HYPERDETERMINANTS—INTEGRAL. 
104 
Hyperdeterminants: the term, i, 81, 95, 114, 585; note on, i, 352—5, 588; a system of certain formulae, 
i, 533; theory, i, 577—9; theory of permutants, ii, 19; theory of intermutants, n, 26; qualities, n, 
225; theory of seminvariants, xii, 344; Sylvester’s work in, xm, 46; an identity, xm, 210—11; (see 
also Covariants, Invariants). 
Hyper dimensional Space: quadrics in, ix, 79—83; {see also Hypergeometry, Hyperspace). 
Hyperelliptic Functions: trisection of, vi, 594; and theta functions, x, 162—5, 166—79, 184—214, 
551—5; and triple theta functions, x, 432—6; addition-theorem, x, 455—62; the term, xi, 533—4; 
and nodal quartics, xn, 196—208; {see also Theta-Functions). 
Hyperelliptic Integrals: of first order, xii, 98—9. 
Hypergeometric Series : summation of a certain factorial expression, in, 250—3; theorem, in, 268—9; 
differential equations, xi, 17—25; note on, xi, 125—7; and Schwarzian derivative, xi, 176—9. 
Hypergeometry: of n dimensions, i, 55—62 ; a branch of mathematics, vm, xxxiii—v; five-dimensional, 
ix, 79—83; and quadric surfaces, ix, 246—9; 21 coordinates of conic in space, xi, 82—3; Sylvester’s 
work in, xm, 46; {see also Hyperspace, Prepotentials). 
Hyperspace: and quantics, n, 222; and non-Euclidian geometry, n, 606; representation by means of, 
vi, 198; of four dimensions, special theorem, ix, 246—9; {see also Hypergeometry). 
Icosahedra: construction, iv, SI—2; axial systems, v, 531—9; Klein on rotations of, x, 153; as regular 
solids, x, 270—3; automorphic function, xi, 169, 179—83, 185, 212—6. 
Icosahedral Substitutions {see Substitutions). 
Ideal: the term, vi, 483. 
Ideal Numbers : xi, 456. 
Idem: defined, xii, 66. 
Idempotent: the term, xii, 61. 
Identities: cubic, v, 597; trigonometrical, vm, 525, xi, 38, xm, 538—40; elliptic transcendent, vm, 564; 
a transcendental, xi, 37; algebraic, xi, 63—4, 130—1, xm, 76—8; a hyperdeterminant, xiii, 210—11. 
Imaginarles: on an octuple system of, i, 301; eight-square, xi, 368—71, xii, 465; the term, xi, 439; 
theory of equations, xi, 502—6; and function, xi, 523; associative, xii, 61, 105—6 ; perpendicularity, 
xii, 466—72; roots of equation, xm, 36; Sylvester’s work at, xm, 46; quaternions, xm, 542. 
Imaginary Quantities: logarithms, vi, 14—8; geometrical construction relating to, xi, 258—60. 
Immit: defined, iv, 109. 
Improper : conditions for curves, vi, 193. 
Increment: the term, vi, 468. 
Indefinite: applied to integration, ix, 500—3; the term, xm, 290. 
Indeterminate Equations: problem in indeterminate analysis, hi, 205—7. 
Index: to philosophic memoirs, report on, v, 546—8, 620. 
Indicial Equation: of differential equation, xii, 398, 453. 
Indicial Function: of differential equation, xii, 398, 401. 
Inertia : axes and moments of, iv, 478—80, 559—66. 
Ineunt: defined, ii, 574, v, 521, vi, 469; non-Euclidian geometry, xm, 489. 
Infinitesimal Rotations: vi, 24—6. 
Infinity: in geometry, xi, 464. 
Inflexional Tangents: and geodesic lines, vm, 157; {see also Tangents). 
Inflexions: of cubical divergent parabolas, v, 284—8; of cubic curve, i, 584, in, 48; Hesse on, iv, 186, 
v, 493—4, xi, 473; of curves, xi, 471—3, 480. 
Integral Calculus: some formulae of, i, 309—16, 588; transformation, i, 383; Picard’s memoir on, xii, 
408—11. 
Integral Functions: Legendre’s coefficients, i, 375—6; the term, iv, 603—4, xi, 523; prepotential 
surface, ix, 321—30, 330—4, 352—9; potential solid, ix, 334—7; epispheric, ix, 410—17; reduction