DIFFERENTIAL—DOSTOR. 
92 
system of, i, 366—9; Jacobi on theory, hi, 174; theorem of Jacobi on Pfaff’s problem, iv, 
359—63; singular solutions, iv, 426—7; transformation, iv, 574, v, 78—9; umbilici, v, 115—30; solu 
tion when algebraical, vn, 5—7; supposed new integration, vn, 36; note on one, vn, 354—6; 
pair in lunar theory, vn, 535—6, 537—40; integration by series, vm, 458—62; Euler’s, ix, 592— 
608; and theory of elliptic functions, x, 20 ; and sides of quadrangle, x, 33—5 ; theory of partial, 
x, 134—8; elliptic and single theta functions, x, 422—9; hypergeometric series, xi, 17—25 ; Abel’s 
theorem, xi, 27—8; new formulae for integration of Euler’s equation, xi, 68—9 ; mathematics and 
physics, xi, 449; connected with elliptic functions, xn, 30—2: Briot and Bouquet’s theory, xn, 
432—41; of circular functions, xn, 580; a diophantine relation, xn, 596—600; and construction of 
Milner’s lamp, xm, 3—5; Kummer’s, of third order, xm, 69—73; on a partial, xm, 358—61 ; 
Richelot’s integral of Euler’s, xm, 525—9 ; (see also Partial Differential Equations, Riccati, Schwarz, 
Singular Solutions). 
Differential Equations, Linear: invariants of one, xii, 390—3; general theory, xn, 394—403, 444—52, 
453—6 ; theory of decomposition, xii, 403—7. 
Differential Equations of First Order; theory of singular solutions, vm, 529—34, x, 19—24. 
Differential Invariants {see Invariants). 
Differential Operators: vn, 8. 
Differential Relations: of double theta-functions, x, 559—65. 
Differentiation: evaluation of definite integrals, i, 267—72, 587; formulae for, iv, 135—49; fractional, 
xi, 235—6. 
Dimensions in Geometry {see Geometry). 
Dimidiate: the term, xm, 119. 
Dimidiation: the term, xm, 122. 
Diophantine Differential Relation : xii, 596—600. 
Diptich : the term, xii, 596. 
Dirichlet, G. L. {see Lejeune-Dirichlet). 
Director, Nodal {see Nodal Director). 
Directrix: and scrolls, vn, 60; and the absolute, xm, 4S1—9, 501; kinematics of a plane, xm, 505—6. 
Discriminant: and invariant, i, 584; defined, ii, 176, iv, 603, vi, 466—7; of qualities, n, 320; the 
sign □, ii, 528; special, connected with curve, v, 163; of quintic, problem, v, 592; of binary 
quantic, vn, 303, ix, 16—7; example of a special, vm, 46—7; {see also Qualities). 
Discriminant Locus: the term, vi, 198. 
Displacement: the term in Abel’s theorem, xii, 110, 157—62. 
Distance: general theory of, ii, 561, 583—92, 604—6, v, 550; notion of, in analytical geometry, v, 
550 ; the term, vi, 497; angular, of two planets, vn, 377—9 ; Cayley and Klein on theory, vm, 
xxxvi—vii; general notion, vm, 31; Euclidian geometry, xi, 435—7; non-Euclidian geometry, xm, 
480—504; {see also Points). 
Distribution of Electricity : on spherical surfaces, iv, 92—8, 99—107, xi, 1—6. 
Distributively: the term, vi, 459. 
Disturbing Function : in lunar theory, hi, 293—308, 319—43 ; in rotation of solid body, hi, 486. 
Divisors : tables of, ix, 462—70. 
Dodecahedron : construction, iv, 82—3; axial systems, v, 531—9; as regular solid, x, 270—3; auto- 
morphic function for, xi, 169, 179—83, 184, 212—6. 
Donkin, W. F. : expansions in multiple sines, i, 583; differential equations, dynamical, hi, 191—7, 203—4 
344; transformation of trigonometric series, m, 567 ; attractions, hi, 567; a definite integral, iv, 29 
formulae for differentiation, iv, 135—49; central forces problem, iv, 521; spherical pendulum, iv, 
534, 536, 586; dynamical problems, iv, 547, 586; elimination of nodes in three bodies, iv, 551, 
586; rotation of solid body, iv, 578, 586. 
Dostor, G.: polyhedra, iv, 609.