127 
RIGHT-HANDED—SADLERIAN. 
quartic, xi, 221—3; fractional differentiation, xi, 235—6; notion of space, xi, 435—7 ; correspondence 
of points, xi, 440; deficiency of curves, xi, 450; hyperelliptic functions, xi, 454—5 ; transformation, 
xi, 482; elliptic functions, xi, 534, 537, 539, 546; theory of numbers, xi, 616; series, xi, 627 ; 
minimal surface, xi, 639 ; Abelian functions and plane quartics, xn, 74, 87, 95 ; linear differential 
equations, xn, 396; orthomorphosis, xm, 180, 189, 204. 
Right-handed Root-limitation: ix, 22—3. 
Roberts, C. A.: Pellian equation, xm, 467. 
Roberts, M.: geodesic lines on ellipsoid, vn, 34. 
Roberts, S. : description of nodal bicircular quartic, vn, 182—8; points on cubic curve, vii, 549; 
three-bar curve, ix, 551; symmetrical determinant, x, 579—80; theorems of squares, xi, 294; curves, 
xi, 481 ; kinematics of a plane, xm, 505. 
Roberts, W.: transformations of curves, i, 471—5, 478; surface parallel to ellipsoid, iv, 158—65. 
Roberts, W. R. W.: cyclide, ix, 75. 
Rodrigues, O. : motion of solid body, i, 28—35, 124, 405, 583 ; quaternions, I, 124, 586 ; rotation of 
solid body, i, 237; skew determinants, i, 335; expansions in multiple sines, i, 583; attraction of 
ellipsoids, m, 149—53; transformation of coordinates, iv, 558, 559, 592, xi, 575 ; kinematics of solid 
body, iv, 581, 592 ; on rotation formulae, v, 537; correspondence of homographies and rotations, 
x, 153. 
Rohn, K.: quartic surfaces, vn, 609—10 ; quartic surface with twelve nodes, xm, 2. 
Roof: the term in non-Euclidian geometry, xm, 484. 
Root-limitation: geometrical representation, ix, 21—39; general theory, ix, 22—7 ; intercalation theory 
for right line, ix, 28—33; rhizic theory, ix, 34—8. 
Roots: in forms called trees, hi, 243, xi, 365—7; of algebraic equations, iv, 116—9, xi, 506—21, xn, 
33—4, xm, 33—7 ; quadratic equations, v, 160—1; of equations, Cauchy’s theorem, ix, 21—39 ; of 
unity, ix, 263; of quartic, reality of, x, 608; imaginary, of equations, xi, 114—21, 502—6; equal, of 
equations, xi, 405—7; theory of real equations, xi, 497—502; Sylvester’s work at, xm, 46 ; ninth, 
of unity, xm, 66; Waring’s formula for sum of mth powers of, of an equation, xm, 213—6; 
of a quantic, symmetric functions of, xm, 271—85. 
Roots of Unity: prime, xi, 56—60. 
Rosenhain, J. Cr.: theta functions, vm, xlii, x, 464, 499; double theta functions and 16-nodal quartic 
surface, x, 158, 162 ; theory of numbers, xi, 60; double theta functions, xi, 454. 
Rotation: of solid body, I, 28—35, 237, 583, n, 107, ill, 475—504, iv, 566—80, 592; quaternions and 
theory of, i, 405—9, 589; formula of, I, 586; and elliptic motion, in, 475; of earth, in, 485; in 
finitesimal, v, 498—9, vi, 24—6; of group of polyhedra, v, 529, 559; Euler’s memoir of 1758, vi, 
135—46; equilibrium of, vii, 91—5; and homography, x, 153—4; in conformal representation, 
xi, 78. 
Roulette: the term, xi, 447. 
Route: the term, xii, 640. 
Rowe, R. C.: memoir on Abel’s theorem, xi, 29—36; partitions of a polygon, xm, 93, 112. 
Royal Society: Cayley elected a fellow in 1852, vm, xiii; Croonian lecture founded, vm, xv; medals 
bestowed on Cayley, vm, xxi. 
Rudio, F.: inverse centro-surfaces, xii, 457—8. 
Rueb, A. S.: motion of solid body, i, 464; spherical pendulum, iv, 534; rotation of solid body, iv, 
573—4, 592. 
Rule of Signs: and determinants, xi, 492. 
Sabine, Sir E.: death of, xi, 429—30. 
Sadleir, Lady Mary: endowments by, vm, xv. 
Sadlerian Professorship: Cayley appointed to, vm, xvi.