366 THE FORMS OF TISSUES [ch. 



dealing with arcs no greater than a quadrant; and (2), the point 

 {B) where the angle 6 comes to equal the angle a, for after that 

 point the construction becomes impossible, since an anticlinal 

 bisecting partition- wall would be partly outside the cell. The only 

 partition which, after the point, can possibly exist, is a periclinal 

 one. This point, as our diagram shews us, occurs when the angles 

 (a and 6) are each rather under 52°. 



Next I have plotted, on the same diagram, and in relation to 

 the same scales of angles, the corresponding lengths of the two 

 partitions, viz. RS and MP, their lengths being expressed (on 

 the right-hand side of the diagram) in relation to the radius of 

 the circle (a), that is to say the side wall, OA, of our cell. 



The limiting values here are (1), C, C , where the angle of arc 

 is 90°, and where, as we have already seen, the two partition- walls 

 have the relative magnitudes of MP : RS = 0-875 : 1-111 ; (2) the 

 point D, where RS equals unity, that is to say where the periclinal 

 partition has the same length as a radial one; this occurs when 

 a is rather under 82° (cf. the points Z), D'); (3) the point E, where 

 RS and MP intersect ; that is to say the point at which the two 

 partitions, periclinal and anticHnal, are of the same magnitude; 

 this is the case, according to our diagram, when the angle of arc 

 is just over 62|°. We see from this, then, that what we have 

 called an anticlinal partition, as MP, is only hkely to occur in 

 a triangular or prismatic cell whose angle of arc lies between 

 90° and 62|°. In all narrower or more tapering cells, the periclinal 

 partition will be of less area, and will therefore be more and more 

 likely to occur. 



The case {F) where the angle a is just 60° is of some interest. 

 Here, owing to the curvature of the peripheral border, and the 

 consequent fact that the peripheral angles are somewhat greater 

 than the apical angle a, the perichnal partition has a very shght 

 and almost imperceptible advantage over the anticlinal, the 

 relative proportions being about as MP : RS = 0-73 : 0-72? But if 

 the equilateral triangle be a plane spherical triangle, i.e. a plane 

 triangle bounded by circular arcs, then we see that there is no 

 longer any distinction at all between our two partitions; MP 

 and RS are now identical. 



On the same diagram, I have inserted the curve for values of 



