XVI CONTENTS. 



PAGE 



299. Cylindroid Reduced to a Plane 319 



300. A difficulty removed 320 



301. Two Geometrical Theorems . 320 



CHAPTER XXII. 



THE GEOMETRICAL THEORY. 



302. Preliminary 322 



303. One Pair of Impulsive and Instantaneous Screws 323 



304. An Important Exception 325 



305. Two Pairs of Impulsive and Instantaneous Screws 325 



306. A System of _ Rigid Bodies 326 



307. The Geometrical Theory of Three Pairs of Screws 330 



308. Another Method 332 



309. Unconstrained Motion in system of Second Order 332 



310. Analogous Problem in a Three-system 334 



311. Fundamental Problem with Free Body 336 



312. Freedom of the First or Second Order . 338 



313. Freedom of the Third Order. . . . 339 



314. General Case 339 



315. Freedom of the Fifth Order 340 



316. Principal Screws of Inertia of Constrained Body 341 



317. Third and Higher Systems 342 



318. Correlation of Two Systems of the Third Order 344 



319. A Property of Reciprocal Screw Systems 347 



320. Systems of the Fourth Order 348 



321. Systems of the Fifth Order 350 



322. Summary 350 



323. Two Rigid Bodies 351 



CHAPTER XXIII. 



VARIOUS EXERCISES. 



324. The Co-ordinates of a Rigid Body 355 



325. A Differential Equation satisfied by the Kinetic Energy .... 356 



326. Co-ordinates of Impulsive Screw in terms of the Instantaneous Screw . 356 



327. Another Proof of Article 303 357 



328. A more general Theorem 357 



329. Two Three-Systems 357 



330. Construction of Homographic Correspondents 358 



331. Geometrical Solution of the same Problem 359 



332. Co-reciprocal Correspondents in Two Three-systems 360 



333. Impulsive and Instantaneous Cylindroids 361 



334. The Double Correspondents on Two Cylindroids 363 



335. A Property of Co-reciprocals 364 



336. Instantaneous Screw of Zero Pitch 365 



337. Calculation of a Pitch Quadric 365 



