October 6, 1911] 



SCIENCE 



425 



isms, up to the point where the develop- 

 ment of a sljeleton complicates the case, 

 were one and all identical with the plane, 

 sphere, cylinder, unduloid and catenoid, or 

 with combinations of these. 



It was Berthold and Errera who, 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 (according to another 

 law which I have not particularized) to set 

 itself at right angles to the preceding solidi- 

 fied 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 eeU-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 hexa- 

 gonal 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 Trypano- 

 some, or of that around the tail of the 

 spermatozoon of a newt — every one of 

 these, I declare, is a case where the result- 

 ant form can be well explained by, and can 

 not possibly be understood without, the 

 phenomenon of surface-tension: indeed, in 

 many of the simpler case the facts are so 

 well explained by surface-tension that it is 

 difficult to find place for a conflicting, 

 much less an overriding, force. 



I believe, for my own part, that even the 

 beautiful and varied forms of the Foram- 

 inifera may be ascribed to the same cause; 

 but here the problem is just a little more 



complex, by reason of the successive con- 

 solidations of the shell. Suppose the first 

 cell or chamber to be formed, assuming its 

 globular shape in obedience to our law, and 

 then to secrete its calcareous envelope. 

 The new growing bud of protoplasm, ac- 

 cumulating outside the shell, will, in strict 

 accordance with the surface-tensions con- 

 cerned, either fail to "wet" or to adhere 

 to the first-formed shell, and will so detach 

 itself as a unicellular individual {Orbu- 

 lina) ; or "else it will flow over a less or 

 greater part of the original shell, until its 

 free surface meets it at the required angle 

 of equilibrium. Then, according to this 

 angle, the second chamber may happen to 

 be all but detached {Gldhigerina) , or, with 

 all intermediate degrees, may very nearly 

 wholly enwrap the flrst. Take any specific 

 angle of contact, and presume the same 

 conditions to be maintained, and therefore 

 the same angle to be repeated, as each suc- 

 cessive chamber follows on the one before; 

 and you will thereby build up regular 

 forms, spiral or alternate, that correspond 

 with marvelous accuracy to the actual 

 forms of the Foraminifera. And this case 

 is all the more interesting because the al- 

 lied and successive forms so obtained differ 

 only in degree, in the magnitude of a single 

 physical or mathematical factor; in other 

 words, we get not only individual phenom- 

 ena, but lines of apparent orthogenesis, 

 that seem explicable by physical laws, and 

 attributable to the continuity between suc- 

 cessive states in the continuous or gradual 

 variation of a physical condition. The 

 resemblance between allied and related 

 forms, as Hartmann demonstrated and 

 Giard admitted years ago, is not always, 

 however often, to be explained by common 

 descent and parentage.^ 



In the segmenting egg we have the sim- 



' Cf . Giard, ' ' Discours inaugurale, ' ' Bull. 

 . Scientif. (3), 1, 1888. 



