A Treatise on the Theory of Screws

541 Cylindroid, Chiastic Homography on 307; Constants necessary to define a 68; De- fined by two Screws 20; Discovery of by Hamilton 510, 520; Drawing of Plane section 154; Dynamical property dis- covered by Battaglini 20; Equation of 19, 224; Equation of Central Section 166; Equation of Plane Section 152; Funda- mental property 25; Geometrical investi- gation of 146, 150; Hyperbola in triple contact 164; Impulsive and Instantaneous 112; Models of 150, 530; Name suggest- ed by Cayley 20; Nodal line upon 24; Normal 308; Parabola related to Plane Section 156; Permanent Screw on 422; Relation between two 108; Principal Screws on 21, 43; Reducing to a plane 23; Remarkable geometrical property, 535; Represented by a Circle 45; Repre- sented by a Straight line 199; Restraining Screw on 419; Tangential section of 60; Three-system 180 D’Alembert 520 Degrees of certain Surfaces 242 D’Emilio 528 Departure defined 448 Differential equation for Kinetic Energy, 356 Displacement, canonical form of 1 Double Screws 264, 309 Dyname, correspondence of 383; defined 274; Parallel Projections of, 382 Dynamical parable, a 496 Elliott 532 Ellipse of Inertia 114; of Potential 116 Ellipsoid of Inertia 187 Emanants 274, 275, 408, 469 Enclosing Screw Systems defined 233 Energy, Kinetic, Emanant equation of 405; Expression for 296 Equations, Lineal’ Systems of 67 Equilibrium of Four Forces 186; general theorem of 64 Euler 83, 231, 406, 520, 527 Everett 26, 522, 523 Extent defined 434 Fiedler 524 INDEX. Forces in Theory of Screws 11; in Non- Euclidian Space 480 Freedom, various degrees of 63 Fundamental problem with free body 336 Geiser 513 Geometrical Theoi’y of Impulsive and In- stantaneous Screws 322 Goebel 151 Grace 495 Gi'assman 509, 515 Gravelius 531, 532 Grubb (Sir H.) 150, 151 Halphen 522 Halsted 439 Hamilton (Sir W. R.), 509, 510, 512, 515, 517, 521, 537 Harmonic Motion 99 Harmonic Screws 94, 106,118, 133, 193, 397 Heath 452, 485, 522, 527 Henrici 532 Heteronymous Vectors 475, 480 Homography, Chiastic 306, 309; of Content 415 ; Double points 126,127, 342; Screw- chains 370, 393; Screw Systems 262 Hyde, 531 Hyperbola in triple contact with Cylindroid, 164 Impulsive Screws, Chains 392; Cylindroid 112; Defined 71; Fundamental formulæ 298; Theory of two pairs 325 Inertia, Axis of 123; Conjugate Screws 71; Conjugate Screw-chains 395; Ellipse of 114; Ellipsoid of 187; Principal Screws of 69; Principal Screws on Cylindroid 114; Principal Screws on Three-system 188; Principal Screws on Four-system 230; Principal Screws on Five-system 252; Principal Screw-chains of 394 Infinite Pitch, Screws of 22, 39 Infinity, Screws at 291 Instantaneous Screws 71 ; Chains 392; Definition 10 Intensity of a Wrench defined 11 Intervene defined 434 ; Expression for 443 Invariants of Eight Screws 260 Invariants, Pitch 289 Involution, meaning of 249