388 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1911. 



physical facts or laws the morphologist as well as the physiologist 

 may draw important consequences. 



It was Hofmeister who first showed, more than 40 years ago, 

 that when any drop of protoplasm, either over all its surface or at 

 some free end (as at the tip of the pseudopodium of an amoeba), is 

 seen to "round itself off" that is not the effect of physiological or 

 vital contractility, but is a simple consequence of surface tension — 

 of the law of the minimal surface; and on the physiological side, 

 Engelmann, Butschli, and others have gone far in their development 

 of the idea. Plateau, I think, was the first to show that the myriad 

 sticky drops or beads upon the weft of a spider's web, their form, 

 their size, their distance apart, and the presence of the tiny inter- 

 mediate drops between, were in every detail explicable as the result 

 of surface tension, through the law of minimal surface and through 

 the corollary to it which defines the limits of stability of the cylinder; 

 and, accordingly, that with their production the will or effort or 

 intelligence of the spider had nothing to do. The beaded form of a 

 long, thin pseudopodium, for instance, of a Heliozoan, is an identical 

 phenomenon. It was Errera who first conceived the idea that not 

 only the naked surface of the cell but the contiguous surfaces of 

 two naked cells, or the delicate incipient cell membrane or cell wall 

 between, might be regarded as a weightless film whose position and 

 form were assumed in obedience to surface tension. And it was he 

 who first showed that the symmetrical forms of the unicellular and 

 simpler multicellular organisms, up to the point where the develop- 

 ment of a skeleton complicates the case, were one and all identical 

 with the plare, sphere, cylinder, unduloid, and catenoid, or with 

 combinations of these. Berthold and Errera almost simultaneously 

 showed (the former in far the greater detail) that in a plant each 

 new cell partition follows the law of minimal surface and tends (ac- 

 cording to another law, which I have not particularized) to set itself 

 at right angles to the preceding solidified wall, so giving a simple 

 and adequate physical explanation of what Sachs had stated as an 

 empirical morphological rule. And Berthold further showed how, 

 when the cell partition was curved, its precise curvature, as well as 

 its position, was in accordance with physical law. 



There are a vast number of other things that we can satisfactorily 

 explain on the same principle and by the same laws. The beautiful 

 catenary curve of the edge of the pseudopodium, as it creeps up its 

 axial rod in a Heliozoan or a Radiolarian, the hexagonal mesh of 

 bubbles or vacuoles on the surface of the same creatures, the form 

 of the little groove that runs round the waist of a Peridinian even 

 (as I believe) the existence, form and undulatory movements of the 

 undulatory membrane of a Trypanosome, or of that around the tail 

 of the spermatozoon of a newt — every one of these, I declare, is a 



