Quinary Arrangements in Natural History. 45 



for it is the type of a group comprising such as are most conformable. 

 It is encompassed by similar groups consisting of such as bear less affinity 

 to it: but have in hke manner relation to other objects, selected as types, 

 one in the niidst of every such exterior cluster. I say the smallest num- 

 ber of such surrounding groups, that can be assumed, is four ; the re- 

 spective centres of them being equidistant from each other, and situated 

 at like distances (less, however, than their mutual interval) from the com- 

 mon centre of the intire assemblage. This then is the simplest natural 

 arrangement: and hence it is, that the quinary distribution is that which 

 is most affected in the classification of natural objects. 



Were the utmost perfection in arrangement attainable, the chosen 

 common centre of the whole ought to be truly in the middle ; and the 

 selected centres of exterior groups would be equally distant from it, and 

 alike remote from each other. 



There would not be greater affinity between any two than between the 

 rest; neither between any two of the groups, nor between their assumed 

 middle points. But, if there be any notable deviation from the greatest 

 precision, from extreme accuracy of selection, the assumed middle point 

 of the whole assemblage will in fact be excentric ; or some one at least 

 of the selected centres of groups will be out of the right place. Now, 

 as the utmost precision can hardly be deemed attainable, it will neces- 

 sarily follow, that the assumed common centre inclines more towards one 

 of the exterior than towards the rest : and therefore it ordinarily, not to 

 say invariably, happens, that, in the quinary distribution, one cluster, com- 

 prising two subdivisions or groups, is normal ; and a second, comprising 

 other three, is aberrant : that is, one of the five divisions, being typical, 

 is nearly but not perfectly central ; another is conform, being proxi- 

 mate ; three others are dissimilar and remote. 



Allusion has been made to the analogy which an indefinitely numerous 

 assemblage of objects presents to indefinitely vast space contemplated as 

 from a central point. It has been assimilated to the celestial sphere. 

 Were the stars distributed throughout space at equal distances, and did 

 they possess equal power of illumination, such a distribution would offer 

 to the view twelve stars of the first magnitude, being those nearest to us, 

 equally distant from each other cind nearly the same from our sun. 

 Their relative positions would make the solid angles of an icosahedron 



