119 
POINT-PAIRS-POLYZOMAL. 
geometry, vi, 458; potential of, ix, 278—80; singularities of curves, xi, 468; coordinates of, as 
functions of parameter, xii, 290—1; and line distance, xm, 495—7; two-way, xm, 507 ; for- 
forwards, and back-backwards, xm, 510. 
Point-pairs: the term, n, 564—5, vi, 202, 206—7, 208, 210, 269, 594—5; degenerate forms of 
curves, xi, 218. 
Points: distances of, I, 1—4, 581; some theorems in geometry of position, i, 317—28; of inflexion, 
i, 345—9, 354; of osculation, i, 349—51 ; harmonic relation of two, n, 96—7; of cesser, defined, 
iv, 130; critical defined, iv, 130; five in a plane, v, 480—3; correspondence on plane curve 
of, v, 542—5; and circle, problem, v, 560; correspondence of two on a curve, vi, 9—13, 264—8, 
vn, 39; notation of, in Pascal’s theorem, vi, 116—23; abstract geometry, vi, 463; consecutive, 
vi, 467—9; system of 16, and polyzomal curves, vi, 501—3, 504—5; problem of random, vn, 
585; problem and solution of four in plane or space, vil, 585; four and conic, vil, 587; on 
particular sextic curve, ix, 504—7; branch- and cross-, x, 317; and lines, problem and solution, x, 
570; on a circle, function of, xi, 130; double- and pinch-, xi, 227; Mill on, xi, 432—3; 
representation on plane, xi, 442; evolution theory of curves, xi, 450—1 ; at infinity, xi, 464; 
relation between the distance of five in space, xn, 581—3; analytical formulae in regard to octad 
of, xn, 590—3; Sylvester’s facultative, xhi, 46; non-existence of a special group, xm, 212; 
syzygetic relations, xm, 224—7; non-Euclidian geometry, xm, 480—504; coordinates of, and 
non-Euclidian geometry, xm, 489—91; (see also Orthomorphosis). 
Point-systems: and one-dimensional geometry, n, 563—9, 583—86; and two-dimensional geometry, ii, 
569—83, 586—92. 
Poisson, S. D.: attraction of ellipsoids, hi, 155; planetary theory, in, 159, 201 ; variation of arbitrary 
constants in mechanical problems, hi, 163—5, 200, 201, 202; coefficient (a, b) of, m, 163; Hamilton’s 
method of dynamics, hi, 173—4, 200; integration of differential equations, hi, 180; distribution 
of electricity, iv, 92—5, 100—7, x, 299, xi, 1; elliptic motion, iv, 522; relative motion, iv, 535, 
591; motion of projectile, iv, 541, 591; inertia, iv, 563, 591; rotation of solid body, iv, 566, 
569, 573, 591 ; rotation round fixed point, iv, 582, 591; motion of solid body, iv, 583, 591 ; 
attraction of ellipsoidal shell, ix, 302; Jacobi’s theorem, x, 108—9, 110—3. 
Polar: of point, v, 570, x, 54, xi, 465. 
Polar Conjugate: of curve of third class, ii, 383. 
Polar Reciprocal: i, 230, 378, 416. 
Polarization: MacCullagh’s theorem, iv, 12—20. 
Poles: conjugate, of cubic curve, n, 382—5; two-dimensional geometry, n, 579—83, 586—92; the 
term, xi, 465. 
Pollock, Sir F.: on circumscribed triangle, in, 29—34. 
Poloid Curve: iv, 571—2. 
Polyacra: triangle-faced, and enumeration of polyhedra, v, 38—44. 
Polygons: in-and-circumscribed, ii, 87—9, 91—2, 138—44, 145—9, iv, 292—308, 435—41, v, 21—2, 
vin, 14—21, 212; partitions of close-, v, 62—5, 617; and triangles, problem, v, 589; potential 
of, ix, 266—80; automorphic function for, xi, 169, 179—83, 212—6; partitions of, xm, 93— 
113. 
Polyhedra: Poinsot’s four new regular solids, iv, 81—5, 86—7, 609; the problem of, iv, 182—5, 
609 ; autopolar, iv, 185; enumeration of, and triangle-faced polyacra, v, 38—40; partitions of 
close-, v, 62—5, 617; axial properties, v, 529—39; potential of, ix, 266—80. 
Polyhedral Functions (see Ilypergeometric Series, Schwarzian Derivative). 
Polyzomal Curves, Memoir on: vi, 470—576, vn, 115; introductory, vi, 470—2; Part I, polyzomal 
curves in general, vi, 473—97; definitions and preliminary remarks, vi, 473—4; the branches, vi, 
474—6; points common to two branches, vi, 476—8; singularities of a v zomal, vi, 478—9; 
zomals with common point or points, vi, 479—81; depression of order of v zomal curve from