since "a student of physics finds a difficulty in principle of quaternions which makes the square of a vector negative." The second paper is "The Imaginary of the Algebra". Similar to Homersham Cox (1882/83), Macfarlane uses the hyperbolic versor as the hyperbolic quaternion corresponding to the versor of Hamilton. The presentation is encumbered by the notation Later he conformed to the notation exp(A α) used by Euler and Sophus Lie. The expression is meant to emphasize that α is a right versor, where π/2 is the measure of a right angle in radians. The π/2 in the exponent is, in fact, superfluous. Papers three and four are "Fundamental Theorems of Analysis Generalized for Space" and "On the definition of the Trigonometric Functions", which he had presented the previous year in Chicago at the Congress of Mathematicians held in connection with the World's Columbian Exhibition. He follows George Salmon in exhibiting the hyperbolic angle, argument of hyperbolic functions. The fifth paper is "Elliptic and Hyperbolic Analysis" which considers the spherical law of cosines as the fundamental theorem of the sphere, and proceeds to analogues for the ellipsoid of revolution, general ellipsoid, and equilateral hyperboloids of one and two sheets, where he provides the hyperbolic law of cosines. In 1900 Alexander published "Hyperbolic Quaternions" with the Royal Society in Edinburgh, and included a sheet of nine figures, two of which display conjugate hyperbolas. Having been stung in the Great Vector Debate over the non-associativity of his Algebra of Physics, he restored associativity by reverting to biquaternions, an algebra used by students of Hamilton since 1853. Works 1879: Principles of the Algebra of Logic from Internet Archive. 1885: Physical Arithmetic from Internet Archive. 1887: The Logical Form of Geometrical Theorems from Annals of Mathematics 3: 154,5. 1894: Papers on Space Analysis. 1898: Book Review: “La Mathematique; philosophie et enseignement” by C.A. Laissant in Science 8: 51–3. 1899 The Pythagorean Theorem from Science 34: 181,2. 1899: The Fundamental Principles of Algebra from Science 10: 345–364. 1906: Vector Analysis and Quaternions. 1910: Unification and Development of the Principles of the Algebra of Space from Bulletin of the Quaternion Society. 1911: Book Review: Life and Scientific Work of P.G. Tait by C.G. Knott from Science 34: 565,6. 1912: A System of Notation for Vector-Analysis; with a Discussion of the Underlying Principles from Bulletin of the Quaternion Society. 1913: On Vector-Analysis as Generalized Algebra from Bulletin of