CONTENTS. 
PAGE 
INTRODUCTION 
PART I. THE GENERAL CASE 
5 
A. BINARY FAMILIES IN AN «-TUPLY CONNECTED REGION. 
§ 1. The Regions T n and S 7 
* 
§ 2. Definition op a Binary Family 7 
§ 3. The Group op a Binary Family 8 
§ 4. The Doubly Connected Region 9 
§ 5. Fundamental Bases for an ti-tuply Connected Region. Connecting 
Formula 11 
§ 6. Kindred Families . 13 
§ 7. Relations between Kindred Binary Functions 
B. CLASSIFICATION OF BINARY FAMILIES FOR THE CASE > n = 3 
15 
§ 1. The Problem 17 
§ 2. The Four Types 
§ 3. Classification of Families under each Type 
§ 4. Tabulation of Classes ........ 
18 
20 
25 
§ 5. The Four Equations Proceeding from the Relation S e S b S a = 1 . . . . 28 
PART II. HYPERGEOMETRIC FAMILIES. 
A. DEFINING PROPERTIES. 
§ 1. Regular Singular Points for Binary Families. Exponents 30 
§ 2. The Exponent Sum and Apparently Singular Points. The Determinant D 32 
§ 3. The Differential Equation. Accessory Parameters 37 
