194 



Mr. A. B. Kempe. 



[Mar. 24, 



sidered in Sees. 73//, and we shall there see that an aspect of a 

 collection of n units, i.e., of an w-ad, is itself an w-ad. It will be 

 convenient to speak of the aspects of the pairs, triads, &c, contained 

 in a collection, as if they were themselves pairs, triads, &c, of the 

 collection. 



For Sections 73 to 77 substitute — 



73. If with each unit of a collection of n units a, b, c, .... of any 

 form, we mentally associate one of a given discrete heap (Sec. 37) 

 of n marks, so that each unit is thereby distinguished from each of 

 the others, and from all other units, we obtain what I have, in 

 Sees. 6 and 7, termed a-n aspect of a, 6, c, ... . 



It may assist in arriving at a proper idea of the use and importance 

 of aspects, and may justify the use of the expression " aspect," to 

 point out that when, in the consideration of a collection of units, we 

 give different degrees of prominence in our minds to different units 

 of the collection, we are mentally affixing distinctive marks to those 

 units, and have a particular "aspect" of the collection before our 

 mind's eye. It may be, in some cases, that we give a distinctive 

 degree of prominence to one unit only of the collection, and equal 

 degrees of prominence to the rest : thus, when we consider the 

 relations of a number of things to a particular thing, we affix a 

 distinctive mental mark to the latter things and marks undis- 

 tinguished from each other to the former things. It is convenient, 

 however, for our present purposes to confine the use of the word. 

 " aspect " to the case in which a different degree of prominence, 

 or other distinctive mental mark, is affixed to each unit of the 

 collection. 



The n marks may be associated with the n units, a, t, c, .... 

 in \n different ways, giving rise to In aspects of a, b, c, . . . . ; each 

 aspect being derivable from the others by transpositions of the 

 marks. When we regard a unit a as associated with a particular 

 mark g in a particular aspect of a, b, c, . . . . , we deal with a unit 

 A, which is a different unit from a, and may be called an aspect of a. 

 Thus an aspect of the w-ad, a> b, c, . . . . , is an w-ad composed of 

 n unit aspects, A, B, C, . . . . 



The unit aspects composing one aspect of a, b, c, * > . . are each 

 distinct units from those composing another aspect, and thus the \n 

 aspects of a, b, c, ... . derived by employing a particular collection 

 of n marks, furnish in all n\n unit aspects such as A. 



Since the marks employed are all distinguished from each other, the 

 n unit aspects A, B, C, . . . . composing a particular aspect of 

 a, b, Cj . . . . are all distinguished from each other. 



We may associate the same collection of n marks with any number 

 of collections of n units a, &, c, . . . . ; p, q, f , . . . . ; &c, and 

 obtain \n aspects of each collection. 



