LAGUERRE-LETTERS. 
108 
157—8, 201, 202; equations of motion, ill, 158, 200, ix, 198—200; planetary theory, hi, 159—61, 
162—3, 201; variation of arbitrary constants in mechanical problems, hi, 161—5, 200, 201; coefficient 
(a, b) of, hi, 163; Hamilton’s method of dynamics, hi, 171—3, 200; disturbed elliptic motion, hi, 
271—2 ; equations of differences, iv, 240, 252 ; resolvents, iv, 309 ; central forces problem, iv, 
519—20, 589 ; elliptic motion, iv, 521—2, 589 ; expansion of anomalies, iv, 522 ; spherical pendulum, 
iv, 532—3, 589 ; rotation of solid body, iv, 566, 569, 589 ; homotypical functions, v, 50 ; invariable 
plane, vi, 142; invariants, vm, xxx; demonstration of Taylor’s theorem, vm, 493—5, 519; virtual 
velocities, ix, 205—8; prime roots of unity, xi, 57; Schwarzian derivative, xi, 149; theory of-' 
equations, xi, 455, 498—500, 514—5, 517, 520; envelopes, xi, 475; minimal surfaces, xi, 638; five 
points in space, xii, 581—3; theorem of expansion and partitions of polygon, xm, 113; Waring’s 
formula, xm, 215—6; reciprocals, xm, 366; Richelot’s integral of Euler’s equation, xm, 526. 
Laguerre, E. : theory of matrices, ii, 604. 
Lamb, H. ; conformal representation, x, 290. 
Lambdaic : defined, ii, 523, iv, 49, 53 ; of binary quartic, ii, 550. 
Lambert, J. H. : theorem on circular hodograph of, in, 262—5 ; theorem for elliptic motion, ill, 562—5, 
vii, 387—9; central forces problem, iv, 519, 520, 589; equation of planet’s orbit from three observ 
ations, vii, 412—5. 
Lamé, G. : curvilinear coordinates, vm, 146, xi, 637, xn, 17; orthogonal surfaces, vm, 280, 291, 292. 
Lamp, Milner’s : a differential equation, and construction of, xm, 3—5. 
Lancret, M. A. : curves of curvature, xii, 601. 
Landen, J. : theorem of, in elliptic functions, xi, 337—9 ; biographical notice, xi, 583—4. 
Languages : Cayley’s knowledge of, vm, xxiii. 
Laplace, P. S. : on Lagrange’s theorem, i, 42, ii, 7 ; determinants, i, 63 ; functions of, I, 397—401, 588 ; 
attraction of ellipsoids, I, 581, III, 53—65, 567 ; planetary theory, ill, 159, 201 ; disturbed elliptic 
motion, hi, 505, 510—11; on secular variation, hi, 568; elliptic motion, iv, 524, 589; relative motion, 
iv, 534, 536, 589 ; motion of three bodies, iv, 540—1, 589 ; prepotentials, ix, 393 ; finite differences, 
xii, 412. 
Last Multiplier: iv, 530, 547, 551, 590. 
Latin Squares : xm, 55—7. 
Latitude: parametric, vii, 16, ix, 238. 
Lattice : in theory of numbers, iii, 40. 
Laverty, W. H. : systems of equations, vii, 578. 
Law, The : Cayley’s work at, vm, xiii—xv, xix. 
Lebesgue, V. A. : determinants, i, 63. 
Lectures : delivered by Cayley, vm, xvi—xvii, xlv. 
Lefort, F. : elliptic motion, iv, 522, 589. 
Left-handed : circuits in root-limitation, ix, 22—3. 
Legendre, A. M. : elliptic functions, i, 136, 156, 507, v, 618, xi, 452, 537, 584, xii, 35—7 ; elliptic 
integrals, i, 224 ; coefficients of, i, 375—6 ; attraction of ellipsoid, I, 432—7, 442 ; functions of, iv, 
99, 106; rectilinear motion, iv, 516, 590; central forces problem, iv, 521, 590; problem of two 
centres, iv, 530, 590 ; rotation of solid body, iv, 570, 590 ; geodesic lines on oblate spheroid, VH, 
15—25 ; reduced latitude, vii, 16 ; orbit of planet from three observations, vii, 414 ; mathematical 
tables, ix, 467—8, 478, 487 ; Landen’s theorem, xi, 339 ; theory of numbers, xi, 455, 602—4, 616, 
xii, 35—7 ; second kind of coefficients, xii, 562—3 ; gamma function, xm, 49. 
Le j eune-Dirichlet, P. G. : multiple integrals, I, 195, 582—3 ; integration, i, 588 ; theorem of, ii, 10, 
47—8 ; binary quadratic forms, v, 141; prepotentials, ix, 321, 417—23; attractions, xi, 448; theory 
of numbers, xi, 456, 616. 
Lemniscate Function : xi, 65 ; and orthomorphosis, xm, 191—205. 
Letters: substitution groups for two to eight, xm, 117—49.