MOllPHOLOGICAL DIFFERENTIATION IN PJ.ANTS. 117 



cut by any plane througli the centre, the separated parts are 

 equal and similar. This is a kind of symmetry which stands 

 alone, and will be hereafter spoken of as spherical symmetry. 



When a sphere passes into a spheroid, either prolate or ob- 

 late, there remains but one set of planes that will divide it 

 into halves which are in all respects alike ; namely, the 

 planes in which its axis lies, or which have its axis for their 

 line of intersection. Prolate and oblate spheroids may 

 severally pass into various forms without losing this pro- 

 perty. The prolate spheroid may become egg-shaped or py- 

 riform, and it will still continue capable of being divided into 

 two equal and similar parts by any plane cutting it down 

 its axis ; nor will forming constrictions round it deprive it 

 of this property. Similarly with the oblate spheroid. The 

 transition from a slio^ht oblateness like that of an orano-e 

 to an oblateness reducing it nearly to a flat disc, does not 

 alter its divisibility into like halves by every plane passing 

 through its axis. And clearly the moulding of any such 

 flattened oblate spheroid into the shape of a plate, leaves it 

 as before, symmetrically divisible by all planes at right 

 angles to its surface and passing through its centre. Tl is 

 species of symmetry is called radial symmetry. It is familiarly 

 exemplified in such flowers as the daisy, the tulip, and the 

 dahlia. 



From spherical symmetry, in which we have an infinite 

 number of axes through each of which may pass an infinite 

 number of planes severally di\'iding the aggregate into equal 

 and similar parts ; and from radial s}Tnmetry, in which we 

 have a single axis through which may pass an infinite num- 

 ber of planes severally dividing the aggregate into equal and 

 similar parts ; we now turn to hilateral symmewy, in which 

 the divisibility into equal and similar parts becomes very 

 limited. Noting, for the sake of completeness, that there is 

 a sextuple bilateralness in the cube and its derivative forms, 

 which admit of division into equal and similar parts by planes 

 passing through the three diagonal axes and by planes passing 



