44 Mr. Colebrooke on Dichotomous and 



It may be easily shown, therefore, that the simplest distribution of a large 

 assemblage of objects, marshalled in the manner here assumed, around 

 a select one, or that distribution, which taking one central or interior 

 group, makes a few and but a few equidistant exterior ones, is quinary. 

 The centres of the exterior groups will stand at the solid angles of a 

 tetrahedron within a sphere, of which the centre is the middle point in 

 the interior group. That is, the entire assemblage, encompassing every 

 way one select object, around which they are clustered, is in the first 

 place divided concentrically, at more than half the depth to which it is 

 considered to extend : and from equidistant points being taken within the 

 substance of the outer shell, this is divisible into four equal parts, in 

 which those mean points are centrical, or as nearly so as the irregular 

 figure of the group allows. 



Rejecting the assumption of one central primary object, the division of 

 the entire assemblage would become simpler. It would be quaternary. * 

 The middle points of each of the four segments would stand, as those of 

 the exterior distribution did, at the solid angles of a tetrahedron within 

 the sphere above supposed. The whole assemblage may be conceived, 

 first as a cluster of four balls ; one resting upon three others : and then 

 the interstices and remaining space, to complete a circumscribed sphere, 

 are shared among the four. 



But the mind is prone to fix upon some primary object of its attention, 

 which becomes the centre of comparison for every other ; and on this 

 account it is, that the quinary arrangement is practically a more natural 

 one than the quaternary. 



I am here supposing an assemblage consisting of a single sample of 

 every species ; for species alone is in truth acknowledged by nature ; and 

 every larger group, whether genus, order or class, or family or tribe, is 

 but the creature of abstraction. 



In the middle of this great cluster, I imagine that object placed, which 

 most fixes attention : that, with which all others are compared, or with 

 which they are contrasted. Around it are arranged other objects, nearer 

 or remoter, according to the degree of their resemblance or affinity to it : 



* Ocken maintains that four is the determinate number in natural distribu- 

 tion. Linn. Tr. XIV. p. 56. 



