LIOUVILLE—MANNHEIM. 
no 
Liouville, J.: integration of differential equations, in, 180, 191—2; equations of motion, in, 185; Bour’s 
memoir, hi, 199, 204; a definite integral, iv, 28—9; elliptic motion, iv, 522, 590; problem of two 
centres, iv, 530; motion of three bodies, iv, 541, 590; point moving in plane, iv, 542—6, 590; 
Abelian integrals, iv, 546, 590; on roots of equations, ix, 39; indefinite integration, ix, 500—3; 
geodesic curvature, xi, 323, 328. 
Lipschitz, R.: on Lagrange’s equations, ix, 110—2. 
Listing, J. B.; partitions of a close, v, 617, vi, 22; theorem of, vm, 540—7- 
Lobatschewsky, N. I.: geometry of, v, 471—2, vm, xxxvii, xi, 436, xn, 220—38. 
Locus: defined, iv, 458, vi, 458, 460; from two conics, vi, 27—34; in relation to triangle, vi, 53—64; 
and envelope in regard to triangle, vi, 72—82; in solido, problem and solution, vn, 599; in piano, 
problem and solution, vn, 599 ; the terms nodal-, cuspidal-, envelope-, tac-, vm, 533—4; in Ency. 
Brit., xi, 585. 
Logarithms: theory of, hi, 208—13, 222—8; of imaginary quantities, vi, 14—8; Pineto’s tables, 
vm, 95—6 ; calculation of log 2, xi, 70; origin, xi, 447; function in, xi, 526—7. 
Logic: of characteristics, hi, 51—2; calculus of, vm, 65—6; Mill on, xi, 432—4; recent developments, 
xi, 458—9; geometry and algebra, xn, 459. 
Logistic: and algebra, v, 293—4. 
London Mathematical Society: Sylvester’s connexion with, xm, 45. 
Lottner, C. L. E.: motion of solid body, iv, 583, 590. 
Lubbock, Sir J. W.: theory of the Moon, hi, 309—10. 
Lunar Theory: Hansen’s, hi, 13—24; disturbed elliptic motion, hi, 270—92; development of disturbing 
function, ill, 293—318, 319—43, vn, 511—27; tables, hi, 299—308; theorem of Jacobi, hi, 519—21; 
Plana’s, vn, 357—60, 361—6, 367—70, 371—4, 375—6; Delaunay’s l, g, h, and h+g. vil, 528—33, 
534; pair of differential equations in, vn, 535—6, 537—40; Newcomb’s work, ix, 179—80; note on, 
xm, 206—9; (see also Elliptic Motion, Disturbed). 
Liiroth, J.: six coordinates of a line, vii, 66. 
Luther, E.: theory of equations, xi, 520. 
MacAulay, A. : quaternions and hydrodynamical equations, xm, 8. 
MacClintock, E.: quintics, iv, 609—16. 
MacCullagh, J.: polar plane theorem, iv, 12—20 ; spherical conics, iv, 428 ; inertia, iv, 564—5, 58S ; 
rotation of solid body, iv, 574, 588. 
MacDowell, J.: triangle and circle, v, 564. 
Maclaurin, C.: cubic curves, i, 586 ; attraction of ellipsoids, hi, 27, 62, 155; pedal curves, v, 113—4. 
MacMahon, P. A.: symmetric functions, n, 603; seminvariants and symmetric functions, vm, xxxi, 
xm, 286—8, 290, 292, 293, 302; a differential equation, xn, 30—2; seminvariants, xil, 239, 254, 
261, 275, 349, xiii, 265; a differential operator, xn, 318; Waring’s formula for form of equation 
adopted by, xm, 214 ; reciprocants and differential invariants, xm, 399—404. 
Magic Squares: x, 38. 
Magnetism : Sabine’s work, xi, 430; Gauss’s work, xi, 544. 
Maillard, M. S.: penultimate forms of curves, vm, 258; degenerate forms of curves, xi, 220; systems 
of curves, xi, 487. 
Major Function in Abel’s theorem: xn, ill, 132—56. 
Malet, J. C. : invariants, xii, 390—1. 
Malfatti, G. F. : sextic resolvent equations, xm, 473. 
Malfatti’s Problem : and system of equations, i, 465—70; Steiner’s extension, ii, 57—86, 593; Schell- 
bach’s solution, hi, 44—7; system of equations connected with, ix, 546—50. 
Malus, £. L.: systems of rays, xii, 573. 
Mannheim, A.: epitrochoid, xm, 81.