IX] 



OF MULLER'S LAW 



481 



to a serii^s of five parallel circles on the sphere, corresponding to the 

 equator (c), the tropics (6, d) and the polar circles {a, e) ; and that 

 beginning with four equidistant spines in the equator, we have 

 alternating whorls of four, radiating outwards from the sphere in 

 each of the other parallel zones. This rule was laid down by the 

 celebrated Johannes Miiller, and has ever since been used and 

 quoted as Miiller's law. The chief point in this alleged arrange- 

 ment which strikes us at first sight as very curious, is that there 

 is said to be no spine at either pole ; and when we come to examine 

 carefully the figure of the organism, we find that the received 



Fig. 232. Dorataspis sp. ; diagrammatic. 



description does not do justice to the facts. We see, in the first 

 place, from such figures as Figs. 232, 234, that here, unhke our 

 former cases, the radial spines issue through the facets (and through 

 all the facets) of the polyhedron, instead of through its solid angles ; 

 and accordingly, that our twenty spines correspond (not, as before, 

 to a dodecahedron) but to some sort of an icosahedron. We see 

 in the next place, that this icosahedron is composed of faces, or 

 plates, of two different kinds, some hexagonal and some penta- 

 gonal; and when we look closer, we discover that the whole 

 figure is that of a hexagonal prism, whose twelve solid angles are 

 replaced by pentagonal facets. Both hexagons and pentagons 



T. G. 31 



