125 
QUINTIC-RECIPROCITY. 
iv, 484; the term, iv, 604; MacClintock on, iv, 609—16; theorem of Abel as to soluble, v, 
55—61, xi, 402—4 ; discriminant of, problem, v, 592 ; conditions for existence of systems of equal 
roots, vi, 300—12; concomitant system of, x, 342; syzygies among covariants of, x, 346—55; 
canonical form, x, 355—62 ; resolvent sextic of, xi, 396 ; bitangents of the, xm, 21 ; and semin- 
variants, xm, 363—5 ; (see also Binary Quintics). 
Quintic Seminvariants : and perpétuants, xm, 309. 
Quintic Surfaces: and developables, v, 272—8, 518; recent researches, vu, 244—52. 
Quintic Transformation: of elliptic functions, ix, 122, 148, xn, 522—5. 
Quippian : the word, n, 381, 396—7. 
Quotient : G/H in theory of groups, xm, 336—7. 
Raabe, J. L. : summation of series, n, 15. 
Radiais: the term, xi, 259, xm, 179. 
Radicals: and solvibility of equations, vu, 13—4, x, 8—11; theory of equations, xi, 511—20, 521; 
Galois and theory of, xi, 543; Weierstrassian cubic transformation, xm, 31. 
Radicals (Chemical) : number of univalent, ix, 544—5. 
Radii: the term link- and bar-, vu, 183; curvature of wave-surface, xm, 248. 
Range : defined, n, 577 ; homography, n, 578. 
Rank of Seminvariants : xn, 22. 
Ratio : and abstract geometry, vi, 457—62. 
Rational Functions : the term, iv, 603—4. 
Rationalisation : of algebraic equations, n, 40—4. 
Rational Transformation (see Transformation, Rational). 
Ray, M. N.: solution of equations, x, 610—11. 
Ray Planes: and biaxal crystals, ix, 107—9. 
Rayleigh, Lord: fluctuating functions, ix, 19—20. 
Rays: special symmetrical system of three, vu, 428—9; the term, x, 55; systems of, xn, 571—5. 
Real Generating Function : x, 339. 
Real Intersections of Curves : ix, 21. 
Reciprocal Figures: i, 415—20. 
Reciprocal Matrix: n, 481. 
Reciprocal Polars: i, 416, 421; Monge, xi, 465; Poncelet, xi, 466. 
Reciprocals: of quartic scrolls, vi, 317—27; of cubic surfaces, vi, 368—455; of quartic surfaces, vii, 
305 ; of centro-surface of ellipsoids, vm, 363 ; equation of conic, vm, 522—3 ; reciprocal lines, xm, 
58—9. 
Reciprocal Surfaces, Theory of: vi, 329—58, 577—81, 582—91, 596—601; extension of Salmon’s funda 
mental equations, vi, 329—31; developments, vi, 331—4; new singularities, vi, 334—41; application 
to a class of surfaces, vi, 341—2 ; flecnodal curve, vi, 342 ; surfaces of revolution, in connexion 
with spinodal and flecnodal curve, vi, 342—4 ; flecnodal torse, vi, 345 ; general surface of order 
n without singularities, vi, 345—6; formula for /3', vi, 347—53; recapitulation, vi, 353—5; addition, 
vi, 355—8 ; Zeuthen, vi, 596—601 ; theory, xi, 225—34. 
Reciprocants : of quantic, n, 320 ; the term, iv, 607, xm, 366 ; and sextactic points, v, 618 ; of 
cubic, vi, 73 ; and invariants, xn, 393 ; Sylvester on, xm, 47—8 ; tables of pure, to weight eight, 
xm, 333—5 ; and differential invariants, xm, 366—404 ; Halphen on, xm, 366, 368—81, 381—98 ; 
Cockle, xm, 366, 367—8; Ampère and Lagrange, xm, 366; Sylvester, xm, 366, 379—81, 381—98; 
MacMahon, xm, 399—404. 
Reciprocation of Quartic Developable : v, 505—10. 
Reciprocity : geometrical, i, 377—82 ; and quantics, n, 232, 234 ; law of, for invariants, n, 516 ; and 
homography, n, 578.