QUARTIC-QUINTICS. 
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centres of 9 points, vn, 156; result as to dianomes, vn, 156; the symmetroid, (lineo-linear 
correspondence of quartic surfaces), vn, 157—9; ditto and Jacobian, vii, 160—3; symmetroid with 
given nodes, vn, 163—6, 259; Jacobian with given lines, vn, 167; correspondence on the Jacobian, 
vii, 168—70; further investigations as to Jacobian, vn, 171—5; persymmetrical case: Hessian 
of a cubic, vii, 175; quartics with 11 or more nodes, vii, 176—7; quadric surface through three 
given lines, vii, 177; condition that five given lines may lie in a cubic surface, vii, 177—8; 
condition that seven given lines may lie in a quartic, vii, 178; Jacobian of 6 points, vii, 178—9; 
locus of vertex of quadric cone which touches each of six given lines, vii, 180—1. 
Quartic Surfaces, Second Memoir: vii, 256—60, 609—10. 
Quartic Surfaces, Third Memoir: vii, 264—97, 609—10; preliminary considerations and classification, 
vii, 264—7; sextic curves, vii, 267—71; nodal determination, vii, 271—3; quartic surfaces resumed, 
vii, 273—4; enumeration of the cases, vii, 274—80; notation for cases afterwards considered, vii, 
280—1; 16-nodal surface and table, vii, 281—4; 15-nodal surface and table, vii, 285—8; equation 
of ditto, vii, 288—9; 14-nodal surface and table, vii, 289—92; 13-nodal surface and table, vii, 
293—7. 
Quartic Surfaces: on, v, 66—9; Steiner, v, 421—3, ix, 1—2; 16-nodal, v, 431—7, vii, 126—7, 
x, 157—65, 180—3, 604, xn, 95—7; note on, v, 465—7; recent researches, vii, 244—52; 
Pliicker’s models, vii, 298—302; some special, vii, 304—13, vm, 2—11, 25—8; surface and sphere, 
problem, vii, 589 ; section of surface, problem, vii, 593; penultimate forms of, vm, 262—3; 
symmetrical determinant = 0, x, 50—6; 12-nodal, x, 60—2, xm, 1—2; Hessian of, x, 274—7; 
tetrahedroid as 16-nodal, x, 437—40; equation of, x, 609; in Ency. Brit., xi, 633—4; (sre also 
Cyclide). 
Quartic Syzygy: and elliptic integrals, n, 191, iv, 68—9, 609. 
Quartic Transformation: of elliptic functions, ix, 103—6. 
Quartinvariants: of quantic, n, 516, 520. 
Quartisection: theory of numbers, xi, 84—96. 
Quasi-inversion: and orthomorphosis, xm, 192—3. 
Quasi-minima: the term, xm, 42. 
Quasi-normal: the term, xm, 228. 
Quaternary: the term, vi, 464. 
Quaternary Function: Hessian of, ix, 90—3. 
Quaternions: certain results, i, 123—6, 127; algebraic couples, I, 128—31 ; rotation, I, 405—9, 589, 
v, 537; formulae of, n, 107; transformation of quadrics, n, 135; skew determinants, n, 214; 
transformation of coordinates, iv, 559; the equation qQ—Qq'=0, xn, 300—4, 311—3; matrices, 
xii, 303; multiple algebra, xii, 474; hydrodynamical equations, xm, 8; versus coordinates, xm, 
541—4. 
Quet, J. A. : relative motion, iv, 536, 592. 
Quetelet, M. A.: theory of Gergonne, and on caustics, n, 339 ; wave surface, iv, 433 —4. 
Quinquisection : theory of numbers, xi, 314—6, xii, 72—3. 
Quintic Curves: and developables, I, 500—6; in space, v, 15—6, 20, 24—30, 552, 553, 613; in 
connexion with cubic and quartic, v, 580. 
Quintic Developables: and surfaces, v, 272—8, 518. 
Quintic Equations: conditions for systems of equal roots, n, 468—70; equation of differences, iv, 
150—1, 246—61, 276—91 ; Tschirnhausen’s transformation, iv, 375—94 ; tables, iv, 379—80, 387—90 ; 
Jerrard’s researches, v, 50—4, 77, 89; character of, vi, 161—5; solvibility by radicals, vii, 13—4, 
x, 11; theorem of Abel, xi, 132—5; solvable case of, xi, 402—4; and elliptic functions, xm, 
473; their sextic resolvents, xm, 473—9. 
Quintic Matrix : xii, 376—80. 
Quintics: auxiliary equation for, iv, 309—24; Jerrard’s form, iv, 392; soluble by elliptic functions,