XVlll CONTENTS. 



PAGE 



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 



