93 
DOTS-DYNAMICS. 
Dots : notation for lines and planes of cubic surfaces, vi, 365—6, 373—449 ; and seminvariants, xiii, 267. 
Double Algebra : xn, 465. 
Double Contact : conics having with each other, iv, 456—9. 
Double Point: the term, vi, 1; on ground-curve, xii, 110, 129. 
Double Pyramid {see Polygons). 
Double-Sixer : and cubic surfaces, vi, 372, vu, 316—29 ; construction, vm, 366—84. 
Double Tangents {see Bitangents), 
Double Theta Functions: x, 155—6, 166—79, 180, 422—9, 474—5, 497, 565; in connexion Avith 
16-nodal quartic surface, x, 157—65; memoir on, x, 184—213; (Part I, preliminary investigations, 
x, 184—9; Part II, the double theta functions, x, 189—213); addition of, x, 455—62; evolution, 
xi, 454 ; transformation, xii, 358—89 ; {see also Theta functions). 
Doubly Infinite Products: I, 120—2, 132—5, 136—55, 156—82, 585, 586, X, 492—4, XI, 46, XII, 50—5; 
and doubly periodic functions, II, 150—63 ; and definite integrals, lx, 60 ; transformation of, x, 494—7. 
Doubly Periodic Functions : i, 156—82 ; and doubly infinite products, ii, 150—63 ; and definite in 
tegrals, ix, 61 ; the term, xi, 530. 
Drawing: geometrical, vi, 19; of quartic curves mechanically, vm, 151—5; curves generally, vm, 179—80; 
{see also Representation). 
Droop, H. R. : isochronism of circular hodograph, hi, 265 ; central forces problem, iv, 520, 587. 
Duality : in geometry, n, 561—2, 568, xi, 450, 467. 
Du Bois-Reymond, P. L. : uniform convergence, xm, 343. 
Dumas, W. : spherical pendulum, iv, 534, 587. 
Dupin, C.: cyclide of, v, 467, ix, 64, xii, 615; quartic and quintic surfaces, vii, 246; theorem of, 
VIII, 264—8, 562, ix, 84—9. 
Duplication of Groups : x, 149—52. 
Durège, H. : Landen’s theorem, xi, 339. 
Durfee, W. P. : symmetric functions, n, 602—3. 
Dynamics: differential equations of, i, 276—84; a class of problems, iv, 7—11; similarity of two 
dynamical systems, vm, 558—63 ; Lagrange’s general equation in, ix, 110—2, 198—200 ; general 
equations in, ix, 215—7; and time, xi, 444; transformation of coordinates, xi, 575. 
Dynamics, Recent Progress in Theoretical: hi, 156—204, iv, 514; introduction, hi, 156—7; Lagrange, 
Mécanique Analytique, m, 157—8, 201, 202; Lagrange, equations of motion, hi, 158, 200; lunar 
theory, hi, 158—9; Poisson, planetary theory, hi, 159, 201; Laplace’s theory, hi, 159, 201; 
Lagrange’s planetary theory, hi, 159—61, 162—3, 201 ; Lagrange, variation of arbitrary constants 
in mechanical problems, in, 161—5, 200; also Poisson, in, 163—5, 200, 201, 202; Cauchy, 
differential equations, in, 166 ; Hamiltonian method of dynamics, in, 166—74, 200, 202 ; its relations 
to Lagrange’s, in, 171—3, 200; and Poisson, in, 173—4, 200; Jacobi, calculus of variations and 
differential equations, in, 174—82, 200, 202; De Motu Puncti Singularis, in, 182—3, 202; problem 
of three bodies, in, 183; Jacobi, Theoria Novi Multiplicatoris, in, 1S3—5; Jacobi, theory of ideal 
coordinates, in, 185; Liouville, equations of motion, in, 185; Desboves, planetary perturbation, in, 
185, 203; Serret, integration of differential equations, in, 185—6, 203; Sturm, integration of dynamical 
equations, in, 186, 203 ; Ostrogradsky, dynamical equations, in, 186, 203 ; Brassinne, differential 
equations, in, 186—7, 203; Bertrand, integrals to mechanical problems, in, 187, 203; and integration 
of differential equations, in, 188—9, 203; and Mécanique Analytique, in, 189—90, 203; Brioschi, 
Sulla Variazione, and Teorema di Meccanica, in, 190, 203 ; Liouville, integration of differential 
equations, in, 191—2, 203; Donkin, dynamical differential equations, in, 191—7, 203—4; Bour, 
integration of differential equations of analytical mechanics, in, 197—8, 204; Liouville on Hour’s 
memoir, in, 199, 204 ; Brioschi, Degli Integrali di un Problema di Dinamica, in, 199—200, 203 ; 
Bertrand, integrals of several mechanical problems, in, 200, 203 ; summary, in, 200. 
Dynamics, Report on Progress of Solution of Certain Problems: iv, 513—93; introductory, iv,