A Treatise on the Theory of Screws

542 INDEX. Joly 30, 178, 182, 390, 492, 522, 534, 537, 538, 539 Kinetic Energy, Differential Equation for 356; Expression for 296; Property of 401 Klein 17, 18, 33, 34, 241, 249, 286, 433, 439, 517, 518, 520, 521, 533 Kotelnikof 522, 535 Kronecker 531 Kummer 517 Lagrange 76, 96, 97, 98, 395, 406, 489 Law Prize Examination 537 Lewis 46, 151 Lindemann 433, 523 Linear Complex 20 Linear Equations, note on 67 Lobachevsky 521 Lornoff 531 M'Aulay (Alex.) 37, 84, 522, 536 MacAulay (F. S.) 437 Manchester, address at 496 Mannheim 45, 513, 519, 521, 522, 533 Mass-chains 367 Minchin 151, 529 Möbius 31, 102, 248, 255, 511, 512, 524 Models of Cylindroid 150, 530 Motion, Equations of, in Screw-chain Co-or- dinates 405 Motor defined 477 Non-Euelidian Space 433 Normal Cylindroids 308 Notation, fundamental 11 Object, Definition of 433 Octonions 536 Orthogonal Transformation 280, 465 Oscillations about a fixed point 194 Oscillations, Screw-chain 397 Padeletti 522, 526, 527 Panton 244 Parable, a Dynamical 496 Parabola in contact with Cylindroid 158 Parallel Projections, 379 Parameters of a Screw-System 65 Pascal line 307 Peetenoid 255 Permanent Screw-chains 410; Cylindroid 422; Definition 399; Different Degrees of Freedom 432 ; Equations of 421 ; Geo- metrical Construction for 427 Pitch, Axis of 46; Conic 24, 204, 210; Co-ordinates 36 ; Co-reciprocals 282 ; on Cylindroid 20; Definition of 7 ; Infinite 22,39; Invariant 289,294; Non-Euclidian Space 478, 527 ; Quadrics 227; Stationary 221 Planes, Four imaginary, in 3-system 202 Plane representative Cylindroid 45; Dy- namical problems 120; Three-System 197 Plticker 17, 20, 34, 150, 177, 249, 274, 515, 516, 517, 520, 524, 531 Poinsot 4, 297, 510, 511, 513, 524, 536 Poisson 536 Polar Screw 238, 241 Potential 87; Conjugate Screws of 89; Ellipse of 116 ; Principal Screws of 90 Principal Axis of a Rigid Body 260, 400 Principal Screws on Cylindroid 21, 43 Principal Screws of Inertia 69 ; on a Cylin- droid 114; Chains 394; Five-System 252 ; Four-System 230 ; Three-System 188, 207 Principal Screws of Potential 90 Projections, Parallel 379 Quadratic Screw-Systems 233 Quadric, The Pitch- 172 Quadric of Potential 192 Quadrics in Three-System 173 Quaternions 30, 512, 515 Range defined 434 Reaction of Constraints 64 Reality of the Principal Screws of Inertia 77 Reciprocal Screws, Cylindroid 37 ; Chains 288; Defined 26; Property of 347; System 63 Reduced Wrench 84 René de Saussure 536 Representation of Cylindroid in a Plane 45 Résal 521 Resolution of Twists and Wrenches 31 Restraining Screw-chain 407 ; Cylindroid 419 ; Co-ordinates 314 ; Locus 416 Restrictions on Forces 11; Movement 13