
1904,] The Dual Force of the Dividing Cell. 559 
bourhood of the axis, we reach on either side a zone where the viscidity of the 
medium is strong enough to resist it, and to inhibit the motion of the chains. 
Thus the spindle becomes thickened and denser from the lateral crowding in 
of chains (fig. 10) while peripherally there is left a clear space from which the 
chains have passed inwards; the result being a clearer differentiation ito 
central spindle and polar asters. Our figures show how much closer an 
approximation we have obtained in our model to the cell-figure by combination 
of the two devices, (a) the provision of a permeable envelope, and (b) the 
production of the figure in a medium where the prolonged action of the stresses 
may have its due effect. The clear space has been recognised in the cell, and 
received the name of “ Biitschli’s Space ” (Rhumbler). We.can reproduce the 
same effect on smooth paper if the tapping be sufficiently energetic or 
prolonged: it has doubtless been often obtained involuntarily by the 
physicist, who has evidently not thought it worth his while to reproduce a 
“failure” so far as his object was concerned ; for that has merely been the 
delineation of the direction of the lines of force in a uniform medium of 
indeterminate extension. 
XI, 
In certain cases, more than two centres appear in cells, united by spindles, 
and constituting “ tri-,” “tetr-,’ and “ poly-asters.” It has often been laid down 
as a mathematical truth that the action of a dual force is incompatible with 
the formation of a field with an odd number of centres all joined by spindles. 
Rhumbler definitely states as a law: “ Magnetic lines of force can never form 
three spindles between three consecutive poles ... three adjacent poles 
even when there are more than three poles in the field, can never be joined 
up by three spindles’*; and his argument would certainly apply to all dual 
forces. There is, however, a flaw in his exposition: as Gallardo had pointed 
out some years before, two opposite poles, and a third point at zero, behave as 
three distinct centres in his electrostatic model (above, p. 552). We may call 
two unlike magnetic poles “positive” and “negative” respectively, when a 
mass of soft iron will correspond to a “zero” centre. Thus we place below 
our stage two unlike magnetic poles at the ends of the base of an obtuse- 
angled triangle, and a core (without a coil) at the vertex, with a wafer-like 
disc of iron lying on the plate above; the figure obtained is seen to be a triaster 
* “Mechanische Erklirung der Ahnlichkeit zwischen Magnetischen Kraftliniens 
systemen und Zelltheilungsfiguren,” ‘Arch. Entwicklungsmech,” vol. 16, 1903. 
‘“Von magnetischen Kraftlinien kénnen niemals drei Spindeln zwischen drei Polen 
hervorgebildet werden .... auch wenn mehr als drei Polen im Diagramm vertreten 
sind, kénnen niemals drei benachbarte Polen durch drei Spindeln verbunden sein” 
(p. 482). 
