362 THE FORMS OF TISSUES [cii. 



We see accordingly that the equation is solved (as accurately 

 as need be) when 6 is an angle somewhat over 34° 38'^ or say 

 34° 38|'. That is to say, a quadrant of a circle is bisected by a 

 circular arc cutting the side and the periphery of the quadrant 

 at right angles, when the arc is such as to include (90° — 34° 38'), 

 i.e. 55° 22' of the quadrantal arc. 



This determination of ours is practically identical with that 

 which Berthold arrived at by a rough and ready method, without 

 the use of mathematics. He simply tried various ways of dividing 

 a quadrant of paper by means of a circular arc, and went on doing 

 so till he got the weights of his two pieces of paper approximately 

 equal. The angle, as he thus determined it, was 34-6°, or say 

 34° 36'. 



(2) The position of M on the side of the quadrant OA is 

 given by the equation OM = a cosec 6 — a cot 6 ; the value of 

 which expression, for the angle which we have just discovered, 

 is -3028. That is to say, the radius (or side) of the quadrant will 

 be divided by the new partition into two parts, in the proportions 

 of nearly three to seven. 



(3) The length of the arc MP is equal to ad cot 6 ; and the 

 value of this for the given angle is •8751. This is as much as to 

 say that the curved partition- wall which we are considering is 

 shorter than a radial partition in the proportion of 8f to 10, or 

 seven-eights almost exactly. 



But we must also compare the length of this curved " antichnal " 

 partition- wall {MP) with that of the con- 

 centric, or periclinal, one {RS, Fig. 147) by 

 which the quadrant might also be bisected. 

 The length of this partition is obviously 

 equal to the arc of the quadrant (i.e. the 

 peripheral wall of the cell) divided by v'2 ; 

 or, in terms of the radius, = 7r/2V2 = 1-111. 

 ^^* So that, not only is the anticlinal partition 



(such as we actually find in nature) notably the best, but the 

 periclinal one, when it comes to dividing an entire quadrant, is 

 very considerably larger even than a radial partition. 



The two cells into which our original quadrant is now divided, 

 while they are equal in volume, are of very different shapes ; the 



