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of mathematics, any more than do the drops and jets of ordinary 

 fluids or the quickly drawn and quickly cooling tubes in the glass- 

 worker's hands. 



Plateau says that in most hquids the influence of viscosity is such 

 as to cause the cylinder to segment when its length is about four 

 times, or even six times, its diameter, instead of a fraction over 

 three times, as theory would demand of a perfect fluid. If we take 

 it at four times, the resulting spherules would have a diameter of 

 about 1-8 times, and their distance apart would be about 2-2 times, 

 the original diameter of the cylinder; and the calculation is not 

 difficult which would shew how these dimensions are altered in the 

 case of a cylinder formed around a solid core, as in the case of a 

 spider's web. Plateau also observed that the time taken in the 

 division of the cyUnder is directly proportional to its diameter, 

 while varying with the nature of the hquid. This question, of the 

 time taken in the division of a cell or filament in relation to its 

 dimensions, has not so far as I know been enquired into by biologists. 



From the simple fact that the sphere is of aU configurations that 

 whose surface-area for a given volume is an absolute minimum, we 

 have seen it to be the one figure of equilibrium assumed by a drop 

 or vesicle when no disturbing factor is at hand; but such freedom 

 from counter-influences is likely to be rare, and neither does the rain- 

 drop nor the round world itself retain its primal sphericity. For one 

 thing, gravity will always be at hand to drag and distort our drop 

 or bubble, unless its dimensions be so minute that gravity becomes 

 insignificant compared with capillarity. Even the soap-bubble will 

 be flattened or elongated by gravity, according as we support it 

 from below or from above; and the bubble which is thinned out 

 almost to blackness will, from its small mass, be the one which 

 remains most nearly spherical*. 



Innumerable new conditions will be introduced, in the shape of 

 comphcated tensions and pressures,, when one drop or bubble 

 becomes associated with another, and when a system of inter- 

 mediate films or partition-walls is developed between them. This 

 subject we shall discuss later, in connection with cell-aggregates or 

 tissues, and we shall find that further theoretical considerations are 



* Cf. Dewar, On soap-bubbles of long duration, Proc. Roy. Inst. Jan. 19, 1929. 



