DIAGRAMS AND EXAMPLES. 



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right angles, they must represent hyperbolas, and in such a way that around each of 

 the two foci// a larger or smaller number of hyperbolas run, the axes of which coincide 

 at the same time with the major axis of the confocal ellipses : or, in other words, the 

 anticlines A and a are confocal hyperbolas. In each case, according as we wish 

 to have large or small cells in the disc, the number of confocal ellipses and hyper- 

 bolas may be increased. It is noticed — to remark it by the way — that those 

 hyperbolas the apices of which lie nearest to the foci X/" there make a strong curve : on 

 the contrary, the apical curvature of the hyperbolas is so much the smaller the further 

 they are distant from the io<i\ff, and the nearer they approach the minor axis of the 

 ellipse. If we further suppose the wHole figure so altered that the two axes become 

 equal to one another, then the two foci_/y coincide in one focus, the confocal ellipses 



Fig. 276. 



become converted into concentric circles, and the hyperbolas A and a then appear 

 as straight lines which run from the centre to the periphery, and are thus radii 

 of the circle. 



We have thus, by means of our geometrical construction, obtained a general 

 scheme for the way in which the cells must approximately be arranged in the 

 supposed disc, if we divide it up into cells by periclinal and anticlinal partition-walls 

 cutting one another at right angles : it will scarcely be necessary to say that the 

 quadrangular portions of surface, or areolae, between the anticlines and periclines 

 jepresent the cell-cavities. 



Having, then, closely impressed on the mind this scheme, the geometrical 

 significance of which is readily understood, we find everywhere in such flat objects 

 the cells arranged in patterns which obviously accord with our scheme. In order 



