396 



Mr. A. B. Kempe. 



[June 18, 



§§ 18 — 24. Some Definitions. 



A collection of units selected from a larger collection is termed a 

 component of the latter. 



A collection of units containing some nnits selected from each of a 

 number of other collections is said to connect the latter. 



There are other definitions which need not be referred to. 



§§ 25—36. Systems. 



A collection of nnits which is snch that every component nnit is 

 distinguished from every unit which is not a component is termed a 

 system. A single system is one in which all units are undistinguished. 

 We have also double, treble, fyc, systems. The sections contain 

 general observations about systems. 



§§ 37 — 49. Heaps — Graphical Representation of Units. 



We may graphically represent units by small circles of different 

 colours, spots, &c. These are termed graphical units. 



A large class of systems called heaps may be represented by means 

 of these alone, without further graphical adjuncts. 



A single heap is one which is graphically represented by graphical 

 units all undistinguished from each other. 



A discrete heap is one which is graphically represented by graphical 

 units which are all distinguished from each other. 



There are intermediate forms called double, treble, fyc, heaps. 



§§ 50 — 72. Pairs — Graphical Representation. 



The three different forms which pairs can assume are considered, 

 viz. : — 



(1.) The two units a, b, maybe distinguished from each other. 



(2.) The two units may be undistinguished but unsymmetrical, i.e., 

 ab distinguished from ba. 



(3.) The two units may be undistinguished and symmetrical, i.e., 

 ab undistinguished from ba. 



Certain modes are discussed of distinguishing pairs of graphical 

 units, so as to make a graphical diagram represent a system the form 

 of which depends upon pairs being distinguished. These involve the 

 use of plain lines, or " links" joining pairs of graphical units ; also, 

 where necessary, lines of various sorts, coloured, wavy, dotted, &c. ; 

 and, where unsymmetrical pairs have to be represented, the use of 

 barbs on the lines. 



§§ 73—83. Aspects. 

 These sections are devoted to a consideration of the real nature of 

 aspects of collections of units, and of the units which are dealt with 



