360 THE FORMS OF TISSUES [ch. 



concentric with the outer border of the cell, or else (as in c) cuts 

 that outer border; in other words, our partition may (b) cut both 

 radial walls, or (c) may cut one radial wall and the periphery. 

 These are the two methods of division which Sachs called, respec- 

 tively, (b) periclinal, and (c) anticlinal*. We may either treat the 

 walls of the dividing quadrant as already solidified, or at least as 

 having a tension compared with which that of the incipient 

 partition film is inconsiderable. In either case the partition must 

 meet the cell-wall, on either side, at right angles, and (its own 

 tension and curvature being everywhere uniform) it must take the 

 form of a circular arc. 



Now we find that a flattened cell which is approximately a 

 quadrant of a circle invariably divides after the manner of 

 Fig. 145, c, that is to say, by an approximately circular, anticlinal 

 wall, such as we now recognise in the eight-celled stage of 

 Erythrotrichia (Fig. 144) ; let us then consider that Nature has 

 solved our problem for us, and let us work out the actual 

 geometric conditions. 



Let the quadrant OAB {in Fig. 146) be divided into two 

 parts of equal area, by the circular arc MP. It is required to 

 determine (1) the position of P upon the arc of the quadrant, 

 that is to say the angle BOP ; (2) the position of the point M 

 on the side OA ; and (3) the length of the arc MP in terms of a 

 radius of the quadrant. 



(1) Draw OP; also PC a tangent, meeting OA in C; and 

 PN, perpendicular to OA. Let us call a a radius ; and 6 the angle 

 at C, which is obviously equal to OPN, or POB. Then 



CP = a cot d; PN = a cos 6; NC = CP cos 6 = a . cos^ ^/sin d. 



The area of the portion PMN 



= \CP'- e - IPN . NC 



= \a^ cot^ 6 — la cos d . a cos^ 6 /sin 6 



= \a^ (cot2 d - cos3 djsm 6). 



* There is, I tliink, some ambiguity or disagreement among botanists as to the 

 use of this latter term : the sense in which I am using it, viz. for any partition 

 which meets the outer or peripheral wall at right angles (the strictly radial partition 

 being for the present excluded), is, however, clear. 



