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 jm and the transverse 

 120 ft. 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 succession. 



Division of Qiiartet 5.3, foi'ming 6.5 and 6.6. 



Plate VI. Figs. 37, 39, 41. 



The division of this quai-tet does not take place, in some instances at 

 least, until after the forty-cell 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 a^''^ and d^^ have divided, and 6^-^ is in a mitotic 

 state, but c^-^ is as yet undivided. In b^-^ 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 tlie 

 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 (juartet divide. In Figure 

 41 (Plate VI.) 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 a^-^-d^% a^-^-d^-^, but owing to the rotundity 



