A Treatise on the Theory of Screws

XvÜi CONTENTS. §§ TAGE 377. Different Screws on the same Axis..............................414 378. Co-ordinates of the Restraining Wrench for a Free Rigid Body . . 414 379. Limitation to the position of the Restraining Screw .... 416 380. A Verification......................'..................................416 381. A Particular Case......................................................417 382. Remark on the General Case ......... 418 383. Two Degrees of Freedom.................................................419 384. Calculation of T.......................................................420 385. Another Method.........................................................420 386. The Permanent Screw....................................................421 387. Geometrical Investigation..............................................422 388. Another Method ............ 423 389. Three Degrees of Freedom...............................................426 390. Geometrical Construction for the Permanent Screws......................427 391. Calculation of Permanent Screws in a Three-system......................428 392. Case of Two Degrees of Freedom.........................................430 393. Freedom of the Fourth Order............................................431 394. Freedom of the Fifth and Sixth Orders .................................432 395. Summary................................................................432 CHAPTER XXVI . An Introduction to the Theory of Screws in Non-Euclidian Space. 396. Introduction...........................................................433 397. Preliminary notions....................................................433 398. The Intervene..........................................................434 399. First Group of Axioms of the Content...................................435 400. Determination of the Function expressing the Intervene between Two Objects on a Given Range...........................................435 401. Another Process........................................................441 402. On the Infinite Objects in an Extent...................................442 403. On the Periodic Term in the Complete Expression of the Intervene . 443 404. Intervenes on Different Ranges in a Content ...... 444 405. Another Investigation of the possibility of Equally Graduated Ranges . 446 406. On the Infinite Objects in the Content.................................447 407. The Departure..........................................................448 408. Second Group of Axioms of the Content..................................448 409. The Form of the Departure Function.....................................449 410. On the Arrangement of the Infinite Ranges..............................449 411. Relations between Departure and Intervene . . . . . . 450 412. The Eleventh Axiom of the Content......................................451 413. Representation of Objects by Points in Space...........................453 414. Poles and Polars.......................................................454 415. On the Homographic Transformation of the Content .... 454 416. Deduction of the Equations of Transformation...........................455 417. On the Character of a Homographic Transformation which Conserves Intervene..........................................................456