364 ■ THE FORMS OF TISSUES [ch. 



sector, such as that shewn in Fig. 149, that a periclinal partition 

 is the smallest by which we can possibly bisect the cell ; we want, 

 accordingly, to know the limits below which the perichnal partition 

 is always the best, and above which the anticlinal arc, as in the 

 case of the whole quadrant, has the advantage in regard to small- 

 ness of surface area. 



This may be easily determined ; for the preceding investigation 

 is a perfectly general one, and the results hold good for sectors 

 of any other arc, as well as for the quadrant, or arc of 90°. That 

 is to say, the length of the partition- wall MP is always determined 

 by the angle 6, according to our equation MP = ad cot 6 ; and 

 the angle 6 has a definite relation to a, the angle of arc. 



OA-yfO. 



Fig. 149. 



Moreover, in the case of the periclinal boundary, RS (Fig. 147) 

 {or ab, Fig. 149), we know that, if it bisect the cell, 



RS = a . a/V2. 

 Accordingly, the arc RS will be just equal to the arc MP when 



d cot 6 = a/V2. 



When ^ cot ^ > a/V2, or MP > RS, 



then division will take place as in RS. 



When 6 cot 6 < a/V2, or MP < RS, 



then division will take place as in MP. 



In the accompanying diagram (Fig. 150), I have plotted the 

 various magnitudes with which we are concerned, in order to 

 exhibit the several limiting values. Here we see, in the first 

 place, the curve marked a, which shews on the (left-hand) vertical 

 scale the various possible magnitudes of that angle (viz. the angle 



