SWITZERLAND-SYMMETRIC. 
134 
curve on a, xi, 323—30 ; Gaussian theory, xi, 331—6 ; and solid geometry, xi, 569 ; ruled, in Ency. 
Brit., xi, 572—3 ; in Ency. Brit., xi, 580—2 ; general theory of curvilinear coordinates, хн, 1—18 ; 
determination of order of surface, xn, 42—4 ; minimal, and JoachimsthaPs theorem, xn, 594—5 ; 
with plane or spherical curves of curvature, xn, 601—38 ; quasi-minimal, xiii, 42 ; the absolute, 
xiii, 42 ; applicable to each other, xiii, 253—64 ; and systems of tetrads of circles, xiii, 425—9 ; 
of order n which pass through given cubic curve, xiii, 534—5 ; (see also Developables, Monoid, 
Orthogonal, Parallel, Reciprocal, and Wave Surfaces, Scrolls). 
Switzerland : Cayley’s visits to, viii, xi. 
Syllogism: theory of, viii, 65—6. 
Sylow, L. : theorems on groups, xiii, 530—3. 
Sylvester, J. J. : special factors, i, 337; Sturmian functions, i, 392, n, 471—4; schoolgirl problem, 
i, 483 ; theory of hyperdeterminants, i, 577, 589 ; commutants, I, 584 ; endoscopic, I, 588 ; theory 
of permutants, n, 23, 26, 27; rationalization of algebraical equations, ii, 42; matrices, n, 219, 
604; law of reciprocity, n, 232, 234; partitions, n, 248—9, 506, xii, 217; contravariants, n, 320; 
combinants, n, 322 ; cubic curves, n, 405 ; symmetric functions, n, 465 ; canonical forms, n, 523 ; 
cobezoutiauts, n, 524 ; bezoutiants, n, 526 ; hyperdeterminants, n, 598—601 ; logic of characteristics, 
in, 52 ; a special determinant, hi, 122 ; elimination, hi, 214—5 ; independent variables in differential 
calculus, hi, 246 ; reversion of series, iv, 36, 37, 54—9 ; canonical form of binary quantics, iv, 
43—52, 53 ; double partitions, iv, 166—70 ; conics and five-pointic contact, iv, 231 ; on derivative 
of point on cubic, iv, 231 ; finite differences, iv, 263 ; equation of differences, iv, 277 ; invariants, 
iv, 349; Tschirnhausen’s transformation, iv, 391; volume of tetrahedron, iv, 462; involution of 
six lines, iv, 582, 593, vu, 66 ; lines in involution, v, 1—3 ; quadric cones, v, 6 ; quartic surfaces, 
v, 69 ; canonic root of binary quantic, v, 103—5 ; discriminant of quintic, v, 592 ; conic and cubic, 
v, 608 ; derivation of points of cubic curve, vi, 20 ; quintics, vi, 147—8 ; on roots of algebraical 
equation, vi, 147; bicorn, vi, 158; foci of conics, vu, 1—4; differential operators, vu, 8; cubic 
transformation of elliptic functions, vu, 44 ; Cartesian curves and cubic curve, vu, 556 ; spherical 
problem, vu, 563 ; discussions with, on covariants, viii, xv ; theory of matrices, viii, xxxii—iii ; 
root-limitation, ix, 22, 39; elimination, ix, 43, xm, 545—7; residuation, ix, 211; quartic curves 
and functions of a single parameter, ix, 315—7 ; scalene transformation, ix, 527, 534 ; development 
of idea of Eisenstein, x, 58—9 ; numerical generating function, x, 339 ; linkwork, x, 407 ; N. G. F. 
of binary septic, x, 408—9 ; theorem relating to covariants, x, 430 ; on trees, x, 598—600 ; theory 
of tamisage, xi, 409—10; partitions, xn, 217; perpétuants, xn, 251, 252, 253; non-unitary partition 
tables, xii, 273; d’Alenibert-Carnot geometrical paradox, xu, 305—6; umbræ, xn, 347; invariants 
and reciprocals, xu, 393 ; a Diophantine relation, xu, 596 ; Nature, notice in, xiii, 43—8 ; syzygetic 
relations, xiii, 224 ; reciprocals, xiii, 333—5, 366, 379—81 ; lectures on theory of reciprocants, 
xiii, 381—98. 
Symbolical Forms : of hyperdeterminants, i, 80—94 ; of covariants, i, 577, 585. 
Symbols : modular functions, iv, 484—9. 
Symmetric: the term, i, 410. 
Symmetrical : the term, iv, 599, 604, vi, 524—5, xi, 496. 
Symmetric Covariants : n, 233. 
Symmetric Curve : and system of equations, i, 473. 
Symmetric Functions : of roots of an equation, ii, 417—39, 602—3 ; partitions, n, 418 ; tables, n, 423—39 ; 
resultant of a system of two equations, ii, 440—53 ; tables, n, 445—53, vi, 292—9 ; of the roots of 
certain systems of two equations, n, 454—64, vi, 292—9 ; conditions for existence of given systems of 
equalities among roots of an equation, ii, 465—70, 603—4, vi, 300—12; tables, ii, 467; conditions 
for existence of systems of equal roots of binary quartic or quintic, vi, 300—12 ; and theory of 
equations, x, 6—8 ; non-unitary, and seminvariants, xii, 239—48, 275 ; tables of roots, xii, 263—72, 
273—4; a differential operator, xu, 318; seminvariants, xiii, 265—332; (see also Seminvariants).