A Treatise on the Theory of Screws

INDEX. 543 Ribaucour 513 Rittershaus 524 Roberts, R. A. Ö30 Rodrigues 17, 512 Roubadi 535 Routh 76, 98, 484, 533 Salmon 76, 495, 524, 532 Saussure, M. René de 10 Schell 525 Schilling 530 Schönemann 513 Schönflies 529 Screws, Angle between two 276; Anhar- monic function of eight 267 ; on same axis 41; Cartesian Equation of 38; Con- jugate 71; Co-ordinates 31; Co-ordinates, Transformation of 42 ; Co-reciprocal 33 ; Definition of 7; Harmonic 94; Imaginary on a three-system 201; at Infinity 41, 291 ; Intersecting in a three-system 212 ; Invariants of eight 266 ; Impulsive and Instantaneous, two pairs ol 310; In- stantaneous defined 10; on One Line 109; in Non-Euclidian Space 433 ; Parallel to a plane 277; Permanent 399; Permanent Equations of 421 ; Polar 238 ; Principal of Inertia 69 ; Reciprocal to a Cylindroid 26 ; Reciprocal defined 26 ; Reciprocal to five Screws 30, 246 ; Reciprocal to four Screws, locus of 29; Reciprocal of System 63 ; at Right Angles 276 ; Restraining on Cylindroid 419; Seven 31 ; Stationary pitch 221 ; Theory of, based on two principles 5 Screw-chains, Accelerating 409 ; of Conju- gate Inertia 395 ; defined 369; Equations of motion of 405 ; of Fifth order 378, 384; of First order 369 ; of Fourth order 377 ; Harmonic 395 ; Homography in 370 ; Impulsive 392 ; Instantaneous 392 ; In- termediate Screws of 368; Lagrange’s equations applied to 406 ; Oscillations on 397; Permanent 410 ; Principal of Inertia 394 ; Reciprocal 388 ; Second order 370 ; Third order 375 Screw Systems 62 ; Correspondence m 271; of Fifth order 246; of First order 101; of Fourth order 218; Homographic 262; Parameters of 65 ; Permanent Screws in 399 ; of Second order 107 ; of Sixth order 258; of Third order 170; two of Thir order correlated 344 Segre 528 Sexiant 248 Sextic Surface, Joly on 493 Seydler 530 Signs, Theorem as to 285 Sixth order, Permanent Screws in 432 Skatow 522 Solid angle, Formulæ with 495 Somoft' 521 Spottiswoode 516 Stationary pitch, Screws of 214 Steiner’s quartic 179 Stoney, G. J., His lecture experiment 519 Study 538, 539 Sturm 524 Surfaces, Degrees of certain 242 Sylvester 249, 250, 514 Tangential Section of Cylindroid 60 Tarleton 76, 530 Three pairs of Impulsive and Instantaneous Screws 330 Three-System 170; Permanent Screws in 428 ; Plane representation of 197 Townsend 465 Transformation, Orthogonal 465 ; Screw Co- ordinates 42 Triangle of Twists 49 Triple Contact of Conic and Cubic 490 Twist, Amplitude of 11; Composition of 18 ; Definition of 7 ; Triangle of 49 Twist Velocity, Acquired by an impulse 81; Defined 11; Expression for 297; Theorem relating to 305 Vanishing Emanant 408 Vectors 464; Analogy with twists 10; Composition of 473 ; Fundamental laws of 475 ; Orthogonal Co-ordinates 470 Velocity, Twist defined 11 ; Expression for 297 Virtual Coefficient in Co-ordinates 36 ; De- fined 17 ; as Emanant 278 ; Symmetry of 18 Vivanti 530 Weiler 523