91 
DERIVATIONAL-DIFFERENTIAL. 
Derivational Function: the term, i, 63. 
Derivations: extension of Arbogast’s method, n, 257, iv, 265—71, 272—5, 609, xi, 55; binomial 
theorem and factorials, vm, 463—73. 
Derivatives: and hyperdeterminants, i, 95; of point on cubic, iv, 231; of three binary qualities, x, 
278—86; [and covariants, x, 340, 377—94; of a function, x, 590—2; in binary forms, xi, 272 ; (see 
also Schwarz). 
de St Laurent, T.: caustic by reflexion, i, 273—5. 
Desboves, A.: planetary perturbation, m, 185, 203; problem of two centres, iv, 532, 586. 
Descartes, R.: ovals of, and transformation of curves, i, 478, 479—80, 589 ; oval of, hi, 66; formulae 
in Epistolcv, iv, 512; geometry of, xi, 437 ; (see also Cartesians). 
Determinants: applied to distances of points, i, 1—4, 581, iv, 510—2; Pascal’s theorem, i, 43—5; 
the term, i, 63; theory of, i, 63—79; theory of linear transformations, i, 80—94, 5S4; of vis 
viva, i, 284; note on hyperdeterminants, i, 352—5, 588; geometrical reciprocity, i, 377—82; 
“skew” and “symmetric,” i, 410—3; history, i, 581; multiplication, i, 581, xi, 495; value of 
certain, iii, 120—3, iv, 460—2; the term, iv, 594, 596—9; and Pfaffian, iv, 600; development of, 
v, 45—9; tables of binary cubic forms for negative, vm, 51—64; Smith’s Prize dissertation, vm, 
551—5; symmetrical, ix, 185—90, x, 579; notation, x, 95—7; theorem in, x, 265—6; in Ency. 
Bril., xi, 490—7; decomposition, xi, 495—6; theory of numbers, xi, 604—9; (see also Hyper 
determinants, Skew Determinants). 
Determinator: defined, n, 59. 
Determinirende: (indicial), and differential equations, xn, 398, 401, 453. 
Developables: and curves, I, 207—11, 586—7; the term, I, 486, xi, 573; from two quadrics, I, 
486—95; from quintic curve, I, 500—6; planar, I, 505; from quartic, v, 135—7; prohessians, 
v, 267—83; quartics, v, 268—71 ; general theory, v, 271—2; special quintic, v, 272—8; special 
sextic, v, 279—83; reciprocation of quartic developable, v, 505—10; a special sextic, v, 511—9; 
sextic, and sextic surfaces, vi, 87—100; focals of a quadric surface, xiii, 51—4; (see also Torse). 
Development: of factorial, ii, 98—101; coefficients in powers of (1 +n*x) m/n , xiii, 354—7. 
Dew-Smith, A. G.: portrait of Cayley, xi (frontispiece). 
Diagonals: and partitions of a polygon, xiii, 93—113. 
Diagrams: the term, vn, 405; of planet’s orbit from three observations, 5 plates, vn, to face 478; 
solar eclipse, vn, to face 492; geodesic lines on ellipsoid, vn, 510; coloured, representing groups, 
x, 328—30; transformation of elliptic functions, xi, 26; seminvariants, and solution by square-, 
xiii, 288—98; (see also Tables). 
Diameter: as used by Newton, v, 362. 
Diametral planes (see Planes). 
Dianome : the term, vn, 133, 148; (see also Quartic Surfaces). 
Diaphoric: the term, xi, 156. 
Dickinson, L.: portraits of Cayley, vi (frontispiece), vn (frontispiece), vm, xx. 
Differences: equation of squared, for cubic, iv, 463—5; relation between certain products of, x, 
293—4; on a functional equation, x, 298—306 ; (see also Equation of Differences). 
Differential Equation Memoir: x, 93—133; introductory, x, 93—4, 94—5; notations, x, 95—7; de 
pendence of functions, x, 97; general differential system, x, 98—102; the Multiplier, x, 102—5; 
Pfaffian theorem, x, 106; Hamiltonian system, derived from general system, x, 106—7; Poisson- 
Jacobi theorem, an identity in regard to functions (11, 0), x, 108—9; peculiar to Hamiltonian 
system, x, 110—3; conjugate integrals of Hamiltonian system, x, 113—5; Hamiltonian system—the 
function V, x, 115—8; partial differential equation //-constant, x, 119—25; examples, x, 125—32; 
partial differential equation containing the dependent variable, reduction to standard form, x, 
132—3. 
Differential Equations: and lines of curvature of ellipsoid, i, 36—9 ; dynamical, i, 276—84; Jacobi’s 
12—2