TORSION—TRANSFORMATION. 
138 
and certain octic surfaces, x, 79—92; kinds of, xi, 227; in Ency. Brit., xi, 628, 629—32; and 
surfaces, xi, 632; and non-Euclidian plane geometry, xn, 222 ; (see also Developables). 
Torsion: the term, I, 234, xm, 232, 234. 
Tortolini, B.: envelopes, parallel curves and surfaces, iv, 123—33; parallel surfaces of ellipsoid, iv, 133. 
Tortuous Curves (see Curves). 
Torus: the term, vii, 246, vm, 25; paper by Darboux, vn, 247; the conic-, ix, 519—21. 
Townsend, R.: inertia, iv, 566, 593; confocal quadrics, vm, 520. 
Tractor: the term, vn, 73—5, x, 269; six coordinates of a line, vn, 85—6, 93—5. 
Trajectories: root-limitation, ix, 22—7; and orthomorphosis, xm, 170. 
Transcendental Analysis (see Function). 
Transcendental Function: the term, xi, 524. 
Transcendental Integrals (see Abelian Integrals). 
Transcendent, Gudermannian: v, 86—8, 617. 
Transformation: of quadratic forms, n, 145—9, 192—201, 215; of two quadric functions, in, 129—31; 
the term modulus of, iv, 605 ; plane curves, vi, 1—8, 593, vm, 387 ; Cremona’s, vi, 22—3; polyzomal 
curves, vi, 553, 565—6; two quantics into each other, vm, 385—7; unicursal surfaces, vm, 388—93; 
binary quadratic form, vm, 398—400; doubly infinite products, x, 494—7 ; theories, xi, 482; Landeu’s, 
xi, 584; double theta functions, xn, 358—89; of order 11, and modular equation, xm, 38—40; 
modular equation for cubic, xm, 64—5; (see also Special Headings below). 
Transformation, Automorphic: iv, 416, v, 439; of binary cubic function, xi, 411—6. 
Transformation, Cubic: in elliptic functions, ix, 522—6. 
Transformation, Geometric: vn, 121—2. 
Transformation, Homographic: xi, 189—90, 196—208. 
Transformation, Linear: n, 225, xi, 237—41; imaginary linear, vi, 183—6; lineo-linear, vn, 215—6, 
236—8 ; of theta functions, xn, 337—43. 
Transformation of Coordinates: i, 123—6, 586, iv, 552—9, vii, 95, 415—7, xi, 136—42, 558—61; 
formulae, vii, 97—8. 
Transformation of Elliptic Functions: i, 120—2, 585, v, 472, ix, 103—6, 244—5, x, 333—8, 611, xi, 
26, xil, 416—7, 535—54, XIII, 29—32, 490—2, 505—34, 535—55, 556—7. 
Transformation of Elliptic Integrals: i, 508—10, iv, 60—9, 609. 
Transformation of Equations: ix, 42, 48—51; of differential, v, 78—9. 
Transformation of Integrals: i, 383, hi, 1—4, 438—44, ix, 250—2. 
Transformation of Tschirnhausen: vi, 165—9, xi, 396; for cubics, iv, 364—7, xm, 421; quartics, iv, 
368—74; quartics and quintics, iv, 375—94, v, 449—53; theory of equations, xi, 509. 
Transformation, Orthomorphic: of a circle into itself, xm, 20. 
Transformation, Quadric: of elliptic functions, xn, 58; between two planes, xn, 100—1. 
Transformation, Rational, between Two Spaces, Memoir: vii, 189—240; introductory, vii, 189—90; 
general principle, vii, 190—3; homographic transformation between two lines, vii, 193—7; rational 
ditto between two planes, vii, 197—213, 216—21 ; tables, vii, 210—3; quadric transformation 
between two planes, vii, 213—6; quadric transformation any number of times repeated, vii, 219—21 ; 
reduction of general rational transformation to a series of quadric transformations, vii, 222—4; 
rational transformation between two spaces, vn, 224—9, 238—40 ; ditto quadri-quadric, VII, 229—30 ; 
ditto quadri-cubic, vn, 230—3; ditto cubo-cubic, vn, 233—8; this principal system consists of 
six lines, vn, 234—6; principal system of a proper sextic curve—the lineo-linear transformation 
between two spaces, vn, 236—8. 
Transformation, Rational: of plane curves, vi, 1—8; does not alter deficiency, vi, 3; between two 
planes and special systems of points, vn, 253—5; note on a theory of, xm, 115—6. 
Transformation, Rectangular : xi, 421—8. 
Transformation, Scalene: of plane curve, ix, 527—34.