79 
BINARY—BOOLE. 
Binary Quantics: canonical form, iv, 43—52, 53; canonical root, v, 103—5; involution, v, 296—301; 
transformations, vi, 187—90; discriminants of, vn, 303; and covariants, vm, 566—7, x, 430—1, xi, 
272—8; geometrical interpretation, ix, 16—7 ; factions, ix, 426; derivatives of three, x, 278—86; 
literal table for, xi, 357—64; finite number of covariants of, xn, 558. 
Binary Quartics: covariants of, ii, 189—91 ; fifth memoir on quantics, ir, 545—56; theorem of four, 
vn, 100; generating function of, x, 341. 
Binary Quintics: tables of covariants M to W of, n, 282—309 ; covariants and syzygies of degree 6, 
vi, 148—53; and sextic, vi, 190; irreducible covariants, vn, 334; tables, vn, 341—6; asyzygetic 
covariants of, vn, 399—400; (#$«, yf, x, 339—400; theorem relating to covariants, x, 430—1; 
concomitant system for, xi, 272. 
Binary Septic: minimum N.G.F., x, 408—21. 
Binary Sextic: and quintic, vi, 190; and squared cubic and cubed quadric, xi, 105; concomitant 
system for, xi, 272 ; tables for, xi, 372—6, 377—88. 
Binet, J. : determinants, i, 63, 64, 581 ; variation of arbitrary constants, hi, 181; relative motion, iv, 
535, 584 ; inertia, iv, 562—3, 584. 
Binodal Quartic: transformed to bicursal sextic, ix, 581 ; graphical representation of elliptic functions, 
xiii, 9—19 ; (see also Quartics). 
Binode : the term, vi, 330, 335, 361, 362, 583—5. 
Binomial Equation: theory of numbers, xi, 84—96. 
Binomial Theorem: factorials and derivations, n, 101, 102, vm, 463—73. 
Binormal: the term, xiii, 253. 
Biography: of Cayley, vm, ix—xliv. 
Bipartite: the term, vi, 464. 
Biplanar-node: the term, vi, 360. 
Biplanes: the term, vi, 360—1, 362. 
Bipoint-locus: the term, vi, 198. 
Biquaternions: Clifford, xi, 458, xiii, 481. 
Bisection: theory of numbers, xi, 84—96. 
Bitangents: of a plane curve, iv, 186—206; of quartic curve, iv, 342—8, vn, 123—4, x, 244, xi, 
221—3, xn, 74—94; of quartic, and triple theta functions, x, 444, 446; of curves, xi, 473—4, 480; 
of quintic, xiii, 21. 
Bitetrad: the term, xiii, 551. 
Bitrope : the term, vi, 330, 335, 583—5, 591, xi, 228. 
Björling, E. Gr.: root limitation, ix, 39; difference table, xi, 144. 
Blissard, J.: factorials, v, 574. 
Blunt: the term in seminvariants, xm, 265, 287, 291, 304—6. 
Bodies, Problem of Three: in, 183; Hamilton’s method, in, 97—103; Jacobi’s theorem, iii, 519—21, v, 23. 
Body (see Solid Body). 
Bolyai, J.: hyperbolic geometry, vm, xxxvii. 
Bondset: the term, xn, 642. 
Bonnet, Ossian: problem of two centres, iv, 528, 585; imaginary coordinates, vm, 569; minimal surfaces, 
xn, 595; curves of curvature, xn, 601, 629—31; skew surfaces, xm, 231, 237. 
Book-keeping: pamphlet by Cayley, vm, xxiv. 
Boole, Gr. : linear transformations, I, 80, 92, 93—4, 428, 584 ; multiple integrals, I, 198, 384—7, 588; 
attractions, i, 285, 289; theorem of Jellett, I, 388; transformation of elliptic integral, i, 508—10; 
discriminants, i, 584; theory of permutants, n, 26; theory of attractions, ii, 35; probabilities, ii, 
103, 594—8, v, 80—4, 85; hyperdeterminants, n, 598—601; transformation, in, 129 ; formulae for 
differentiation, iv, 135; differential equations, iv, 515, v, 301; involution, v, 301; invariants, vm, 
xxx; calculus of logic, vm, 65—6; integration of differential equations by series, vm, 458;