87 
CRYSTALS-CUBIC. 
Crystals : biaxal and ray planes, ix, 107—9. 
Cube : axial systems, v, 531—9; automorphic function for, xi, 169, 179—83, 212—6. 
Cubic : canonical form of binary, ii, 542 ; equation of differences for, iv, 242, 279 ; ternary, iv, 325—41 ; 
and tables, iv, 333—41; the term, iv, 604; resultant of two binary, v, 289—91 ; asyzygetic covariants 
of binary, vii, 338—9; automorphic transformation of binary cubic, xi, 411—6; (see also Binary 
and Ternary Cubics). 
Cubic Centres : of lines, v, 73—6. 
Cubic Cone: kinds of, v, 401—5, 551, 553; anharmonic property, v, 411—2. 
Cubic Curve Classification : v, 354—400, vm, xxxviii ; seven head divisions, v, 355—6 ; their equations, 
v, 356—9; thirteen divisions, v, 360—1; notion of group, v, 361; osculating asymptotes, v, 361—3; 
Newton’s classification, v, 364—6, xi, 464 ; Plucker’s, v, 366—8 ; theory of groups, v, 368—9 ; groups 
of hyperbolas A, v, 369—70 ; hyperbolas A redundant, v, 370—6 ; ditto defective, v, 376—88 ; hyper 
bolas O, v, 388—9; ditto redundant, v, 3S9—90; ditto defective, v, 390—1; groups of parabolic 
hyperbolas, v, 391—4 ; of central and parabolic hyperbolisms, v, 394 ; groups of divergent parabolas, 
v, 395; trident curve and cubical parabola, v, 395; division into species, Newton and Pliicker, 
v, 396—9. 
Cubic Curve Memoirs: first, i, 183—9, 586; remarks, i, 190—4, 586; second memoir, ii, 381—416, iv, 
188 ; definitions, ii, 382—3 ; theorems relating to conjugate poles, n, 383—5 ; their proof, n, 
385—96 ; geometrical definition of Quippian, ii, 396—7 ; theorems, n, 397—403 ; formulae for inter 
section of curve and line, n, 404—5; formulae for satellite point and line, n, 405—9; theorems 
relating to satellite point, n, 409—12 ; first polar point of cubic, n, 412—5 ; recapitulation of 
geometrical definitions of Pippian, n, 416. 
Cubic Curves: tangential of, ii, 558—60; cones through, in, 219—21; note on, iv, 120—2; five pointic 
contact, iv, 231—6 ; ninth point of intersection of those passing through eight given points, iv, 
495—504 ; twisted, v, 1 ; sextactic points of plane, v, 233—5 ; and cones, v, 401—15, 551, 553 ; 
inflexions of, v, 493—4, xi, 473 ; in connexion with quintics and quartics, v, 580 ; problem, v, 586 ; 
derivation of points, vi, 20 ; intersection of, vi, 20 ; in pencil of six lines, vi, 105—15, 593—4 ; 
nodal, vi, 171—4; foci of circular, vi, 521—2; theory of circular, vi, 526—8; symmetrical circular, 
vi, 549—50, 550—3 ; quartic and three, vii, 546 ; points on, vn, 549 ; and Cartesian curves, vii, 
556; rectangular, vn, 591; mechanical description, vm, 147—50; residuation in regard to one, ix, 
211—4; problem and solution, x, 592—4; equation of, x, 603; and conic, x, 605—7; Abel’s theorem 
applied to, xi, 27—8 ; degenerate, xi, 220 ; date of theory, xi, 449 ; forms and classification, xi, 
478—80 ; circular, xi, 481 ; systems of, xi, 487 ; Abel’s theorem, xn, 30 ; elliptic functions, xn, 35—7 ; 
as ground-curve in Abel’s theorem, xii, 38, 109—216; twisted, on quadric surface, xn, 307—10; 
notion of, xiii, 79—SO ; and non-existence of a special group of points, xm, 212. 
Cubic Equations : solution of, n, 542 ; Tschirnhausen’s transformation, iv, 364—7, 377 ; equation of 
squared differences, iv, 463—5 ; Sturmian constants, iv, 473—7 ; relation between roots, vn, 548 ; 
solution by radicals, x, 9 ; constants of, xi, 556 ; note on, xn, 421—3 ; Cardan’s solution, xn, 299 ; 
on two, xm, 348—9. 
Cubic Forms : letters on, hi, 9—12. 
Cubic Identity: problem, v, 597. 
Cubic Scrolls (see Scrolls). 
Cubic Seminvariants : generating function, xm, 306. 
Cubic Surfaces Memoir : vi, 359—455, 595—6 ; Introductory, vi, 359 ; twenty-three cases, explanations, 
and tables of singularities, vi, 359—63 ; determination of number of certain singularities, vi, 364—5 ; 
lines and planes of cubic surface, facultative lines, diagrams, vi, 365—6 ; different kinds of 
axis, vi, 367 ; determination of reciprocal equation, vi, 368—70 ; explanation of sections of memoir, 
vi, 370—1; equations, 1 = 12, vi, 371—83; 12 — , vi, 383—90; 12-# 3 , vi, 391—6; 12-2C 2 , vi, 
397—402; 12-#j, vi, 403—7; 12-# 3 -(7 2 , vi, 407—11; 12-# 5 , vi, 411—8; 12-3(7 2 , vi, 418—