105 
INTEGRALS—ISOCHRONIC. 
of transcendental, x, 214—22; hyperelliptic, of first order, xn, 98—9; regular, of differential equation, 
xn, 395—6; number of, xii, 399; subregular of differential equation, xn, 444—52; {see also Abelian 
Integrals, Definite Integrals, Elliptic Integrals, Transformations). 
Integrals: transformation of double, ix, 250—2; of differential equations of first order, x, 19. 
Integration: a supposed new, vn, 36; theorem of, vn, 588; by series of differential equations, vm, 
458—62; a process of, ix, 257—8, x, 15, 29; indefinite, ix, 500—3; Aronhold’s formula, x, 12—14; 
of Euler’s equation, xi, 68—9. 
Integrator: mechanical, xi, 52—4. 
Intercalation: root-limitation, ix, 22—7; for right line, ix, 28—33; Sylvester’s theory of, xm, 46. 
Intermediates: of two qualities, defined, n, 515; of binary quartic, ii, 549; and ternary cubics, iv, 326. 
Intermutants: the term, n, 19, 26, iv, 594, 600. 
Interpolation: Smith’s Prize dissertation, vm, 551—5. 
Intersect-developable: of two quadrics, i, 486—95. 
Intersections: the term, vn, 546; of two curves, ix, 21, xn, 117—20; of cubic and line, xn, 100. 
Invariable Plane: and rotation of solid body, i, 237, vi, 142. 
Invariants: the term, I, 577, 589, n, 176, 224, iv, 594, 605, xm, 46; and discriminants, I, 584; 
determined by differential equations, n, 164—78; and roots, n, 176; differential equation satisfied 
by, ii, 176—8; and binary quantics, n, 266—8; of quartic, and covariants of cubic, analogous, 
II, 553; bibliography, n, 598—601 ; of biternary quantics, iv, 349—58; 18-thic of quintic in terms 
of roots, vi, 154—6; Cayley founder of, vm, xxviii—xxx; his work, vm, xxx—xxxii; and trans 
formation of quantics, vm, 385—7; quadratic transformation of a binary form, vm, 398—400; 
identical equation connected with theory, ix, 52—5; Hessian of quaternary function, ix, 90—3; 
minimum N. g. p. of binary septic, x, 408—21; stereographic projection, xi, 187—9; in geometry, 
xi, 474; of a linear differential equation, xn, 390—3; Sylvester’s work at, xm, 46, 47; two, of 
quadri-quadric function, xm, 67—8; differential, and reciprocants, xm, 366—404; Pfaff-, xm, 
405—14; {see also Covariauts, Linear Transformations, Seminvariants). 
Invariants and Covariants: xn, 22—9; standard solutions of system of linear equations, xn, 19— 
21; finite number of the covariants of a binary quantic, xii, 558. 
Inversion: of quadric surface, vm, 67—71; note on, ix, 18. 
Inverts: quadric function of, xi, 153—6. 
Involutant: of two binary matrices, xm, 74—5. 
Involution: theory of geometrical, i, 259—66, 587; and two or more quadrics, n, 529—40; of six 
lines, iv, 582, vn, 66, 85, 95; lines in, v, 1—3; theory, v, 295—313; the term, vi, 460; of four 
circles, vi, 505—8 ; and ternary quadrics, xm, 350—A 
Involution of Cubic Curves, Memoir: v, 313—53, vn, 238; explanations, definitions, and results, v, 
314—8; general formulae for critic centres, v, 318—9; twofold and one-with-twofold centre, v, 
319—24; tangents at a node, v, 325—8; triangle of critic centres, v, 328—9; the three-centre conic, 
v, 329—36, 337—8; transformation equation of cubic, v, 339—41; cubic locus, harmoconics, and 
harmonic conic, v, 341—5 ; miscellaneous, v, 345—53. 
Irrational: and subrational, ix, 315. 
Irreducible: the term, vn, 336, xii, 23. 
Irreducible Concomitants: of quintic, x, 342. 
Irreducible Covariants: and invariants, n, 250. 
Irreducible Syzygies {see Syzygies). 
Irregular: the term, vi, 457, 459. 
Iseccentric Lines: and planet’s orbit, vn, 468. 
Isobaric: the term, xm, 266. 
Isobarism: of covariants, n, 233. 
Isochronic: the term, nodal and cuspidal, vn, 473. 
C. XIV. 
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