EARTH—ELLIPSOIDS. 
94 
513—5; rectilinear motion, iv, 515—6; central forces, iv, 516—26; elliptic motion, iv, 521—4; 
problem of two centres, iv, 524—32; spherical pendulum, iv, 532—4; motion as affected by the Earth 
and relative motion generally, iv, 534—7; motion of single particle, iv, 537—8; motion of three 
mutually attracting bodies in a right line, iv, 538—40 ; motion of three bodies, iv, 540—1 ; motion 
in resisting medium, iv, 541; integration of equations of motion, iv, 542—6 ; memoirs by Jacobi, 
Bertrand and Donkin, iv, 546—7 ; problem of three bodies, iv, 548—52 ; transformation of coordinates, 
iv, 552—9 ; principal axes and moments of inertia, iv, 55.9—66; rotation of solid body, iv, 566— 
80 ; kinematics of solid body, iv, 580—2; rotation round fixed point, iv, 582—3 ; other cases of 
the motion of a solid body, iv, 583—4. 
Earth, The : rotation of, hi, 485, iv, 534—7 ; (see also Gravity). 
Eclipses (see Solar Eclipses). 
Edge : defined, v, 63. 
Eindeutig: (Uniform function), xn, 433. 
Eisenstein, F. G.: linear transformations, i, 90, 101, 111, 113—6, 585; hyperdeterminants, i, 353, ir, 
598—601; elliptic functions, i, 586; cubic forms, hi, 9; quadratic residues, hi, 39—43; finite 
differences, iv, 263; mathematical tables, ix, 492—3; “ development of an idea of,” x, 58—9; 
development of (1 + n' 2 x) m ^ n , xm, 357. 
Elastic Strings : problem with, hi, 78—9. 
Electricity : distribution on spherical surfaces, iv, 92—8, 99—107, x, 299, 307, xi, 1—6. 
Elements: Jacobi’s canonical, hi, 77 ; of arc, x, 235—7 ; a reduction to elliptic integrals, x, 239—42. 
Eliminant: the term, iv, 597 ; of two qualities, xi, 100—2. 
Elimination: and theory of curves, i, 337—51, v, 162—7, 416—20; from connected equations, i, 
370—4 ; and linear transformations, i, 457 ; theorem of Schlilfli, n, 181—4 ; a result of, hi, 214—5 ; 
general theorem, iv, 1—4; Bezout’s method, iv, 38—9, v, 555—6 ; of nodes in three bodies, rv, 
551 ; the term, iv, 594; text-books on, iv, 60S; note on, v, 157—9 ; problem, vi, 40—2, vm, 
22—4; the resultant of a system of two equations, vi, 292—9 ; theorem, ix, 43—4 ; formula of, 
xi, 100—2 ; theory of equations, xi, 490; a problem of Sylvester’s, xm, 545—7. 
Ellipse : curves parallel to, iv, 123—33, 152—7 ; and circle, v, 561; foci of, v, 586 ; and quadri 
lateral, v, 604; circles of curvature, vn, 555, xm, 537; potential, ix, 281—90; negative pedals, 
x, 576; cubic curves, xi, 478; in Ency. Brit., xi, 561—4; focáis of quadric surface, xm, 54; and 
epitrochoid, xm, 82—7 ; orthomorphosis into a circle, xm, 188—9, 422—4. 
Ellipsoid, Attraction of: I, 388—91, 432—44, 582, VII, 380—3, XI, 448; Jacobi’s method, i, 511—18; 
Gauss’s method, hi, 25—8, 149—53; Laplace’s method, hi, 53—65 ; Rodrigues’ method, hi, 149—53 ; 
theory of, hi, 154—5; and terminated straight line, vn, 31—3. 
Ellipsoid, Centro-Surface of, memoir: vm, 316—65; introductory, vm, 316—7; the ellipsoid, vm, 
317—20; sequential and concomitant centro-curves, vm, 320; expressions for coordinates of point on 
centro-surface, vm, 320—4; discussion by means of equations, principal sections, &c., vm, 324—30; 
generation of surface considered geometrically, vm, 330—1 ; nodal curve, vm, .332—52; eight cuspidal 
conics, vm, 352—7; centro-surface as envelope of quadric, vm, 357—8 ; another generation of centro- 
surface, vm, 359—61; a third generation of centro-surface, vm, 361—2; reciprocal surface, vm, 363; 
delineation of centro-surface for particular case, vm, 363—5. 
Ellipsoid, Geodesic Lines on, memoir: vn, 493—510; introductory, vii, 493—4; course of the lines, vn, 
494—5; lines through an umbilicus, vn, 495—501 ; formula?, vn, 501—3 ; umbilicar geodesics, vii, 503 ; 
tables, vii, 504—6; projection on umbilicar plane, vii, 507; elliptic function formulae, vii, 507—10 ; 
diagram, vii, to face 510. 
Ellipsoids: lines of curvature, i, 36—9; surface parallel to, rv, 123—33, 158—65, x, 575; the momental, 
iv, 560 ; of gyration, iv, 560; central, iv, 564 ; projection, v, 487—8; geodesic lines on, vii, 34—5 ; 
centro-surface and sextic torse, vii, 113—4; centro-surface, vii, 130—2; geodesic lines, vm, 174—8;