UEBERSCHIEBUNG—WARREN. 
140 
Ueberschiebung: the word, i, 585; {see also Derivations). 
Ultra-elliptic Functions {see Hyperelliptic Functions). 
Umbilicar Centres: the term, vm, 326, 351. 
Umbilici: and differential equations, v, 115—30; curves of curvature near, vn, 330—1; on surface of 
nWi order, vm, 320; the term, xi, 581; {see also Geodesic Lines). 
Umbral: theory of seminvariants, xm, 266; notation of, and seminvariants, xm, 301—6. 
Umbrae: the term, xn, 347. 
Unibasic: the term, xn, 642. 
Unicursal Curves: vi, 2. 
Unicursal Octics: xn, 310. 
Unicursal Quartics: standard equation, vii, 101; tangent line and osculating plane, vn, 101; its 
final form, vn, 102. 
Unicursal Surfaces: transformation of, vm, 388—93. 
Unicursal Twisted Quartic: xn, 428—31. 
Uniform Convergence: xm, 342—5. 
Uniform Function: xii, 433. 
Uniform Series: defined, iv, 457. 
Unipartite: the term, vi, 464. 
Uniplanar-node: the term, vi, 361. 
United Points: in correspondence, vi, 9. 
Unity: prime roots, xi, 56—60; imaginary roots, ix, 263; ninth roots, xm, 66. 
Universal Algebra: Sylvester’s theory of, xm, 47. 
Unode: the term, vi, 362. 
Uranus: Newcomb’s work, ix, 180—4. 
Vacuity: Sylvester’s theory of, xm, 47. 
Valentiner, H.: curves in space, v, 613—7; theory of surfaces, xi, 14—6. 
Values: principal, of complex expression, i, 309; of m' = r(l+i), xm, 522—4. 
Vandermonde, A. T.: solution by radicals, x, 11; theory of equations, xi, 513. 
Variables: (2, 2) correspondence of two, ix, 94—5; normal in dynamics, ix, 111; imaginary, xi, 
439—41. 
Variation: of parameters in rotation of solid body, i, 242; of arbitrary constants, hi, 161—200; of 
planet’s orbit, hi, 516—8, vn, 541—5. 
Variations, Calculus of: Jacobi on, in, 174; problem in, vii, 263. 
Velocities, Virtual: general equation, ix, 205—8. 
Veronese, G.: Pascal’s theorem, vi, 594; four-dimensional space, xi, 442. 
Vertices of Cones {see Cones). 
Vicinal Surfaces: conormal correspondence of, vm, 301—8; {see also Surfaces). 
Vieta, F.: tactions, xm, 152. 
Virginia: Key and Sylvester, professors at, xm, 43. 
Virtual Velocities: general equation, ix, 205—8. 
Walker, S. C.: the anharmonic-ratio sextic, vii, 314—5; orbit of Neptune, ix, 180. 
Wallis, John: biographical notice, xi, 640—3; multiple algebra, xii, 466 ; his expression for n, xm, 22—5. 
Walton, W.: root-limitation, ix, 39; maxima and minima, ix, 40—1 ; transformation of equations, 
ix, 42; integration and definite integrals, ix, 56—63; ray planes and biaxal crystals, ix, 107—9. 
Waring, E.: equation of differences, iv, 240, 252; sum of mth powers of the roots of an equation, 
xm, 213—6. 
Warren, J.: on binary cubics v, 289; curvilinear coordinates, xn, 1—18; multiple algebra, xii, 460, 468.