109 
LEVERRIER—LINK-WORK. 
Leverrier, U. J. J. : disturbing function in planetary theory, hi, 321, vu, 511—27; elliptic motion, in, 
361, 362, iv, 523, 590 ; position of orbit in planetary theory, vn, 545. 
Lévy, M. ; orthogonal surfaces, vni, 269, 569—70 ; Lupin’s theorem, ix, 85. 
Light, Polarized : MacCullagh’s theorem, iv, 12—20. 
Limaçon of Pascal : i, 480, xi, 477. 
Lindemann, F. ; non-Euclidian geometry, xm, 481. 
Linear ; and omal relations in abstract geometry, vi, 463. 
” Linear Differential Equations : invariants of, xn, 390—3 ; general theory, xn, 394—402, 444—52 ; 
decomposition, xn, 403—7. 
Linear Equations : and determinants, xi, 490 ; standard solutions of system of, xn, 19—21. 
Linear Function : the term, xi, 492. 
Linear Quantics (see Qualities). 
Linear Substitutions : note on a function in, x, 307—9. 
Linear Transformations: theory of, i, 80—94, 95—112, 117, 584, 585; Eisenstein’s and Hesse’s formulae, 
i, 113—6, 585; homogeneous functions of third order with three variables, I, 230—3; hyperdeterm 
inants, i, 352—5, 577—9, 588, 589 ; theory of permutations, i, 423—4 ; simultaneous, of two homo 
geneous functions of second order, i, 428—31 ; theory of permutants, n, 19—23 ; the term, iv, 594, 
605 ; of elliptic integrals, ix, 618—21 ; of theta functions, xn, 50—5 ; Sylvester’s work in, xm, 46 ; 
(see also Covariants, Invariants, Quantics). 
Line-geometry : and congruences, xm, 228—30 ; (see also Coordinates, Lines). 
Lineo-linear : the term, ii, 517, iv, 604, vi, 464. 
Lineo-linear Transformation : between planes, vii, 215—6, 236—8. 
Line-pairs: the term, vi, 206, 209, 210, 211 ; through three given points and touching given conic, 
VI, 201, 244, 594. 
Line-pair-point: the term, vi, 202, 210, 211, 269, 594—5. 
Lines: on cubic surfaces, i, 445—56, vm, 371—6; harmonic relation of two, n, 96—7; of cubic curve, 
ii, 382 ; satellite, n, 383, v, 359 ; formulae, n, 405—9 ; line, plane and point, defined, n, 561—2 ; 
contour and slope, iv, 108—11, 609; cubic centres and cones, iv, 173—8, 179—81; geometry of, 
iv, 446—55, 616—8 ; involution, iv, 582, v, 1—3 ; cubic centres of three lines and a line, v, 73—6 ; 
theorem of conic and triangle, v, 100—2; intersections of pencils of four and two, v, 484—6; 
formulae for intersections of line and conic, v, 500—4 ; circle and parabola, problem, v, 607 ; notation 
in Pascal’s theorem, vi, 116—23 ; facultative, vi, 365—6, 450 ; dot-notation for, and planes and cubic 
surfaces, vi, 365—6, 373—449; twenty-seven on cubic surface, vi, 371—87; attraction of terminated 
straight, vn, 31—3; five on cubic surface, vii, 177—8; homographie transformation, vii, 193—7; 
spherogram and isoparametric, vn, 467—8 ; iseccentric and <?-spherogram, vn, 468—70 ; isochronic 
and time spherogram, vn, 470—7 ; Cayley’s work on six coordinates of, vm, xxxv • potentials of, 
ix, 278—80 ; formulae relating to right, x, 287—9 ; and points, x, 570 ; and conics, x, 602 ; contact 
with a surface, xi, 281—93 ; Mill on, xi, 432—3 ; non-Euclidian geometry, xi, 437, xm, 480—504 ; 
evolution of theory of curves, xi, 450—1 ; singularities of curves, xi, 468 ; in Ency. Brit., xi, 
548, 571—2; equation of right, xi, 558—61; and surface, xi, 629; Mascheroni’s geometry of the 
compass, xn, 314—7 ; reciprocal, xm, 58—9, 481 ; identity relating to six coordinates of a line, xm, 
76—8 ; and notion of plane curve of given order, xm, 79—80 ; syzygetic relations, xm, 224—7 ; 
of striction, on skew surface, xm, 232—7 ; system of in a plane, and their orthotomic circle, xm, 
346—7 ; and point, distance, xm, 495—7 ; theory of two lines, xm, 497—504 ; (see also Coordinates, 
Curvature, Geodesic Lines). 
Line Systems: two-dimensional geometry, n, 569—83. 
Link : the term, v, 521, vn, 183, xm, 506. 
Linkage: the MacMahon, xm, 265, 292, 293, 298—301. 
Link-work: x, 407.