XIV CONTENTS. 



PAGE 



226. Polar Screws 238 



227. Dynamical Application of Polar Screws ....... 241 



228. On the Degrees of certain Surfaces . . . 242 



CHAPTER XVII. 

 FREEDOM OF THE FIFTH ORDER. 



229. Screw Reciprocal to Five Screws 246 



230. Six Screws Reciprocal to One Screw ........ 247 



231. Four Screws of a Five-system on every Quadric 250 



232. Impulsive Screws and Instantaneous Screws ...... 251 



233. Analytical Method. 252 



234. Principal Screws of Inertia .......... 252 



235. The Limits of the Roots 253 



236. The Pectenoid 254 



CHAPTER XVIII. 

 FREEDOM OF THE SIXTH ORDER. 



237. Introduction 258 



238. Impulsive Screws 258 



239. Theorem . 259 



240. Theorem 260 



241. Principal Axis 260 



242. Harmonic Screws 261 



CHAPTER XIX. 



HOMOGRAPHIC SCREW SYSTEMS. 



243. Introduction 262 



244. On Plane Homographic Systems . . . 262 



245. Homographic Screw Systems 263 



246. Relations among the Co-ordinates 263 



247. The Double Screws 264 



248. The Seven Pairs 264 



249. Homographic Ti-systems ........... 265 



250. Analogy to Anharmonic Ratio 266 



251. A Physical Correspondence .......... 267 



252. Impulsive and Instantaneous Systems 267 



253. Special type of Homography 268 



254. Reduction to a Canonical Form ......... 269 



255. Correspondence of a Screw and a System 270 



256. Correspondence of m and n Systems 271 



257. Screws common to the Two Systems 271 



258. Corresponding Screws denned by Equations 272 



259. Generalization of Anharmonic Ratio . . 273 



