129 
SCHWARZIAN-SERRET. 
polyhedra, xi, 190—5; system of fifteen circles, xi, 208—12; regular polyhedra as solid figures, 
xi, 212—6. 
Schwarzian Derivative, and Polyhedral Functions: xi, 149, 173, 177; and Kummer’s differential 
equation, xm, 69 ; and reciprocante xin, 366. 
Schwarzian Function: Sylvester on the, xm, 381. 
Scientific Memoirs Catalogue : report on, v, 546—8, 620. 
Scrolar: the term, vi, 334. 
Scrolls, First Memoir: v, 168—200. 
Scrolls, Second Memoir: v, 201—20, vi, 360; degeneracy, v, 201—3; with two directrix lines, v, 203—5; 
twofold directrix line, v, 205—7 ; scroll equations, v, 207—10 ; cubic scrolls, v, 210—3 ; quartic 
scrolls, v, 214—9 ; general theory, v, 219—20. 
Scrolls, Third Memoir: vi, 312—28; quartic scrolls, vi, 312—4, 314—7, 328; reciprocals, vi, 317—25, 
325—7. 
Scrolls: cubic, v, 90—4, 110—2; quartic, vi, 451; tetrahedral, vii, 48—53; on certain, vn, 54—65; 
recent researches, vn, 250—1 ; and octic surfaces, x, 79—92 ; flexure and equilibrium, xi, 317—22 ; 
the term, xi, 573 ; applicable upon a given skew surface, xm, 231—7. 
Secondary Caustics (see Caustics). 
Secular Acceleration of Moon’s Mean Motion : hi, 522—561. 
Seeber, L. : mathematical tables, ix, 491—2. 
Segar, H. W. : development of (1 +n 2 x) m ^', xm, 354—6. 
Segner, J. A. v. : inertia, iv, 561—2, 592. 
Segregates : the term, x, 339, 345 ; table of, x, 349—55. 
Semi-cubical Parabola : and Abel’s theorem, xn, 180—6. 
Seminvariants, memoir: xn, 239—62; introductory, xii, 239—40; multiplication of two symmetric 
functions, xii, 240—8 ; capitation and decapitation, xn, 248—50 ; perpetuants, etc., xn, 250—7 ; 
sextic perpetuants and sextic syzygies, syzygants, xii, 257—62. 
Seminvariants: the term, iv, 241, 606; theory of, xii, 22—9, 344—57, xm, 362—5; tables, xii, 
275—89, xm, 217—23 ; theorem relating to, xii, 326—7 ; (see also Covariants, Invariants). 
Seminvariants and Symmetric Functions, Memoir : xm, 265—332 ; introductory, xm, 265—6 ; the 
coefficients (a, b, c,...), xhi, 266—71 ; symmetric functions of the roots, xm, 271—85; MacMahon form 
of equation, xm, 286—8 ; the I-and-F problem, and solution by square diagrams, xm, 288—98 ; 
MacMahon linkage, xm, 298—301 ; umbral notation, Stroll’s theory, xm, 301—6 ; symmetric 
functions of a given degree : generating functions, xm, 306—8 ; reducible seminvariants—per 
petuants, xm, 308—13 ; Strohian theory resumed : application to perpetuants, xm, 314—8 ; investi 
gation of the values of the foregoing functions, xm, n l0 (x+y) n 15 (x + y) and n 10 (x+y+z), xm, 
318—21 ; the operators, xm, 322—32. 
Senate House Problems : ix, 246—9, xi, 265—7, xm, 538—40 ; (see also Smith’s Prize Papers). 
Separations of Partitions : n, 603 ; (see also Partitions). 
Separator: the term, vn, 402. 
Septic, Binary : generating functions of, x, 408—21. 
Septic Transformation in Elliptic Functions : ix, 148—52, x, 333—8. 
Series: a double infinite, n, 8—10, 593; sums of, III, 124—8, xm, 49—50; reversion, iv, 30—7; 
formula for reversion, iv, 54—9 ; in integration of differential equations, vili, 458—62 ; hyper 
geometric, xi, 17—25, 125—7; in Ency. Brit., xi, 617—27 (finite, xi, 617—20; infinite, xi, 620—7). 
Serpoloid Curve: iv, 571—2. 
Serret, J. A.: attractions, I, 288; integral calculus, I, 313; elliptic functions, ill, 3; integration of 
differential equations, hi, 185—6, 203; problem of two centres, iv, 528, 531, 592; theory of sub 
stitutions, vii, 47; curves of curvature, vn, 331, xii, 601—38; orthogonal surfaces, vm, 279, 292; 
indefinite integration, ix, 500—3 ; transformation of cubic function, xi, 411 ; minimal surfaces, xii, 595. 
17 
C. XIV.