114 MICHELSON— FORM ANALYSIS. [April 18 



In contemplating the variety of exquisitely graceful forms which 

 are exhibited in such abundance by the lower organisms, it is difficult 

 to realize that their building up may be the result of the action of 

 purely physical causes — and in truth it may be long before the 

 theory of their formation is complete. 



It is safe to say, however, that such general characters as 

 symmetry of parts, rhythmic arrangements, systems of branching — 

 which occur in strikingly similar fashion in such widely dissimilar 

 objects as vegetation, protozoa, crytals, even liquids — must have 

 some very general and fundamental explanation. 



In many of the simpler cases such explanations are almost self- 

 evident. For instance, the very frequent occurrence of spherical or 

 spheroidal forms may be accounted for by the action of capillary 

 forces ; and the regular segmentation figures shown in many pro- 

 tozoan cells may be explained by the geometrical necessities of the 

 case. An experimental study of such geometrical relations for fig- 

 ures in one plane was published by Alfred Mayer, and his results 

 furnish many suggestive analogies which bear on the structure of 

 the molecule as well as that of the micro-organism. An extension 

 of the results to three dimensions would doubtless encounter serious 

 experimental difficulties ; but these may be overcome, or at least 

 reduced sufficiently for practical purposes. The problem is really 

 however a geometrical one — though the figures resulting from a 

 purely mathematical investigation would be complicated by con- 

 siderations of stability. 



As an instance in which the cause of regularity is reasonably 

 certain, let us consider the forms produced by a drop of colored 

 liquid falling into a body of liquid of nearly the same density. As 

 the drop descends it flattens out, the edge advancing more rapidly 

 than the flattened surface. The equilibrium, already unstable, is 

 still further disturbed by the momentum acquired by the peripheral 

 parts, which causes them to assume a bell-shape. This form is still 

 unstable, and if any accidental cause starts a thickening into drops, 

 this will be assisted by the thinning of the adjacent parts which 

 then lag behind. The same forces act at other points on the 

 bell, to form " drops," the distance from the other drops being just 

 enough to save being thinned. This distance (which depends on 



