117 
PEIRCE-PLANE. 
Peirce, B.: orbit of Neptune and Uranus, ix, 180, 182; multiple algebra, xi, 457—8, xn, 60—71 ; 
associative algebras, xn, 106, 459, 465; imaginaries, xn, 303. 
Pellian Equation: iv, 40—2; tables, ix, 477—80 ; and theory of numbers, xi, 615; report of com 
mittee on, xiii, 430—67. 
Pencils: defined, ii, 577 ; homography of, ii, 578; intersections of four- and two- lined, v, 484—6; of six 
lines and cubic curves, vi, 105—15, 593—4. 
Pendulum, Spherical: iv, 532—4, 535—7, 541. 
Peninvariants: and seminvariants, iv, 241; the term, iv, 606. 
Pentagon: a theorem relating to, i, 318—9 ; Gauss’s Pentagrammci Mirificum, vn, 37—8 ; Schroter’s 
construction of regular, xii, 47; (see also Polygons). 
Pentagramma Mirificum: of Gauss, vii, 37—8. 
Pentagraph: illustrating a function, xi, 440; curve tracing, xiii, 515—6. 
Penultimate Forms : of curves, vm, 258—61 ; of surfaces, vm, 262—3. 
Penultimate Quartic Curve : vm, 526—8. 
Penumbral Curve {see Solar Eclipse). 
Periodic Functions : the term, xi, 529; {see also Doubly Periodic Functions). 
Periods: of elliptic integrals, ix, 618; of theta functions, x, 467—9. 
Permissive Points: in differential equations, xn, 434—41. 
Permutants: theory of, n, 16—26, 27; defined, ii, 17, iv, 594, 596, 600; Sylvester on, n, 26—7. 
Permutations: theory of, i, 423—4; idea of group, ii, 124; problem of geometric, v, 493—4; corn- 
mutants, v, 495—7 ; colours on faces of polyhedra, v, 539; {see also Arrangements, Combinatory 
Analysis). 
Perott, J.: binary quadratic forms, v, 618. 
Perpendicular: in non-Euclidian geometry, xiii, 480—1, 481—9. 
Perpendicularity: and imaginaries, xn, 466—72. 
Perpetuants: and seminvariants, xii, 250—7, xiii, 266; sextic, xn, 257—62 ; reducible seminvariants, 
xiii,. 308—13 ; Strohian theory of, xiii, 314—8. 
Perspective: of triangles, in, 5 ; five points in a plane, v, 480—3; theory, xi, 442. 
Pfaff, J. F.: problem, iv, 359—63. 
Pfaffian Differentials: xiii, 361, 405—14. 
Pfaffian Equations: Natani and Clebsch, iv, 515. 
Pfaffians: and skew determinants, i, 411, ii, 203; the term, i, 589, ii, 19, iv, 594, 600; and differential 
equations, x, 96—7, 106. 
PfafF-invariants: xiii, 405—14. 
Physics : relation to mathematics, xi, 444, 449; {see also Dynamics, Electricity, Light). 
Picard, E.: integral calculus, xii, 408—11. 
Pinch-planes: the term, vi, 330, 335, 583—5, x, 53—6. 
Pinch-points: the term, vi, 123, 330, 335, 582—5, x, 53—6, xi, 227. 
Pineto, S.: tables of logarithms (review), vm, 95—6. 
Pippian: defined, i, 586, ii, 381, 397—400, 400—3; and Hessian, ii, 383—95; geometrical definition, 
ii, 416. 
Pirie, B.: inertia, iv, 564. 
Plana, G. A. A.: lunar theory, hi, 536, 568, vii, 357—60, 361—6, 367—70, 371—4, 375—6; distribution 
of electricity, iv, 92, 100—7. 
Planar Developables : the term, i, 505. 
Planarity : of developables, v, 517. 
Plane Curves {see Curves, Plane). 
Plane-integral: prepotential, ix, 337—43. 
Plane of Orbit: variation in, iii, 516—8.