PHILOSOPHICAL TRANSACTIONS. 
I. A Memoir on the Theory of Mathematical Form 
By A. B. Kempe, M.A., F.B.S. 
Received May 18,—Read June 18, 1885. 
Table of Contents. 
SECTIONS. ' PAGE. 
1- 2.—Scope of the memoir. 2 
3- 13.—Fundamental principles... 2-4 
14- 17.—Units... 4, 5 
18- 24.—Some definitions.... 5, 6 
25- 36.—Systems.. 6, 7 
37- 49.—Heaps—Graphical representation of units . 7, 8 
50- 72.—Pairs—Graphical representation . 9-14 
73- 83.—Aspects... 14-16 
84- 86.—Letters, their sorts and positions ..... 16 
87- 88.—Representation of aspects of collections by arrays of letters . 16, 17 
89— 99.—Elementary properties of aspects.. 17, 18 
100-111.—Tabular representation of systems ... 18-20 
112-129.—Correspondences of undistinguished collections. 20-23 
130-136.—Sets . 23,24 
137-142.—Aspects unique with respect to collections. 24, 25 
143-151.—Associates.... 25, 26 
152-161.—Unified aspects... 26, 27 
162-169.—Correspondences of systems of like forms. 27-29 
170-173.—Replicas... 29, 30 
174-188.—Independent and related systems. 30, 31 
189-193.—Three modes of compounding systems. 31, 32 
194—195.—General method of graphically representing a system . 32 
196-210.—Networks... 32-34 
211-221.—Chains ... 34, 35 
* In accordance with criticisms and suggestions of the referees, an alteration has been made in the 
title of the memoir, and certain sections towards the end have been omitted. There is consequently a 
slight want of complete correspondence between the memoir and the abstract given in the Proceedings, 
vol. 38, p. 393 —A. B. K. 
