420 THE FORMS OF CELLS [ch. 



and by subtraction, 



p = tlr + tjr'. 



Now if r< r\ t/r > tjr'. 



Therefore, in ordei to produce the small increment of pressure p, 

 it is easier to do so by increasing tjr than tjr' ; that is to say, the 

 easier way is to alter or diminish r. And the same will hold good 

 if the tension and pressure be diminished instead of increased. 



This is as much as to say that, when corrugation or "ripphng" 

 of the walls takes place owing to small changes of surface-tension, 

 and consequently of pressure, such corrugation is more Hkely to 

 take place in the plane of r — that is to say, in the 'plane of greatest 

 curvature. And it follows that in such a figure as an ellipsoid, 

 wrinkling will be most likely to take place not only in a longitudinal 

 direction but near the extremities of the figure, that is to say again 

 in the region of greatest curvature. 



The longitudinal wrinkUng of the flask-shaped bodies of our 

 Lagenae, and of the more or less cyhndrical cells of many other 

 Foraminifera (Fig. 134), is in complete accord with the above con- 

 siderations ; but nevertheless, we soon find that .our result is not 

 a general one but is defined by certain hmiting conditions, and is 

 accordingly subject to what are, at first sight; important exceptions 

 For instance, when we turn to the narrow neck of the Lagena we 

 see at once that our theory no longer holds ; for the wrinkling which 

 was invariably longitudinal in the body of the cell is as invariably 

 transverse in the narrow neck. The reason for the difference is not 

 far to seek. The conditions in the neck are very different from 

 those in the expanded portion of the cell : the main difference being 

 that the thickness of the wall is no longer insignificant, but is of 

 considerable magnitude as compared with the diameter, or circum- 

 ference, of the neck. We must accordingly take it into account in 

 considering the bending moments at any point in this region of the 

 shell-wall. And it is at once obvious that, in any portion of the 

 narrow neck, flexure of a wall in a transverse direction will be very 

 difficult, while flexure in a longitudinal direction will be compara- 

 tively easy; just as, in the case of a long narrow. strip of iron, we 

 may easily bend it into folds running transversely to its long axis, 

 but not the other way. The manner in which our little Lagena-sheW 



