95 
ELLIPTIC—ENCKE. 
attraction of ellipsoidal shell on exterior point, ix, 302—11 ; negative pedals, x, 576; in Ency. Brit., 
xi, 576—9. 
Elliptic Coordinates : equation of wave surface in, xi, 71—2. 
Elliptic Functions: Bronwin on, i, 118, 119; of Jacobi, i, 127, 507, 586; integral calculus, i, 383; 
multiplication of, i, 534—9, 568—76, 589 ; addition of, i, 540—9, 589, xii, 294—8; connected with 
theory of numbers, n, 48; system of modular symbols, iv, 484—9; Weierstrass, v, 33—7; treatise by 
Cayley, viii, xviii, xxviii, xm, 560; a general differential equation, ix, 592—608 ; a differential equation in 
theory of, x, 24 ; and integration, x, 25—7 ; torse depending on, x, 73—8 ; reduction of Abelian integrals 
to, x, 214—22; and single theta functions, x, 422—9, 463, 472; certain algebraic identities, xi, 
130—1; evolution of, xi, 451—5; and quartic function, xi, 483; kinds of, xi, 529; symmetrical 
differential equation and, xn, 30—2; solution of x 3 + y' i -1=0, xn, 35—7; Weierstrassian and 
Jacobian compared, xn, 425—7 ; Kiepert’s ¿-equations, xn, 490—2; graphical representation, xm, 
9—19; and sextic resolvent equations, xm, 473—9; theta and omega functions, xm, 558—9; 
(see also Gudermannian, Theta functions). 
Elliptic Functions Formulae: Serret’s, hi, 3; for geodesic lines on special ellipsoid, vn, 507—10; one, 
xi, 65, xii, 292—3; connexion of certain, xi, 250—1; geometrical interpretation of certain, xn, 107. 
Elliptic Functions, Inverse: i, 136—55, 156—82, 586; and definite integrals, ii, 3. 
Elliptic Functions, Memoir on Transformation of: ix, 113—75; introductory, ix, 113—4; the general 
problem, ix, 114—7; Qk modular equations, ix, 117—8; equation-systems, ix, 119—20; Q.k form, 
ix, 121—6; modular equation, ix, 126—37; tables, ix, 128—35, 163; multiplier equation, ix, 
138—40; multiplier as rational function of u, v, ix, 140—4; multiplication of elliptic functions, ix, 
144—7; transformations, ix, 147—55; general theory of ^-transcendents, ix, 155—69; four forms of 
modular equation and curves represented thereby, ix, 169—75. 
Elliptic Functions, Theorems in: xi, 73—7; Landen’s, xi, 337—9, 584; Ilermite’s /¿product, xii, 
584—6. 
Elliptic Functions, Theory of: i, 290—300, 364—5, 402—4, 587, 589 ; and quadri-quadric curve, xii, 
321—5. 
Elliptic Functions, Transformation of: i, 120—2, 132—5, 585, ix, 543, x, 333—8, 611, xi, 26, xii, 416—7, 
505—34, 535—55, xm, 29—32; cubic, III, 266—7, VII, 44—6, 244—5, 253—6, XII, 46, 556—7, XIII, 
64—5; special quartic, ix, 103—6; geometric illustration of cubic, ix, 522—6; orthomorphosis, 
xm, 191—205. 
Elliptic Integrals: reduction of i, 224—7; transformation, i, 508—10, ix, 618—21; geometrical 
representation, ii, 53—6, 113—7; discussion, n, 93—5; and covariants, n, 189—92; transformation 
formulae, iv, 60—9, 609; expression for second kind of, x, 25—7; note on theory, x, 139—42; 
some formulae in, x, 143—8; of third kind, x, 489—92; problem, x, 614; theta functions, xi, 41—6; 
note on, xi, 64 ; reduction of an integral to, xi, 270—1 ; of third kind, formulae, xi, 340—1. 
Elliptic Motion: expansion of true anomaly, in, 139—42, 567; trilinear equation of second degree, 
hi, 143—8; theory of, in, 216—8; tables of functions in theory, in, 360—474, vii, 516; Lambert’s 
theorem, in, 562—5, vii, 387—9; and dynamical progress, iv, 521—4; a theorem, ix, 191—3; and 
body let fall at equator, ix, 241—3. 
Elliptic Motion, Disturbed : memoirs on, in, 270—92, 344—59, 505—15. 
Elliptic Space : and non-Euclidian geometry, xm, 481. 
Elliptic-Transcendent Identity : viii, 564. 
Ellis, R. L.: orthogonal surfaces, viii, 272; differential equations, viii, 458; Dupin’s theorem, ix, 88. 
Emanants : of qualities, ii, 321; theory, ii, 518; Bezoutoidal, ii, 525, 526; the term, iv, 604, xm, 46. 
Emanation: theory of, n, 321. 
Encke, J. F.: über die speciellen Störungen, in, 179—80; fluctuating functions, ix, 19; roots of 
numerical equations, x, 5.