x TABLE OF CONTENTS 
PAGE 
§ 24. Alternants 41 
§ 25. Seminvariants as Leaders of Binary Covariants 42 
§26. Number of Linearly Independent Seminvariants 43 
§ 27. Hermite’s Law of Reciprocity 45 
Exercises 46 
• §§28-31. Fundamental System of Covariants 47 
§§ 32,33. Canonical Form of Binary Quartic; Solution of Quartic Equations.. 50 
§ 34. Seminvariants in Terms of the Roots 53 
§ 35. Invariants in Terms of the Roots 54 
Exercises 55 
§ 36. Covariants in Terms of the Roots 56 
Exercises 58 
§ 37. Covariant with a Given Leader ... 58 
§ 38. Differential Operators Producing Covariants 59 
Exercises 61 
PART III 
Symbolic Notation 
§§ 39-41. The Notation and its Immediate Consequences 63 
Exercises 65, 66 
§§ 42-45. Covariants as Functions of Two Symbolic Types 67 
§ 46. Problem of Finiteness of Covariants , 70 
§ 47. Reduction to Problem on Invariants 71 
§ 48. Hilbert’s Theorem on a Set of Forms 72 
§§ 49, 50. Finiteness of a Fundamental System of Invariants 73 
§51. Finiteness of Syzygies 76 
§ 52. Transvectants 77 
§§ 53, 54. Binary Forms Apolar to Given Forms 78 
§§ 55,56. Rational Plane Cubic Curves 81 
§ 57. Rational Space Quartic Curves 83 
§§ 58,59. Fundamental System of Covariants of Linear Forms; of a Quadratic 
Form; Exercises 84 
§ 60. Theorems on Transvectants; Convolution 85 
§ 61. Irreducible Covariants Found by Induction 87 
§ 62. Fundamental System for a Binary Cubic 89 
§ 63. Results and References on Higher Binary Forms 91 
§64. Hermite’s Law of Reciprocity Symbolically 91 
§ 65. Ternary Form in Symbolic Notation 92 
Exercises 93 
§§ 66, 67. Concomitants of Ternary Forms 93 
§ 68. Quaternary Forms 97 
Index 99