58 BULLETIN : MUSEUM OF COMPARATIVE ZOOLOGY. 



Division of Quartet 5.2, forming 6.3 and 6.4. 



Sauie Figures as for 5.1. 



Figure 23 shows the quartet at the close of the division which has 

 resulted iu the formation of the quartets 6.3 aud 6.4. The nuclear con- 

 ditions in like manner show that this division has also taken place in a 

 right spiral. The remnants of the spindles are parallel to those of the 

 quartet 5.1, and the upper derivative lies to the right of the lower one. 

 These divisions are also approximately equal and synchronous. The 

 arrangement of the cells of the vegetative pole is very regular. The ven- 

 tral cross furrow remains approximately at right angles to the dorsal 

 furrow. The two cells b 61 and d G1 meet in this ventral furrow, and are 

 hexagonal in outline, while the other two members of the quartet a 61 

 and c 61 are pentagonal. All four cells of the quartet 6.2 are hexagonal, 

 as will be seen in Plate IV. Figs. 27-29, and 31. A comparison of the 

 quartet 6.1 of Figure 27 with 5.4 of Figure 28 shows how little differ- 

 ence there is in the size of the cells of the two poles in the superficial 

 view. In optical section, however, a distinct difference can be detected 

 in the size of the deeper lying parts of these cells. In Figure 30 (Plate 

 IV.) is represented such a section taken from the egg in the position 

 shown in Figure 29. The section passes through the vertical axis in 

 the plane corresponding to that of the paper in Figure 29, thus cutting 

 the ventral cross furrow at right angles, and passing through the quad- 

 rants b and d. It will be seen that one of the two cells of the vegeta- 

 tive pole, labelled d 61 in the drawing, is much larger than the othei*, b 61 . 

 This is the cell which at the next generation gives rise to the first 

 mesoderm cell, d 72 , or M. 



The generalization which Eabl made in his paper on Planorbis ('79), 

 — "dass bei den Keimen mit reichlichem Nahrungsdotter von dem Zeit- 

 punkte an, als Aequatorialfurchen auftreten, die Zellvermehrung in 

 arithmetischer, bei den Keimen mit sparlichem Nahrungsdotter dagegen 

 zuerst in arithmetischer, sodann aber in geometrischer Progression 

 erfolgt," — is not borne out by the cleavage in Limax, as the twelve-cell 

 stage does not regularly occur. The cleavage in Limax runs, 



4 . . 8 . . . 16 . . . 24 40. 



or, (4) : (4) : (4) + (4) : (4) + (4) : (4) + (4) + (4) + (4). 



This is fundamentally an arithmetical progression, a series whose common 

 difference is four, the mathematical expression of the increase in the 

 number of cells in the spiral type of cleavage. It varies, however, from 



