multiple of the common difference 
is sometimes added as a result of the approximated or even synchro- 
nous division of two or more quartets. Thus the series may in some of 
its parts, like the twelve- to twenty-four-cell period of Planorbis, take 
the form of a geometrical series; but this is not fundamental, and, as 
Warneck in 1850 expressed the law, **In jedem Stadium des Furchungs- 
processes entstehen nur vier Furchungskugeln, d. h. die Theilung geht 
nicht in einer geometrischen sondern einer arithmetischen Progression 
vor sich." 
The general contour of the egg in the twenty-four-cell stages figured 
(Plate III. Figs. 23-25, Plate IV. Figs. 27-32, Plate IV. Figs. 33, 34) 
has been spherical, the transverse and vertical diameters being approx- 
imately the same. In the period leading up to this stage, however, 
eggs are found showing a considerable flattening in the dorso-ventral 
direction, i. e. a shortening of the vertical axis. In one egg showing 
the flattening, the dorso-ventral diameter was 70 u and the transverse 
120 u. This change may be dependent upon an elimination of such a 
cleavage cavity as is shown in Plate V. Fig. 34. A similar flattening is 
often found in those eggs in which the divisions leading to the forty- 
cell stage are taking place. These divisions will now be discussed. 
The order of their discussion does not, however, indicate their chrono- 
logical suceession. 
Division of Quartet 5.3, forming 6.5 and 6.6. 
Plate VI. Figs. 37, 39, 41. 
The division of this quartet does not take place, in some instances at 
least, until after the forty-coll stage ; i. e. it is accompanied by divisions 
of the succeeding generation in other quartets. See Figures 39 and 41. 
In Figure 39 the cells a5? and d%* have divided, and 0"? is in a mitotic 
state, but ° is as yet undivided. In 0% the end plates have been formed, 
but the cytoplasm is not yet constricted. The axis of the spindle lies 
parallel to the plane of the equator. There is every indication that the 
division is very nearly meridional. Figure 39 has forty-two cells; in 
Figure 41 there are forty-five cells; here, however, it is cells a’? and 
d”? that have but recently divided, the other cells of the quartet having 
evidently been divided for some time. Thus there is no constancy as 
to the sequence in which the cells of this quartet divide. In Figure 
41 (Plate VL) this division still shows some slight traces of a right 
spiral. Figure 37 (Plate VI.), a forty-cell stage, is described in my notes 
as containing the cells a99— 499, 495—495, but owing to the rotundity 
