123 
QUANTICS—QUARTIC. 
154—6 ; character of equation, auxiliars, facultative and non-facultative space, vi, 156—8 ; application 
to quartic equation, vi, 158—61; characters of quintic equation, vi, 161—5; Tschirnhausen’s 
transformation, vi, 165—9 ; Hermite’s application of Tschirnhausen’s transformation to quintic, vi, 
170; nodal cubic, vi, 171—4; Hermite’s criteria, vi, 174—6; his canonical form of quintic, vi, 
177—83; imaginary linear transformations, vi, 183—6; application to auxiliars of quintic, vi, 186—7; 
theorem of binary quantic, vi, 187—90 ; the binary quintic and sextic, vi, 190. 
Quantics, Ninth. Memoir : vu, 334—53, IX, 537—42 ; introductory, VII, 334—5 ; theory of number 
of irreducible covariants, vu, 336—7 ; new formulae for number of asyzygetic covariants, vii, 
337—40; the 23 fundamental covariants, vii, 341—8; tables, vii, 341—6; Gordan’s proof for the 
complete system of 23, and concomitants of quintic, vii, 348—53. 
Quantics, Tenth Memoir : x, 339—400 ; introductory, x, 339—40 ; numerical and real generating 
functions, x, 341—8 ; table 96, x, 349—55 ; theory of the canonical form, x, 355—62 ; table 97, 
x, 362—9 ; table 98, x, 370—6 ; derivatives and tables, x, 377—94 ; numerical generating functions, 
N. G. f. of a sextic, x, 394—6; table, x, 397—400. 
Quantics : defined, n, 221, iv, 594, 604 ; resultant of, II, 320 ; discriminants, n, 320 ; notation of 
abstract geometry, vi, 464—6 ; and nilfactum, vi, 466 ; character of the ten memoirs, viii, 
xxx—xxxi ; transformable into each other, viii, 385—7 ; éliminant of two, xi, 100—2 ; Sylvester’s 
work in, xiii, 47 ; syzygetic relations among the powers of linear, xm, 224—7 ; and seminvariants, 
xin, 363 ; (see also Binary Quantics, Quadratics). 
Quarterly Journal of Pure and Applied Mathematics : viii, xii. 
Quartic Curves : transformation, i, 476—80, 589 ; special family of, i, 496—9 ; bitangents of, iv, 342—8, 
vii, 123—4, x, 244, xi, 221—3, 474; cuspidal defined, v, 10; in space, v, 11—5; and ovals, v, 
468—70; triangle iu-and-circumscribed to a, v, 489—92; with three double points, v, 550, 553; 
in connexion with cubic and quintic, problem, vi, 580 ; problem, v, 596 ; and sextic torse, vii, 
99—100; tricuspidal, problem, vii, 589; mechanical description, viii, 151—5; a penultimate, viii, 
526—8 ; construction of bicircular, ix, 13—5 ; and functions of a single parameter, ix, 315—7 ; 
with two odd branches, x, 36—7 ; bicircular, x, 223—42 ; triple theta functions, x, 446—54 ; 
problem and solution, x, 582—6 ; trinodal, problem, x, 602 ; singular tangents of, problem, x, 603 ; 
degenerate, xi, 220; with cusp at infinity, xi, 408; forms and classification, xi, 480; circular, xi, 
481; ground curve in Abel’s theorem, xn, 3S, 109—216; bitangents of plane-, xii, 74—94; twisted, 
xii, 428—31 ; (see also Bicircular, Binary, Binodal, and Nodal Quartics). 
Quartic Developables : and developable surfaces, v, 268—71; reciprocation of, v, 505—10. 
Quartic Equations : conditions for systems of equal roots, n, 467—8 ; evolution, n, 547 ; Tscliirn- 
hausen’s transformation, iv, 368—74, v, 449 ; Sturmian constants, iv, 473—7 ; nodal curve of 
developable from, v, 135—7; and quantics, vi, 158—61; solution of aU+6/3H=0, vii, 128—9; 
roots, vii, 551, x, 575 ; solution by radicals, x, 10. 
Quartic Matrix: Hermite’s, xii, 367—72. 
Quartics : canonical form, n, 548 ; equation of differences for, iv, 243, 279 ; the term, iv, 604 ; 
roots of, problem, v, 610; conditions for existence of systems of equal roots, vi, 300—12; and 
three cubics, problem, vii, 546 ; reality of roots, problem, x, 608. 
Quartic Scroll (see Scrolls). 
Quartic Seminvariants: xii, 20; generating functions, xm, 306; and perpétuants, xm, 316. 
Quartic Surfaces, First Memoir: vu, 133—81, 609—10; introductory, vii, 133—4; Jacobian surfaces, 
vii, 134—6; surface by equating to zero a symmetrical determinant, vii, 136—7; surfaces 
F (P, Q)- 0, etc., vii, 138; nodes of quartic surface, vii, 138—40; number of constants contained 
in a surface, vii, 140—1; general theory of quartic surface with given nodes, vii, 141—4; Jacobian 
surface of six given points, vii, 144—5; ditto of seven, or an octad of points, vii, 145—8; the 
diauodal surface, vii, 148—52 ; octadic surfaces with 9 or 10 nodes, vii, 152—5 ; dianomes with 
9 or 10 nodes, vii, 155; dianodal curve of 8 points, vii, 155—6; ten nodes, vii, 156; dianodal 
16—2