137 
TETRAZOMAL—TORSES. 
Tetrazomal (see Polyzomal Curves). 
Text-Books: on determinants, elimination and higher algebra, iv, 608. 
Theory of Equations (see Equations, Theory of). 
Theory of Groups (see Groups). 
Theory of Numbers (see Numbers, Theory of). 
Theta Functions, Memoir on Single and Double: x, 463—565; historical, x, 463—4; Part I, x, 
464—76; definitions, x, 464—5; allied functions, x, 465—6; even-integer alteration of characters, 
x, 466; odd ditto, x, 466; even and odd functions, x, 467; quarter-periods unity, x, 467—8; 
conjoint quarter quasi-periods, x, 468—9; product-theorem, x, 469—71 ; resume of ulterior theory 
of the single functions, x, 471—3; ditto, double functions, x, 474—5; remark as to notation, x, 
475—6 ; Part II, x, 476—97; notation, x, 476 ; constants of the theory, x, 477—8; product 
theorem, x, 478—80; the square-set, x, 481—2; relation between the constants, x, 482—3; 
product-sets, x, 483—4; comparison with Jacobi’s formulae, x, 485; the square set, x, 485—7, 
488—9; elliptic integrals of third kind, x, 489—90; addition formulae, x, 491—2; doubly infinite 
product forms, x, 492—4; transformation q to r, x, 494—7; Part III, the double theta functions, 
x, 497—565; product-theorem, x, 497—506; tables, x, 506—8; product-theorem and its results, x, 
509—39; tables, x, 513—39; the first set, x, 539; second ditto, x, 540; third ditto, x, 541; 
fourth ditto, x, 542; considerations, x, 543—8; resume, x, 548; 16-nodal quartic surfaces, x, 
548—51; x, y expressions of theta functions, x, 551—5; further results of product-theorem, x, 
555—7; differential relations connecting theta and quotient functions, x, 557—9 ; differential relations 
of theta functions, x, 559—61; ditto, u, v, x, y, x, 561—5. 
Theta Functions: of Jacobi, i, 136, 290; and elliptic integrals, xi, 41—6; theory of multiple, xi, 
242—9; notation, xi, 243—5; evolution, xi, 451—5; the term, xi, 532; linear transformation, 
xn, 337—43; formula relating to zero value of, xn, 442—3; Smith’s memoir, xm, 558—9; (see 
also Abelian, Double Theta, Elliptic, Single Theta, and Triple Theta, Functions). 
Third Class: curves of, n, 395—6. 
Thomae, J.: linear differential equations, xn, 394, 396, 444; theta functions, xn, 442. 
Thomson, F. D.: tangents of conic, v, 578. 
Thomson, J.: mechanical integrator, xi, 53. 
Thomson, W. (see Kelvin, Lord). 
Three-bar Motion: ix, 551—80, xi, 481, xm, 505—16. 
Three Bodies: problem of, hi, 97—103, 183, iv, 548—552; in a line, iv, 538—40; other cases, iv, 
540—1. 
Time and Number: xi, 442—4. 
Tissot, A. : spherical pendulum, iv, 534, 593. 
Titus, Colonel: arithmetical problem, iv, 171—2. 
Todhunter, I.: conics, iv, 481; Taylor’s theorem, vm, 493—5; ^-squares, x, 27; probabilities, x, 600. 
Topography: contour and slope lines, iv, 108—11, 609. 
Topology: of space, vi, 22; of chessboard, x, 609. 
Torsal: the term, vi, 334, 336, 341, 355, 582—5. 
Torse, on a Certain Sextic : vn, 99—114; introductory, vn, 99—100; theorem of four binary quartics, 
vn, 100; standard equation of unicursal quartic, vn, 101; tangent line and osculating plane of 
unicursal quartic, vn, 101; its final form, vn, 102; determination of sextic torse, vn, 102—3; 
principal sections of ditto, vn, 103—5 ; partial determination of equation, vn, 105; determination 
of the unknown coefficients, vn, 106—11 ; equation of sextic torse, vn, 112 ; ditto, and centro-surface 
of ellipsoid, vn, 113—4. 
Torses: the term, v, 182, xi, 573; and scrolls, v, 199—200; and curves, v, 505—10; a special sextic 
developable, v, 511—9; singularities, vi, 601; on some sextic, vn, 116—7, 118—20; circumscribed 
to two quadrics, vm, 520—1; on a sextic, x, 68—72; depending on elliptic functions, x, 73—8; 
C. XIV. 18